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*Single Photon Manipulation*

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**39**

**1. Introduction**

**Chapter 3**

**Abstract**

Generation and Manipulation of

Nonclassical photon sources are key components in quantum information science and technology. Here, the basic principles and progresses for single photon generation and their further manipulation based on second- or third-order nonlinear processes in various degrees of freedom are briefly reviewed and discussed. Based on spontaneous parametric down-conversion and spontaneous four-wave mixing, various nonlinear materials such as quasi-phase-matching crystals, dispersion-shifted fibers, and silicon-on-insulator waveguides are used for single photon generation. The kinds of entanglement generated include polarization, time-energy, time-bin, and orbital angular momentum. The key ingredient for photon pair generation in nonlinear processes is described and discussed. Besides, we also introduce quantum frequency conversion for converting a single photon from one wavelength to another wavelength, while keeping its quantum properties unchanged. Finally, we give a comprehensive conclusion and discussion about future perspectives for single photon generation and manipulation in nonlinear processes. This chapter will provide an overview about the status, current challenge, and future perspectives

about single photon generation and processing in nonlinear processes.

dispersion-shifted fiber, silicon-on-insulator waveguide

**Keywords:** photon pair, spontaneous parametric down-conversion, spontaneous four-wave mixing, polarization, time-bin, time-energy, orbital angular momentum, quantum entanglement, quantum frequency conversion, quasi-phase-matching,

Nonclassical photon sources are fundamental resources for researches in quantum information science and technology (QIST), which are widely used for applications like quantum communications, computations, sensing, and studying fundamental physics of quantum mechanics [1–3]. Therefore the ability to generate and manipulate single photon determines how far we can go in QIST. Generally, there are two distinct methods for generating single photons: one is based on excitation-reemission of photon in a semiconductor quantum dot [4], a single defect in NV center [5], or a single atom [6]; another convenient method is based on spontaneous emission based on a second- [7] or a third-order nonlinear process [8]. In this chapter, we will focus on single photon generation by using nonlinear processes. Usually, there are two nonlinear processes for generating nonclassical photon pairs:

Nonclassical Photon Sources in

Nonlinear Processes

*Zhi-Yuan Zhou and Bao-Sen Shi*

## **Chapter 3**

## Generation and Manipulation of Nonclassical Photon Sources in Nonlinear Processes

*Zhi-Yuan Zhou and Bao-Sen Shi*

## **Abstract**

Nonclassical photon sources are key components in quantum information science and technology. Here, the basic principles and progresses for single photon generation and their further manipulation based on second- or third-order nonlinear processes in various degrees of freedom are briefly reviewed and discussed. Based on spontaneous parametric down-conversion and spontaneous four-wave mixing, various nonlinear materials such as quasi-phase-matching crystals, dispersion-shifted fibers, and silicon-on-insulator waveguides are used for single photon generation. The kinds of entanglement generated include polarization, time-energy, time-bin, and orbital angular momentum. The key ingredient for photon pair generation in nonlinear processes is described and discussed. Besides, we also introduce quantum frequency conversion for converting a single photon from one wavelength to another wavelength, while keeping its quantum properties unchanged. Finally, we give a comprehensive conclusion and discussion about future perspectives for single photon generation and manipulation in nonlinear processes. This chapter will provide an overview about the status, current challenge, and future perspectives about single photon generation and processing in nonlinear processes.

**Keywords:** photon pair, spontaneous parametric down-conversion, spontaneous four-wave mixing, polarization, time-bin, time-energy, orbital angular momentum, quantum entanglement, quantum frequency conversion, quasi-phase-matching, dispersion-shifted fiber, silicon-on-insulator waveguide

## **1. Introduction**

Nonclassical photon sources are fundamental resources for researches in quantum information science and technology (QIST), which are widely used for applications like quantum communications, computations, sensing, and studying fundamental physics of quantum mechanics [1–3]. Therefore the ability to generate and manipulate single photon determines how far we can go in QIST. Generally, there are two distinct methods for generating single photons: one is based on excitation-reemission of photon in a semiconductor quantum dot [4], a single defect in NV center [5], or a single atom [6]; another convenient method is based on spontaneous emission based on a second- [7] or a third-order nonlinear process [8]. In this chapter, we will focus on single photon generation by using nonlinear processes. Usually, there are two nonlinear processes for generating nonclassical photon pairs:

(1) spontaneous parametric down-conversion (SPDC), which is a second-order nonlinear process; (2) spontaneous four-wave mixing (SFWM), which is a thirdorder nonlinear process. In both SPDC and SFWM, energy, linear momentum, and angular momentum conservations should be fulfilled. Due to these conservation laws and the technology of quantum interference used, two photons in each pair generated in SPDC and SFWM can be correlated in various degrees of freedoms, for example, polarization, energy-time, orbital angular momentum, position-linear momentum, angular momentum, and photon number and path [1]; we can utilize these freedoms in a specific application scenario in QIST.

In the subsequent section, we will first introduce the basic principle of SPDC and SFWM for generating photon pairs and then the various materials used for SPDC and SFWM. In the key part of this chapter, we will review the developments of various entangled photon pair sources and methods for charactering these sources. After that we will introduce a nonlinear method for transducing the wavelength of the photon from one to another while keeping its quantum properties unchanged, which is suitable for building up a quantum interface to connect different quantum systems. Finally, we will give a brief summary in which some future perspectives for nonclassical photon pair generation and potential applications are discussed.

## **2. Photon pair generation using SPDC or SFWM**

SPDC is realized in a second-order nonlinear process (see **Figure 1** left image), in which a pump photon at higher frequency (*ωp*) is split into two daughter photons at lower frequencies with certain probability in a nonlinear crystal; these two daughter photons are usually called signal (*ωs*) and idler (*ωi*) photons. The conservation laws of energy, linear momentum, and angular momentum require that the frequency, linear momentum (*k*), and angular momentum (*l*) of the pump, signal, and idler photon fulfill the following conditions: *ωp = ωs + ωi*; *kp = ks + ki*; *lp = ls + li*. These conservation laws are responsible for the generation of various entangled sources.

In correspondence to SPDC, SFWM is a third-order nonlinear process; a big difference is that there are two pump beams in SFWM (see **Figure 1** right image), in comparison to SPDC in which only one pump beam is used. The conservation laws in SFWM require that the corresponding parameters of the pump, signal, and idler photons have the following relationships: *ωp*<sup>1</sup> *+ ωp*<sup>2</sup> *= ωs + ωi*; *kp*<sup>1</sup> *+ kp*<sup>2</sup> *= ks + ki*; *lp*<sup>1</sup> *+ lp*<sup>2</sup> *= ls + li*.

For quantum optical description of SPDC and SFWM, the Hamiltonian of the two processes can be expressed as [9]:

$$
\hat{H} = \hbar \xi \left( \hat{a}\_s^\dagger \hat{a}\_i^\dagger + \text{H.C.} \right) \tag{1}
$$

**41**

*Generation and Manipulation of Nonclassical Photon Sources in Nonlinear Processes*

sources generated from nonlinear processes. For this reason, one needs to choose a proper pump intensity level in order to balance between different experimental

*A simple diagram for SPDC and SFWM. The conservation of energy, linear momentum, and angular* 

All materials have third-order nonlinearity, but only those materials that are central asymmetric have second-order nonlinearity. The commonly used materials for SPDC can be divided into two kinds according to different phase matching: one is birefringent angle phase-matching materials, such as LBO, BBO, KTP, and LN [10]; another is quasi-phase-matching (QPM) crystals such as PPKTP and PPLN [11]. QPM crystals have the advantages of high generation rate and narrow bandwidth, which are frequently used in photon pair generation in modern quantum optics experiments [12–19]. For SFWM, the commonly used materials are hot or cold atomic ensembles [20–24] and guided-wave materials such as dispersionshifted fibers (DSF) [25–29], photonic crystal fibers (PCF), [30–32], and siliconon-insulator (SOI) waveguide [33–41]. To look for new kinds of nonlinear materials

for generating high-quality photon sources is still a very hot topic in QIST.

**3. Various kinds of photon sources generated in SPDC and SFWM**

various kinds of nonclassical photon sources.

**3.1 Polarization-entangled photon source**

cient and long allowable interaction length.

Because of the conservation of energy, linear momentum, and angular momentum in SPDC and SFWM, various kinds of nonclassical sources can be generated; in this section we will review the recent development and key points in generating

A polarization-entangled photon source (PEPS) is one of the most important entangled photon sources that have been studied for decades of years. In the literatures, people generate PEPS using different materials with different experimental configurations [12–19, 42, 43]. For SPDC, in the early times, PEPSs are created using birefringence phase-matching (BPM) crystals, for example, a type-II phasematched BBO crystal is used to create a PEPS in the first practical and effective experiment, in which orthogonal polarized photons are emitted at the intersection cones [42]. Later on, a beam-like design is used for high-brightness photon pair generation, which is widely used in multiphoton quantum experiments [44]. The significant progress in nonlinear crystal fabrication makes a QPM crystal a better choice for researchers in many nonlinear optics applications [11]. The most important merit of using QPM crystals in generation photon pairs is its high spectral brightness in contrast to BPM crystals, due to its large effective nonlinear coeffi-

Recently, to generate PEPS by placing a QPM crystal inside a Sagnac interferometer configuration has been demonstrated to be superior to other configurations (see **Figure 2**). The basic idea for a Sagnac loop-based PEPS is as the following: a pump beam is split into two beams by a double polarized beam splitter (DPBS) and

*DOI: http://dx.doi.org/10.5772/intechopen.90268*

*momentum holds in both nonlinear processes.*

parameters.

**Figure 1.**

where *ξ* depends on the pump intensity, the nonlinear coefficient of the crystal, crystal length, and focusing parameters. Therefore the photon states generated in SPDC and SFWM can be expressed in Fock state basis as [9]:

$$|\Phi\rangle = \text{Exp}\left[-\frac{i\hat{H}t}{\hbar}\right]|0,0\rangle = |0,0\rangle + \kappa|1,1\rangle + \kappa^2/2|2,2\rangle + \dots \tag{2}$$

It can be seen from Eq. (2) that we obtain a vacuum state with a high probability if the pump is weak. The second term is the photon pair state we need, and the other terms are multiphoton states which should be avoided. It is clear from Eq. (2) that the pump beam should be at a moderate intensity level in order to eliminate the effects of higher photon number states. The photon pair generated in SPDC and SFWM is of probability and is undetermined, which is a disadvantage for photon

*Generation and Manipulation of Nonclassical Photon Sources in Nonlinear Processes DOI: http://dx.doi.org/10.5772/intechopen.90268*

**Figure 1.**

*Single Photon Manipulation*

(1) spontaneous parametric down-conversion (SPDC), which is a second-order nonlinear process; (2) spontaneous four-wave mixing (SFWM), which is a thirdorder nonlinear process. In both SPDC and SFWM, energy, linear momentum, and angular momentum conservations should be fulfilled. Due to these conservation laws and the technology of quantum interference used, two photons in each pair generated in SPDC and SFWM can be correlated in various degrees of freedoms, for example, polarization, energy-time, orbital angular momentum, position-linear momentum, angular momentum, and photon number and path [1]; we can utilize

In the subsequent section, we will first introduce the basic principle of SPDC and SFWM for generating photon pairs and then the various materials used for SPDC and SFWM. In the key part of this chapter, we will review the developments of various entangled photon pair sources and methods for charactering these sources. After that we will introduce a nonlinear method for transducing the wavelength of the photon from one to another while keeping its quantum properties unchanged, which is suitable for building up a quantum interface to connect different quantum systems. Finally, we will give a brief summary in which some future perspectives for

SPDC is realized in a second-order nonlinear process (see **Figure 1** left image), in which a pump photon at higher frequency (*ωp*) is split into two daughter photons at lower frequencies with certain probability in a nonlinear crystal; these two daughter photons are usually called signal (*ωs*) and idler (*ωi*) photons. The conservation laws of energy, linear momentum, and angular momentum require that the frequency, linear momentum (*k*), and angular momentum (*l*) of the pump, signal, and idler photon fulfill the following conditions: *ωp = ωs + ωi*; *kp = ks + ki*; *lp = ls + li*. These conservation laws are responsible for the generation of various entangled sources. In correspondence to SPDC, SFWM is a third-order nonlinear process; a big difference is that there are two pump beams in SFWM (see **Figure 1** right image), in comparison to SPDC in which only one pump beam is used. The conservation laws in SFWM require that the corresponding parameters of the pump, signal, and idler photons have the following relationships: *ωp*<sup>1</sup> *+ ωp*<sup>2</sup> *= ωs + ωi*; *kp*<sup>1</sup> *+ kp*<sup>2</sup> *= ks + ki*; *lp*<sup>1</sup>

For quantum optical description of SPDC and SFWM, the Hamiltonian of the

where *ξ* depends on the pump intensity, the nonlinear coefficient of the crystal, crystal length, and focusing parameters. Therefore the photon states generated in

<sup>ℏ</sup> ]|0,0〉 <sup>=</sup> |0,0〉 <sup>+</sup> <sup>κ</sup>|1, <sup>1</sup>〉 <sup>+</sup>κ<sup>2</sup>

It can be seen from Eq. (2) that we obtain a vacuum state with a high probability if the pump is weak. The second term is the photon pair state we need, and the other terms are multiphoton states which should be avoided. It is clear from Eq. (2) that the pump beam should be at a moderate intensity level in order to eliminate the effects of higher photon number states. The photon pair generated in SPDC and SFWM is of probability and is undetermined, which is a disadvantage for photon

† + *H*.*C*.) (1)

/2|2, 2〉 + … (2)

*H* ^ = ℏξ(*a* ^ *s* † *a* ^ *i*

SPDC and SFWM can be expressed in Fock state basis as [9]:

*iH* ^ \_ *t*

nonclassical photon pair generation and potential applications are discussed.

these freedoms in a specific application scenario in QIST.

**2. Photon pair generation using SPDC or SFWM**

**40**

*+ lp*<sup>2</sup> *= ls + li*.

two processes can be expressed as [9]:


*A simple diagram for SPDC and SFWM. The conservation of energy, linear momentum, and angular momentum holds in both nonlinear processes.*

sources generated from nonlinear processes. For this reason, one needs to choose a proper pump intensity level in order to balance between different experimental parameters.

All materials have third-order nonlinearity, but only those materials that are central asymmetric have second-order nonlinearity. The commonly used materials for SPDC can be divided into two kinds according to different phase matching: one is birefringent angle phase-matching materials, such as LBO, BBO, KTP, and LN [10]; another is quasi-phase-matching (QPM) crystals such as PPKTP and PPLN [11]. QPM crystals have the advantages of high generation rate and narrow bandwidth, which are frequently used in photon pair generation in modern quantum optics experiments [12–19]. For SFWM, the commonly used materials are hot or cold atomic ensembles [20–24] and guided-wave materials such as dispersionshifted fibers (DSF) [25–29], photonic crystal fibers (PCF), [30–32], and siliconon-insulator (SOI) waveguide [33–41]. To look for new kinds of nonlinear materials for generating high-quality photon sources is still a very hot topic in QIST.

## **3. Various kinds of photon sources generated in SPDC and SFWM**

Because of the conservation of energy, linear momentum, and angular momentum in SPDC and SFWM, various kinds of nonclassical sources can be generated; in this section we will review the recent development and key points in generating various kinds of nonclassical photon sources.

#### **3.1 Polarization-entangled photon source**

A polarization-entangled photon source (PEPS) is one of the most important entangled photon sources that have been studied for decades of years. In the literatures, people generate PEPS using different materials with different experimental configurations [12–19, 42, 43]. For SPDC, in the early times, PEPSs are created using birefringence phase-matching (BPM) crystals, for example, a type-II phasematched BBO crystal is used to create a PEPS in the first practical and effective experiment, in which orthogonal polarized photons are emitted at the intersection cones [42]. Later on, a beam-like design is used for high-brightness photon pair generation, which is widely used in multiphoton quantum experiments [44]. The significant progress in nonlinear crystal fabrication makes a QPM crystal a better choice for researchers in many nonlinear optics applications [11]. The most important merit of using QPM crystals in generation photon pairs is its high spectral brightness in contrast to BPM crystals, due to its large effective nonlinear coefficient and long allowable interaction length.

Recently, to generate PEPS by placing a QPM crystal inside a Sagnac interferometer configuration has been demonstrated to be superior to other configurations (see **Figure 2**). The basic idea for a Sagnac loop-based PEPS is as the following: a pump beam is split into two beams by a double polarized beam splitter (DPBS) and

#### **Figure 2.**

*The experimental setup for a typical polarization-entangled source based on Sagnac interferometer (figure cited from [13]).*

counter-propagates in the Sagnac loop; each beam generates a pair of photon with orthogonal polarization, in one circulation direction; the photon pair is rotated by a double half wave plate; then two pairs of photons are recombined in the DPBS; and a PEPS with a form of | Φ〉 = 1/ √ \_ 2 (| *HV*〉 + e *i* | *VH*〉) is generated; the relative phase *θ* can be tuned by a pair of wave plates placed in the input port of the Sagnac loop. The merits to use the Sagnac interferometer configuration are its compactness, high stability, and high brightness. The original idea of Sagnac loop-based PEPS is from [43] where a BPM crystal is used, and then this idea is generalized to a QPM crystal by Kim in 2006 [45] for a CW pumped photon source. After that, a pulsed PEPS at 780 nm based on this configuration was developed by Kuzucu and Wong in 2008 [46]. In the early experiments, the wavelengths of the photons generated are in visible range; therefore these photons are not suitable for long-distance quantum communications in fiber. Only recently, telecom band PEPS is developed [13, 16]. A pulsed PEPS at 1584 nm based on a type-II PPKTP was demonstrated by Jin et al. in 2014 [16], and Li et al. reported a tunable CW PEPS in 2015 [13]. Now, PEPS based on QPM crystals in a Sagnac configuration has become a basic tool for many experiments [47–49].

In SFWM, PEPS is generated using an atomic ensemble with different configurations. The PEPS generated with the atomic ensemble has narrow bandwidth; the wavelength is fixed to specific atomic transition lines [50, 51]. Many works report PEPS generation based on guided-wave materials such as DSF [8, 25, 27, 28], PCF [30], and SOI waveguide [37, 52], the advantages of using guided-wave materials are free of free-space coupling, low loss, low cost, and easy to integrate. The guidedwave platform is very promising in large-scale applications which require hundreds of optical components. It is also convenient for building up a compact, versatile photonic source platform for various kinds of applications in QIST.

### **3.2 Time-energy and time-bin-entangled photon source**

Because of conservation of energy in nonlinear processes, the two photons in each pair generated are correlated in frequency and are also generated simultaneously. Although the uncertainty in time and frequency domain for individual

**43**

**Figure 3.**

*time-bin entangled photon pair.*

*Generation and Manipulation of Nonclassical Photon Sources in Nonlinear Processes*

particle should meet the requirement of uncertainty principle, the sum of the frequency of signal and idler multiplies the difference between arrive times of the two photon should have a very small value, and violates an inequality for two photons existed classical correlations [53]. A two-photon Franson-type interference is used to characterize the correlations between the two photons; the phases between the two unbalanced Michelson interferometers (UMI) are correlated [54, 55]. To generate a time-energy entangled photon pair, a laser with long coherent time is needed (see **Figure 3(a)**); the time difference between two paths in UMI should be much larger than the coherence time of the single photon but much shorter than the coherent time of the pump laser [53]. A similar kind of entangled photon source is a time-bin entangled photon source [56], in which a pulse pump is split into two pulses in an UMI, and then these two pulses have a certain probability to generate a pair of photon separately; the photon pairs generated by these two pulses are indistinguishable after passing through two UMIs (the time difference of the UMI in measurement part is the same as the UMI in pump part, see **Figure 3(b)**). The quantum states for a time-energy or a time-bin entangled photon source can be

the UMIs, respectively. A time-bin entangled photon pair is robust for long-distance transmission, which is widely used in demonstrating various quantum communication protocols [57]. A time-energy entangled photon source has been realized in various material systems such as atomic vapor [21], nonlinear crystals [56, 57], and guided-wave platform [26, 28, 34, 35, 39–41]. The differences between various materials are the photon emission bandwidth and spectral ranges. Furthermore, researchers have realized three photon genuine time-energy entangled photon

Another important degree of freedom of photon is orbital angular momentum (OAM), which has been widely investigated since 1992 [59]. OAM has unbounded dimensions, which is very promising for high-capacity communication task in both classical and quantum optical communications [60–62]. OAM entangled photon pairs can be generated in SPDC and SFWM based on crystals [48, 63–69] and atomic vapors [70, 71]. The quantum state for an OAM entangled photon pair generated directly by pumping a nonlinear crystal (**Figure 4**, left image) can be

*Simplified diagrams for (a) time-energy; (b) time-bin entangled photon generation. A narrow bandwidth CW laser is used for generating of time-energy entangled photon pair, while a pulse laser is used for generating* 

sources, and their nonclassical correlations are verified [58].

**3.3 Orbital angular momentum entangled photon source**

*LL*〉), where S and L represent the short and long arm of

*DOI: http://dx.doi.org/10.5772/intechopen.90268*

expressed as |

Φ〉 = 1/ √ \_ 2 (| SS〉 + e *i* | *Generation and Manipulation of Nonclassical Photon Sources in Nonlinear Processes DOI: http://dx.doi.org/10.5772/intechopen.90268*

particle should meet the requirement of uncertainty principle, the sum of the frequency of signal and idler multiplies the difference between arrive times of the two photon should have a very small value, and violates an inequality for two photons existed classical correlations [53]. A two-photon Franson-type interference is used to characterize the correlations between the two photons; the phases between the two unbalanced Michelson interferometers (UMI) are correlated [54, 55]. To generate a time-energy entangled photon pair, a laser with long coherent time is needed (see **Figure 3(a)**); the time difference between two paths in UMI should be much larger than the coherence time of the single photon but much shorter than the coherent time of the pump laser [53]. A similar kind of entangled photon source is a time-bin entangled photon source [56], in which a pulse pump is split into two pulses in an UMI, and then these two pulses have a certain probability to generate a pair of photon separately; the photon pairs generated by these two pulses are indistinguishable after passing through two UMIs (the time difference of the UMI in measurement part is the same as the UMI in pump part, see **Figure 3(b)**). The quantum states for a time-energy or a time-bin entangled photon source can be expressed as | Φ〉 = 1/ √ \_ 2 (| SS〉 + e *i* | *LL*〉), where S and L represent the short and long arm of the UMIs, respectively. A time-bin entangled photon pair is robust for long-distance transmission, which is widely used in demonstrating various quantum communication protocols [57]. A time-energy entangled photon source has been realized in various material systems such as atomic vapor [21], nonlinear crystals [56, 57], and guided-wave platform [26, 28, 34, 35, 39–41]. The differences between various materials are the photon emission bandwidth and spectral ranges. Furthermore, researchers have realized three photon genuine time-energy entangled photon sources, and their nonclassical correlations are verified [58].

### **3.3 Orbital angular momentum entangled photon source**

Another important degree of freedom of photon is orbital angular momentum (OAM), which has been widely investigated since 1992 [59]. OAM has unbounded dimensions, which is very promising for high-capacity communication task in both classical and quantum optical communications [60–62]. OAM entangled photon pairs can be generated in SPDC and SFWM based on crystals [48, 63–69] and atomic vapors [70, 71]. The quantum state for an OAM entangled photon pair generated directly by pumping a nonlinear crystal (**Figure 4**, left image) can be

#### **Figure 3.**

*Single Photon Manipulation*

and a PEPS with a form of |

**Figure 2.**

*cited from [13]).*

experiments [47–49].

counter-propagates in the Sagnac loop; each beam generates a pair of photon with orthogonal polarization, in one circulation direction; the photon pair is rotated by a double half wave plate; then two pairs of photons are recombined in the DPBS;

*The experimental setup for a typical polarization-entangled source based on Sagnac interferometer (figure* 

be tuned by a pair of wave plates placed in the input port of the Sagnac loop. The merits to use the Sagnac interferometer configuration are its compactness, high stability, and high brightness. The original idea of Sagnac loop-based PEPS is from [43] where a BPM crystal is used, and then this idea is generalized to a QPM crystal by Kim in 2006 [45] for a CW pumped photon source. After that, a pulsed PEPS at 780 nm based on this configuration was developed by Kuzucu and Wong in 2008 [46]. In the early experiments, the wavelengths of the photons generated are in visible range; therefore these photons are not suitable for long-distance quantum communications in fiber. Only recently, telecom band PEPS is developed [13, 16]. A pulsed PEPS at 1584 nm based on a type-II PPKTP was demonstrated by Jin et al. in 2014 [16], and Li et al. reported a tunable CW PEPS in 2015 [13]. Now, PEPS based on QPM crystals in a Sagnac configuration has become a basic tool for many

In SFWM, PEPS is generated using an atomic ensemble with different configurations. The PEPS generated with the atomic ensemble has narrow bandwidth; the wavelength is fixed to specific atomic transition lines [50, 51]. Many works report PEPS generation based on guided-wave materials such as DSF [8, 25, 27, 28], PCF [30], and SOI waveguide [37, 52], the advantages of using guided-wave materials are free of free-space coupling, low loss, low cost, and easy to integrate. The guidedwave platform is very promising in large-scale applications which require hundreds of optical components. It is also convenient for building up a compact, versatile

Because of conservation of energy in nonlinear processes, the two photons in each pair generated are correlated in frequency and are also generated simultaneously. Although the uncertainty in time and frequency domain for individual

photonic source platform for various kinds of applications in QIST.

**3.2 Time-energy and time-bin-entangled photon source**

*VH*〉) is generated; the relative phase *θ* can

Φ〉 = 1/ √ \_ 2 (| *HV*〉 + e *i* |

**42**

*Simplified diagrams for (a) time-energy; (b) time-bin entangled photon generation. A narrow bandwidth CW laser is used for generating of time-energy entangled photon pair, while a pulse laser is used for generating time-bin entangled photon pair.*

**Figure 4.**

*Generate HD OAM entangled state directly from SPDC (left image); 2D OAM entangled state generation by converting a polarized entangled state into 2D subspace of OAM entangled state (right image, cited from [48]).*

expressed as | Φ〉 = ∑ *l Cl* <sup>|</sup>*l*,−*l*〉, where *Cl* is the weight for different OAM modes. One can investigate OAM entanglement in a two-dimensional (2D) subspace [48, 63, 67–70] or in high-dimensional (HD) space [65, 66, 71]. The properties and the methods of characterizing a 2D entangled source in different degrees of freedom are similar and can be converted from one kind to another [48, 68] (please see **Figure 4** (right images)). The post-selected OAM entangled states in a 2D subspace can be expressed as | Φ〉 = 1/ √ \_ 2 (|*l*,−*l*〉 + |−*l*,*l*〉). While for a HD entangled source, the properties and the methods of characterization are rather different. [65] reported on the realization of a 11D entangled source, demonstrating the violation of the Bell inequality. Zeilinger's group has demonstrated a 100\*100 HD entanglement by measuring the entanglement witness of the generated state [66]. For a 2D OAM entangled photon source, Zeilinger's group converted a polarized entangled photon source into an OAM entangled source with OAM momenta of 300 h in 2D subspace via a spatial light modulator [48]. Later on, a higher OAM momentum of about 10,000 h for a 2D OAM entangled source is realized by using a vortex reflection mirror [68]. A HD OAM entangled photon source is preferred for studying the basic principle of quantum mechanics and for HD quantum communication applications.

## **4. Methods for characterizing the properties of a nonclassical photon source**

Nonclassical photon sources can be characterized from different aspects. For characterizing the properties of a heralded single photon, the heralded efficiency [72], the coincidence to accidental coincidence ratio (CAR) [73], and the single photon Glauber function [74, 75] are important parameters. The heralded efficiency is the probability of detecting the second photon when the first photon is detected. It is a measurement of the photon collection efficiency, filter and transmission losses, and the single photon detector efficiency. The heralded efficiency is the ratio of the coincidence count to the single count rate of the first detected photon. CAR is a measurement of the signal to background noise ratio for a two-photon experiment; high CAR can ensure the quantum nature existed between the two photons. CAR depends on pump power and detector performance. Usually, CAR will increase when the pump power is increased in the low pump power regime. After reaching the maximum value, CAR will decrease with the increase of the pump power [76]. The single photon Glauber function can be measured as shown in [74]. The measured photon is firstly split by a beam splitter, and then by measuring the three party coincidence, single count and two-photon coincidence, we can

**45**

*Generation and Manipulation of Nonclassical Photon Sources in Nonlinear Processes*

calculate the single photon g(2) function (see **Figure 5**). A near zero g(2)(0) indicates the high quality of single photon nature. For a pulse pumped photon source, the single photon purity is also an important parameter [17, 77]. The purity of photon is a measurement of spectral correlations between two photons; the purity is determined by the Schmitt number in the Schmitt decomposition. The unity single photon purity indicates that the two-photon spectral can be factorized into product of two separate functions of the signal and idler photons. The high single photon purity is very important for realizing high visibility HOM interference between two independent single photon sources, which is the key technique for realizing high

*Experimental setup for measuring heralded single photon autocorrelation function for single photon generated* 

There are various available and faithful methods to characterize the quality of entanglement of an entangled two-photon source, including two-photon interference fringes [65, 78], Bell CHSH inequality [79, 80], and quantum state tomography (QST) [81]. Two-photon interference fringe is much easier to measure; through calculating the interference visibility from the measured data, we can evaluate the quality of an entangled source. A high visibility indicates a high quality of the generated state by comparing the ideal maximum Bell states. When the visibility is greater than a threshold value, the two photons have Bell nonlocality; the threshold value is different for two-photon states in different dimension. For two photons existing in classical correlation, the Bell CHSH parameter *S* is not greater than a certain value. The violation of this value indicates a nonclassical correlation between the twophoton states. Bell CHSH parameter *S* is an indicator of whether the two-photon state has Bell nonlocality and how strong this kind of nonlocal correlation is. The violation of Bell inequality has been widely studied in literatures for a 2D and a HD entangled state. To fully know the content of a generated quantum state, QST can be used to reconstruct the density matrix of a certain quantum state. By the density matrix of a quantum state, all the properties of the quantum state can be predicted.

**5. Quantum frequency conversion for nonclassical quantum state**

There are many quantum systems for QIST based on different materials, including atomic ensembles, trapped ions, solid-state materials, and fibers for transmission [82–86]. Each quantum system has some advantages in QST, and these

*DOI: http://dx.doi.org/10.5772/intechopen.90268*

photon number entangled states.

*from SPDC (image cited from [74]).*

**Figure 5.**

*Generation and Manipulation of Nonclassical Photon Sources in Nonlinear Processes DOI: http://dx.doi.org/10.5772/intechopen.90268*

**Figure 5.**

*Single Photon Manipulation*

expressed as |

**Figure 4.**

expressed as |

**photon source**

Φ〉 = ∑ *l Cl*

Φ〉 = 1/ √ \_ 2

<sup>|</sup>*l*,−*l*〉, where *Cl* is the weight for different OAM modes. One can

(|*l*,−*l*〉 + |−*l*,*l*〉). While for a HD entangled source, the properties

investigate OAM entanglement in a two-dimensional (2D) subspace [48, 63, 67–70] or in high-dimensional (HD) space [65, 66, 71]. The properties and the methods of characterizing a 2D entangled source in different degrees of freedom are similar and can be converted from one kind to another [48, 68] (please see **Figure 4** (right images)). The post-selected OAM entangled states in a 2D subspace can be

*Generate HD OAM entangled state directly from SPDC (left image); 2D OAM entangled state generation by converting a polarized entangled state into 2D subspace of OAM entangled state (right image, cited from [48]).*

and the methods of characterization are rather different. [65] reported on the realization of a 11D entangled source, demonstrating the violation of the Bell inequality. Zeilinger's group has demonstrated a 100\*100 HD entanglement by measuring the entanglement witness of the generated state [66]. For a 2D OAM entangled photon source, Zeilinger's group converted a polarized entangled photon source into an OAM entangled source with OAM momenta of 300 h in 2D subspace via a spatial light modulator [48]. Later on, a higher OAM momentum of about 10,000 h for a 2D OAM entangled source is realized by using a vortex reflection mirror [68]. A HD OAM entangled photon source is preferred for studying the basic principle of

quantum mechanics and for HD quantum communication applications.

**4. Methods for characterizing the properties of a nonclassical** 

Nonclassical photon sources can be characterized from different aspects. For characterizing the properties of a heralded single photon, the heralded efficiency [72], the coincidence to accidental coincidence ratio (CAR) [73], and the single photon Glauber function [74, 75] are important parameters. The heralded efficiency is the probability of detecting the second photon when the first photon is detected. It is a measurement of the photon collection efficiency, filter and transmission losses, and the single photon detector efficiency. The heralded efficiency is the ratio of the coincidence count to the single count rate of the first detected photon. CAR is a measurement of the signal to background noise ratio for a two-photon experiment; high CAR can ensure the quantum nature existed between the two photons. CAR depends on pump power and detector performance. Usually, CAR will increase when the pump power is increased in the low pump power regime. After reaching the maximum value, CAR will decrease with the increase of the pump power [76]. The single photon Glauber function can be measured as shown in [74]. The measured photon is firstly split by a beam splitter, and then by measuring the three party coincidence, single count and two-photon coincidence, we can

**44**

*Experimental setup for measuring heralded single photon autocorrelation function for single photon generated from SPDC (image cited from [74]).*

calculate the single photon g(2) function (see **Figure 5**). A near zero g(2)(0) indicates the high quality of single photon nature. For a pulse pumped photon source, the single photon purity is also an important parameter [17, 77]. The purity of photon is a measurement of spectral correlations between two photons; the purity is determined by the Schmitt number in the Schmitt decomposition. The unity single photon purity indicates that the two-photon spectral can be factorized into product of two separate functions of the signal and idler photons. The high single photon purity is very important for realizing high visibility HOM interference between two independent single photon sources, which is the key technique for realizing high photon number entangled states.

There are various available and faithful methods to characterize the quality of entanglement of an entangled two-photon source, including two-photon interference fringes [65, 78], Bell CHSH inequality [79, 80], and quantum state tomography (QST) [81]. Two-photon interference fringe is much easier to measure; through calculating the interference visibility from the measured data, we can evaluate the quality of an entangled source. A high visibility indicates a high quality of the generated state by comparing the ideal maximum Bell states. When the visibility is greater than a threshold value, the two photons have Bell nonlocality; the threshold value is different for two-photon states in different dimension. For two photons existing in classical correlation, the Bell CHSH parameter *S* is not greater than a certain value. The violation of this value indicates a nonclassical correlation between the twophoton states. Bell CHSH parameter *S* is an indicator of whether the two-photon state has Bell nonlocality and how strong this kind of nonlocal correlation is. The violation of Bell inequality has been widely studied in literatures for a 2D and a HD entangled state. To fully know the content of a generated quantum state, QST can be used to reconstruct the density matrix of a certain quantum state. By the density matrix of a quantum state, all the properties of the quantum state can be predicted.

## **5. Quantum frequency conversion for nonclassical quantum state**

There are many quantum systems for QIST based on different materials, including atomic ensembles, trapped ions, solid-state materials, and fibers for transmission [82–86]. Each quantum system has some advantages in QST, and these

**Figure 6.**

*Left image: simple diagram for sum frequency generation in QPM crystal. Right image: experimental setup of QFC for an OAM qubit, an OAM-polarization hybrid entangled state, and an OAM-OAM entangled state (cited from [99]).*

systems usually work at different frequencies, which may have a big frequency mismatching. To build up a quantum network consisting of various quantum systems for information encoding, storage, transmission, and processing, a quantum frequency converter (QFC) to link different quantum systems is indispensable. Such a frequency transducer can be realized by utilizing nonlinear processes such as sum frequency generation (SFG) and Bragg reflection in four-wave mixing. The theory of quantum frequency conversion for SFG was first proposed by P. Kumar in 1990 [87]. In SFG, a strong pump laser can convert a weak signal beam with high quantum efficiency; the unity quantum efficiency can be reached when the pump beam is strong enough (see **Figure 6** left image), and the quantum correlations are unchanged after frequency conversion. Since it has been proposed, some significant progresses have been made in this field; researchers have realized that frequency up-conversion and down-conversion for a single photon generated from quantum dot, and various qubit states or entangled states such as polarization, time-energy, and OAM entangled state [39, 88–101] have been up- or downconverted. A typical setup for QFC of an OAM qubit, an OAM-polarization hybrid entangled state, and an OAM-OAM entangled state is shown in **Figure 6** (right image). For frequency down-conversion, the visible single photons generated from atomic ensemble, trapped irons, or NV centers have been converted to telecom band successfully [102–105]. In all these demonstrations, the single photon properties and entanglement are preserved in the conversion processes, which ensures that quantum information can be coupled to different quantum systems by using a quantum frequency interface.

In QFC, there are four parameters to evaluate the quality of a converter: quantum conversion efficiency, noise level, spectral bandwidth, and spatial bandwidth. These parameters are not independent; therefore in practical applications, one needs to balance between different parameters [98]. A longer nonlinear crystal is preferred to reach maximum conversion efficiency when the pump power is

**47**

*Generation and Manipulation of Nonclassical Photon Sources in Nonlinear Processes*

limited, but a longer nonlinear crystal would lead to a smaller spectral bandwidth and spatial bandwidth; a proper crystal length should be chosen to balance conversion efficiency and spectral bandwidth. The noise in QFC comes from SPDC and SRS of the intense pump beam; therefore a longer pump wavelength is preferred to reduce the noise photon in QFC [106]. The noise photon can also be dramatically reduced by using a narrow bandwidth filters to filter out the converted photon.

Nonclassical photon sources are used in almost all fields of QIST; the ability to generate and control its properties is at the heart for applications in QIST. Though many progresses have been made in single photon generation and manipulation in nonlinear processes, lots of further techniques should be developed to harness the quality of single photon generated in SPDC or SFWM. The detailed techniques for optimizing the parameter of the photon source depend on the specific applications. For a pulsed heralded single photon source, the heralded efficiency and total photon count are important parameters, but the probability of single photon generation per pulse is very low, which limits the flux of photon pair generation. These defects can be overcome by using time, frequency, and OAM multiplexing to enhance the photon generation probability per pulse and total count rate [41, 107–112]. When the optical elements for multiplexing have low losses, the heralded efficiency and rate can be increased substantially [112]. For applications taking advantages of the sharp time correlations in SPDC, a broadband spectrum of the photon pair is needed. Such a broadband photon pair can be realized with an ultrathin nonlinear crystal or using a chirp quasi-phase-matching crystal; the bandwidth of the photon pair generated can be greater than 100 nm, which has a time correlation of sub-femtosecond [113]. For quantum information applications, a multiplexed time-energy and polarized entangled photon pair is preferred for high-capacity quantum communication by using dense-wave division multiplexing technique. The multiplexed entangled sources are easier to be realized using a waveguide platform such as a PPLN waveguide, a DSF, or SOI waveguide. A SOI ring cavity is also preferred in generating frequency comb entangled states [114]. For generating HD entangled states, by shaping the profile of a pump beam, a much greater Hilbert space can be reached [115, 116]. For QFC of OAM entangled states, the mode-dependent conversion efficiency has not been solved yet. We recently proposed and demonstrated that if we use a flat-top beam to pump the SFG crystal, then we can solve the problem of mode-dependent conversion efficiency by using a

For a compact application, integrated optics will offer a great advantage over free-space implementation; the trends of modern optics are to convert a freespace module to an equivalent integrated optical device, which will be of high compact, robust to environment fluctuations and much easier for larger amounts

In conclusion, most of the advances and progresses for generation and manipulation of single photon sources in nonlinear processes are briefly reviewed in this chapter; this review will provide a glance at the current status, and challenges remain to be solved in this field. The general properties for single photon generation in nonlinear processes are introduced firstly; then we introduce the development of various entangled states and the methods to characterize nonclassical photonic states. Next, we review the progresses for frequency conversion of a photonic state in nonlinear processes. Finally, we give comprehensive discussions about

*DOI: http://dx.doi.org/10.5772/intechopen.90268*

**6. Discussions and conclusion**

Gaussian pump beam [117].

of fabrication [118, 119].

*Generation and Manipulation of Nonclassical Photon Sources in Nonlinear Processes DOI: http://dx.doi.org/10.5772/intechopen.90268*

limited, but a longer nonlinear crystal would lead to a smaller spectral bandwidth and spatial bandwidth; a proper crystal length should be chosen to balance conversion efficiency and spectral bandwidth. The noise in QFC comes from SPDC and SRS of the intense pump beam; therefore a longer pump wavelength is preferred to reduce the noise photon in QFC [106]. The noise photon can also be dramatically reduced by using a narrow bandwidth filters to filter out the converted photon.

## **6. Discussions and conclusion**

*Single Photon Manipulation*

**Figure 6.**

*(cited from [99]).*

systems usually work at different frequencies, which may have a big frequency mismatching. To build up a quantum network consisting of various quantum systems for information encoding, storage, transmission, and processing, a quantum frequency converter (QFC) to link different quantum systems is indispensable. Such a frequency transducer can be realized by utilizing nonlinear processes such as sum frequency generation (SFG) and Bragg reflection in four-wave mixing. The theory of quantum frequency conversion for SFG was first proposed by P. Kumar in 1990 [87]. In SFG, a strong pump laser can convert a weak signal beam with high quantum efficiency; the unity quantum efficiency can be reached when the pump beam is strong enough (see **Figure 6** left image), and the quantum correlations are unchanged after frequency conversion. Since it has been proposed, some significant progresses have been made in this field; researchers have realized that frequency up-conversion and down-conversion for a single photon generated from quantum dot, and various qubit states or entangled states such as polarization, time-energy, and OAM entangled state [39, 88–101] have been up- or downconverted. A typical setup for QFC of an OAM qubit, an OAM-polarization hybrid entangled state, and an OAM-OAM entangled state is shown in **Figure 6** (right image). For frequency down-conversion, the visible single photons generated from atomic ensemble, trapped irons, or NV centers have been converted to telecom band successfully [102–105]. In all these demonstrations, the single photon properties and entanglement are preserved in the conversion processes, which ensures that quantum information can be coupled to different quantum systems by using a

*Left image: simple diagram for sum frequency generation in QPM crystal. Right image: experimental setup of QFC for an OAM qubit, an OAM-polarization hybrid entangled state, and an OAM-OAM entangled state* 

In QFC, there are four parameters to evaluate the quality of a converter: quantum conversion efficiency, noise level, spectral bandwidth, and spatial bandwidth. These parameters are not independent; therefore in practical applications, one needs to balance between different parameters [98]. A longer nonlinear crystal is preferred to reach maximum conversion efficiency when the pump power is

**46**

quantum frequency interface.

Nonclassical photon sources are used in almost all fields of QIST; the ability to generate and control its properties is at the heart for applications in QIST. Though many progresses have been made in single photon generation and manipulation in nonlinear processes, lots of further techniques should be developed to harness the quality of single photon generated in SPDC or SFWM. The detailed techniques for optimizing the parameter of the photon source depend on the specific applications. For a pulsed heralded single photon source, the heralded efficiency and total photon count are important parameters, but the probability of single photon generation per pulse is very low, which limits the flux of photon pair generation. These defects can be overcome by using time, frequency, and OAM multiplexing to enhance the photon generation probability per pulse and total count rate [41, 107–112]. When the optical elements for multiplexing have low losses, the heralded efficiency and rate can be increased substantially [112]. For applications taking advantages of the sharp time correlations in SPDC, a broadband spectrum of the photon pair is needed. Such a broadband photon pair can be realized with an ultrathin nonlinear crystal or using a chirp quasi-phase-matching crystal; the bandwidth of the photon pair generated can be greater than 100 nm, which has a time correlation of sub-femtosecond [113]. For quantum information applications, a multiplexed time-energy and polarized entangled photon pair is preferred for high-capacity quantum communication by using dense-wave division multiplexing technique. The multiplexed entangled sources are easier to be realized using a waveguide platform such as a PPLN waveguide, a DSF, or SOI waveguide. A SOI ring cavity is also preferred in generating frequency comb entangled states [114]. For generating HD entangled states, by shaping the profile of a pump beam, a much greater Hilbert space can be reached [115, 116]. For QFC of OAM entangled states, the mode-dependent conversion efficiency has not been solved yet. We recently proposed and demonstrated that if we use a flat-top beam to pump the SFG crystal, then we can solve the problem of mode-dependent conversion efficiency by using a Gaussian pump beam [117].

For a compact application, integrated optics will offer a great advantage over free-space implementation; the trends of modern optics are to convert a freespace module to an equivalent integrated optical device, which will be of high compact, robust to environment fluctuations and much easier for larger amounts of fabrication [118, 119].

In conclusion, most of the advances and progresses for generation and manipulation of single photon sources in nonlinear processes are briefly reviewed in this chapter; this review will provide a glance at the current status, and challenges remain to be solved in this field. The general properties for single photon generation in nonlinear processes are introduced firstly; then we introduce the development of various entangled states and the methods to characterize nonclassical photonic states. Next, we review the progresses for frequency conversion of a photonic state in nonlinear processes. Finally, we give comprehensive discussions about

### *Single Photon Manipulation*

the remaining challenges in generating high-quality and HD entangled states, the unsolved problems for QFC of HD OAM photonic states, and the development of integrated optics for small footprint optical devices and large-scale quantum information processing on chip. This book chapter should be helpful for new researchers working in this field.

## **Author details**

Zhi-Yuan Zhou\* and Bao-Sen Shi Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei, Anhui, China

\*Address all correspondence to: zyzhouphy@ustc.edu.cn

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**49**

*Generation and Manipulation of Nonclassical Photon Sources in Nonlinear Processes*

four-photon orbital angular momentum entanglement. Physical Review Letters.

[10] Boyd RW. Nonlinear Optics. 3rd ed. Chichester: Academic Press; 2008. 640 p

[11] Armstrong JA, Bloembergen N, Ducuing J, Perhsan PS. Interactions between light waves in a nonlinear

[12] Jin RB, Shimizu R, Kaneda F, Mitsumori Y, Kosaka H, Edamatsu K. Entangled-state generation with an intrinsically pure single-photon source and a weak coherent source. Physical Review A. 2013;**88**:012324. DOI: 10.1103/PhysRevA.88.012324

[13] Li Y, Zhou ZY, Ding DS, Shi BS. CW-pumped telecom band polarization entangled photon pair generation in a Sagnac interferometer. Optics Express. 2015;**23**:28792-28800.

DOI: 10.1364/OE.23.028792

[15] Zhou ZY, Jiang YK,

[14] Zhou ZY, Jiang YK, Ding DS, Shi BS, Guo GC. Actively switchable nondegenerate polarization-entangled photon-pair distribution in dense wave-division multiplexing. Physical Review A. 2013;**87**:045806. DOI: 10.1103/PhysRevA.87.045806

Ding DS, Shi BS. An ultra-broadband continuously-tunable polarizationentangled photon-pair source covering the C+L telecom bands based on a single type-II PPKTP crystal. Journal of Modern Optics. 2013;**60**:720-725. DOI:

10.1080/09500340.2013.807363

[16] Jin RB, Shimizu R, Wakui K, Fujiwara M, Yamashita T, Miki S, et al. Pulsed Sagnac polarization-entangled photon source with a PPKTP crystal at

dielectric. Physics Review. 1962;**127**:1918. DOI: 10.1103/

PhysRev.127.1918

2016;**116**:073601. DOI: 10.1103/ PhysRevLett.116.073601

*DOI: http://dx.doi.org/10.5772/intechopen.90268*

Sciarrino F. Photonic quantum information

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*Generation and Manipulation of Nonclassical Photon Sources in Nonlinear Processes DOI: http://dx.doi.org/10.5772/intechopen.90268*

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*Single Photon Manipulation*

working in this field.

**48**

**Author details**

Zhi-Yuan Zhou\* and Bao-Sen Shi

Technology of China, Hefei, Anhui, China

provided the original work is properly cited.

\*Address all correspondence to: zyzhouphy@ustc.edu.cn

Key Laboratory of Quantum Information, CAS, University of Science and

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

the remaining challenges in generating high-quality and HD entangled states, the unsolved problems for QFC of HD OAM photonic states, and the development of integrated optics for small footprint optical devices and large-scale quantum information processing on chip. This book chapter should be helpful for new researchers

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[3] Kimble J. The quantum internet. Nature. 2008;**453**:1023-1030. DOI: 10.1038/nature07127

[4] Lodahl P. Quantum-dot based photonic quantum networks. Quantum Science and Technology. 2018;**3**:013001. DOI: 10.1088/2058-9565/aa91bb

[5] Kurtsiefer C, Mayer S, Zarda P, Weinfurter H. Stable solid-state source of single photons. Physical Review Letters. 2000;**85**:290. DOI: 10.1103/ PhysRevLett.85.290

[6] Kuhn A, Hennrich M, Rempe G. Deterministic single-photon source for distributed quantum networking. Physical Review Letters. 2002;**89**:067901. DOI: 10.1103/ PhysRevLett.89.067901

[7] Burnham DC, Weinberg DL. Observation of simultaneity in parametric production of optical photon pairs. Physical Review Letters. 1970;**25**:84. DOI: 10.1103/PhysRevLett.25.84

[8] Takesue H, Inoue K. Generation of polarization-entangled photon pairs and violation of Bell's inequality using spontaneous four-wave mixing in a fiber loop. Physical Review A. 2004;**70**:031802. DOI: 10.1103/PhysRevA.70.031802

[9] Hiesmayr BC, de Dood MJA, Löffler W. Observation of

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[80] Collins D, Gisin N, Linden N, Massar S, Popescu S. Bell inequalities for arbitrarily high dimensional systems. Physical Review Letters. 2002;**88**:040404. DOI: 10.1103/ PhysRevLett.88.040404

[81] James DFV, Kwiat PG, Munro WJ, White AG. Measurement of qubits. Physical Review A. 2001;**64**:052312. DOI: 10.1103/PhysRevA.64.052312

[82] Blinov BB, Moehring DL, Duan LM, Monroe C. Observation of entanglement between a single trapped atom and a single photon. Nature. 2004;**428**:153- 157. DOI: 10.1038/nature02377

[83] Matsukevich DN, KA. Quantum state transfer between matter and light. Science. 2004;**306**:663-666. DOI: 10.1126/science.1103346

[84] Togan E, Chu Y, Trifonov AS, Jiang L, Maze J, Childress L, et al.

Quantum entanglement between an optical photon and a solid-state spin qubit. Nature. 2010;**466**:730-734. DOI: 10.1038/nature09256

[85] Piro N, Rohde F, Schuck C, Almendros M, Huwer J, Ghosh J, et al. Heralded single-photon absorption by a single atom. Nature Physics. 2011;**7**:17- 20. DOI: 10.1038/nphys1805

[86] Clausen C, Usmani I, Bussieres F, Singouard N, Afzelius M, de Riedmatten H, et al. Quantum storage of photonic entanglement in a crystal. Nature. 2011;**469**:508-511. DOI: 10.1038/ nature09662

[87] Kumar P. Quantum frequency conversion. Optics Letters. 1990;**15**:1476-1478. DOI: 10.1364/ OL.15.001476

[88] Tanzilli S, Tittel W, Halder M, Alibart O, Baldi P, Gisin N, et al. A photonic quantum information interface. Nature. 2005;**437**:116-120. DOI: 10.1038/nature04009

[89] Takesue H. Single-photon frequency down-conversion experiment. Physical Review A. 2010;**82**:013833. DOI: 10.1103/PhysRevA.82.013833

[90] Curtz N, Thew R, Simon C, Gisin N, Zbinden H. Coherent frequency downconversion interface for quantum repeaters. Optics Express. 2010;**18**:22099- 22104. DOI: 10.1364/OE.18.022099

[91] Zaske S, Lenhard A, Kebler CA, Kettler J, Hepp C, Arend C, et al. Visible-to-telecom quantum frequency conversion of light from a single quantum emitter. Physical Review Letters. 2012;**109**:147404. DOI: 10.1103/ PhysRevLett.109.147404

[92] Takesue H. Erasing distinguishability using quantum frequency up-conversion. Physical Review Letters. 2008;**101**:173901. DOI: 10.1103/PhysRevLett.101.173901

**55**

*Generation and Manipulation of Nonclassical Photon Sources in Nonlinear Processes*

[100] Zhou ZY, Liu SL, Liu SK, Li YH, Ding DS, Guo GC, et al. Superresolving

phase measurement with shortwavelength NOON states by quantum frequency up-conversion. Physical Review Applied. 2017;**7**:064025. DOI: 10.1103/PhysRevApplied.7.064025

[101] Liu SL, Liu SK, Li YH, Shi S, Zhou ZY, Shi BS. Coherent frequency bridge between visible and telecommunications band for vortex light. Optics Express. 2017;**25**:24290- 24298. DOI: 10.1364/OE.25.024290

[102] Walker T, Miyanishi K,

Physical Review Letters. 2018;**120**:203601. DOI: 10.1103/ PhysRevLett.120.203601

2018;**9**:1997. DOI: 10.1038/ s41467-018-04338-x

[104] Bock M, Eich P, Kucera S, Kreis M, Lenhard A, Becher C, et al. High-fidelity entanglement between a trapped ion and a telecom photon via quantum frequency conversion. Nature Communications. 2018;**9**:1998. DOI:

10.1038/s41467-018-04341-2

[105] Dréau A, Tchebotareva A, Mahdaoui AE, Bonato C, Hanson R. Quantum frequency conversion of single photons from a nitrogen-vacancy center in diamond to telecommunication wavelengths. Physical Review Applied.

2018;**9**:064031. DOI: 10.1103/ PhysRevApplied.9.064031

[106] Shentu GL, Pelc JS, Wang XD, Sun QC, Zheng MY, Fejer MM, et al. Ultralow noise up-conversion detector

Ikuta R, Takahashi H, Kashanian SV, Tsujimoto Y, et al. Long-distance dingle photon transmission from a trapped ion via quantum frequency conversion.

[103] Ikuta R, Kobayashi T, Kawakami T, Miki S, Yabuno M, Yamashita T, et al. Polarization insensitive frequency conversion for an atom-photon

entanglement distribution via a telecom network. Nature Communications.

*DOI: http://dx.doi.org/10.5772/intechopen.90268*

[93] Rakher MT, Ma L, Slattery O, Tang X, Srinivasan K. Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion. Nature Photonics. 2010;**4**:786-791. DOI: 10.1038/nphoton.2010.221

[94] Guinness HJ, Raymer MG, McKinstrie CJ, Radic S. Quantum frequency translation of singlephoton states in a photonic crystal fiber. Physical Review Letters. 2010;**105**:093604. DOI: 10.1103/ PhysRevLett.105.093604

[95] Ates S, Agha I, Gulinatti A, Reach I, Rakher MT, Badolato A, et al. Two-photon interference using background-free quantum frequency conversion of single photons emitted by an InAs quantum dot. Physical Review Letters. 2012;**109**:147405. DOI: 10.1103/

PhysRevLett.109.147405

10.1038/ncomms1544

10.1038/lsa.2016.19

[97] Guerrerio T, Martin A,

Sanguinetti B, pelc JS, Langrock C, Fejer MM, et al. Nonlinear interaction between single photons. Physical Review Letters. 2014;**113**:173601. DOI: 10.1103/PhysRevLett.113.173601

[98] Zhou ZY, Li Y, Ding DS, Zhang W, Shi S, Shi BS, et al. Orbital angular momentum photonic quantum interface. Light: Science and Applications. 2016;**5**:e16019. DOI:

[99] Zhou ZY, Liu SL, Li Y, Ding DS, Zhang W, Shi S, et al. Orbital angular momentum-entanglement frequency transducer. Physical Review Letters. 2016;**117**:103601. DOI: 10.1103/ PhysRevLett.117.103601

[96] Ikuta R, Kusaka Y, Kitano T, Kato H, Yamamoto T, Koashi M, et al. Wide-band quantum interface for visible-to-telecommunication wavelength conversion. Nature Communications. 2011;**2**:537. DOI:

*Generation and Manipulation of Nonclassical Photon Sources in Nonlinear Processes DOI: http://dx.doi.org/10.5772/intechopen.90268*

[93] Rakher MT, Ma L, Slattery O, Tang X, Srinivasan K. Quantum transduction of telecommunications-band single photons from a quantum dot by frequency upconversion. Nature Photonics. 2010;**4**:786-791. DOI: 10.1038/nphoton.2010.221

*Single Photon Manipulation*

10.1364/OE.20.016807

[76] Clark AS, Collins MJ, Judge AC, Mägi EC, Xiong C, Eggleton BJ. Raman scattering effects on correlated photon pair generation in chalcogenide. Optics Express. 2012;**20**:16807-16814. DOI:

Quantum entanglement between an optical photon and a solid-state spin qubit. Nature. 2010;**466**:730-734. DOI:

[85] Piro N, Rohde F, Schuck C, Almendros M, Huwer J, Ghosh J, et al. Heralded single-photon absorption by a single atom. Nature Physics. 2011;**7**:17-

20. DOI: 10.1038/nphys1805

Bussieres F, Singouard N, Afzelius M, de Riedmatten H, et al. Quantum storage of photonic entanglement in a crystal. Nature. 2011;**469**:508-511. DOI: 10.1038/

[87] Kumar P. Quantum frequency conversion. Optics Letters. 1990;**15**:1476-1478. DOI: 10.1364/

Halder M, Alibart O, Baldi P, Gisin N, et al. A photonic quantum information interface. Nature. 2005;**437**:116-120.

[89] Takesue H. Single-photon frequency down-conversion experiment. Physical Review A. 2010;**82**:013833. DOI: 10.1103/PhysRevA.82.013833

[90] Curtz N, Thew R, Simon C, Gisin N, Zbinden H. Coherent frequency downconversion interface for quantum repeaters. Optics Express. 2010;**18**:22099- 22104. DOI: 10.1364/OE.18.022099

[91] Zaske S, Lenhard A, Kebler CA, Kettler J, Hepp C, Arend C, et al. Visible-to-telecom quantum frequency conversion of light from a single quantum emitter. Physical Review Letters. 2012;**109**:147404. DOI: 10.1103/

PhysRevLett.109.147404

[92] Takesue H. Erasing

distinguishability using quantum frequency up-conversion. Physical Review Letters. 2008;**101**:173901. DOI: 10.1103/PhysRevLett.101.173901

[86] Clausen C, Usmani I,

nature09662

OL.15.001476

[88] Tanzilli S, Tittel W,

DOI: 10.1038/nature04009

10.1038/nature09256

[77] Mosley PJ, Lundeen JS, Smith BJ, Wasylczyk P, U'Ren AB, Silberhorn C, et al. Heralded generation of ultrafast single photons in pure quantum states. Physical Review Letters. 2008;**100**:133601. DOI: 10.1103/ PhysRevLett.100.133601

[78] Rarity JG, Tapster PR, Jakeman E, Larchuk T, Campos RA, Teich MC, et al. Two-photon interference in a Mach-Zehnder interferometer. Physical Review Letters. 1990;**65**:1348. DOI: 10.1103/PhysRevLett.65.1348

[79] Clauser JF, Horne MA, Shimony A, Holt RA. Proposed experiment to test local hidden-variable theories. Physical Review Letters. 1969;**23**:880-884. DOI:

10.1103/PhysRevLett.23.880

[80] Collins D, Gisin N, Linden N, Massar S, Popescu S. Bell inequalities for arbitrarily high dimensional systems. Physical Review Letters. 2002;**88**:040404. DOI: 10.1103/ PhysRevLett.88.040404

[81] James DFV, Kwiat PG, Munro WJ, White AG. Measurement of qubits. Physical Review A. 2001;**64**:052312. DOI: 10.1103/PhysRevA.64.052312

[82] Blinov BB, Moehring DL, Duan LM, Monroe C. Observation of entanglement between a single trapped atom and a single photon. Nature. 2004;**428**:153- 157. DOI: 10.1038/nature02377

[83] Matsukevich DN, KA. Quantum state transfer between matter and light. Science. 2004;**306**:663-666. DOI:

[84] Togan E, Chu Y, Trifonov AS, Jiang L, Maze J, Childress L, et al.

10.1126/science.1103346

**54**

[94] Guinness HJ, Raymer MG, McKinstrie CJ, Radic S. Quantum frequency translation of singlephoton states in a photonic crystal fiber. Physical Review Letters. 2010;**105**:093604. DOI: 10.1103/ PhysRevLett.105.093604

[95] Ates S, Agha I, Gulinatti A, Reach I, Rakher MT, Badolato A, et al. Two-photon interference using background-free quantum frequency conversion of single photons emitted by an InAs quantum dot. Physical Review Letters. 2012;**109**:147405. DOI: 10.1103/ PhysRevLett.109.147405

[96] Ikuta R, Kusaka Y, Kitano T, Kato H, Yamamoto T, Koashi M, et al. Wide-band quantum interface for visible-to-telecommunication wavelength conversion. Nature Communications. 2011;**2**:537. DOI: 10.1038/ncomms1544

[97] Guerrerio T, Martin A, Sanguinetti B, pelc JS, Langrock C, Fejer MM, et al. Nonlinear interaction between single photons. Physical Review Letters. 2014;**113**:173601. DOI: 10.1103/PhysRevLett.113.173601

[98] Zhou ZY, Li Y, Ding DS, Zhang W, Shi S, Shi BS, et al. Orbital angular momentum photonic quantum interface. Light: Science and Applications. 2016;**5**:e16019. DOI: 10.1038/lsa.2016.19

[99] Zhou ZY, Liu SL, Li Y, Ding DS, Zhang W, Shi S, et al. Orbital angular momentum-entanglement frequency transducer. Physical Review Letters. 2016;**117**:103601. DOI: 10.1103/ PhysRevLett.117.103601

[100] Zhou ZY, Liu SL, Liu SK, Li YH, Ding DS, Guo GC, et al. Superresolving phase measurement with shortwavelength NOON states by quantum frequency up-conversion. Physical Review Applied. 2017;**7**:064025. DOI: 10.1103/PhysRevApplied.7.064025

[101] Liu SL, Liu SK, Li YH, Shi S, Zhou ZY, Shi BS. Coherent frequency bridge between visible and telecommunications band for vortex light. Optics Express. 2017;**25**:24290- 24298. DOI: 10.1364/OE.25.024290

[102] Walker T, Miyanishi K, Ikuta R, Takahashi H, Kashanian SV, Tsujimoto Y, et al. Long-distance dingle photon transmission from a trapped ion via quantum frequency conversion. Physical Review Letters. 2018;**120**:203601. DOI: 10.1103/ PhysRevLett.120.203601

[103] Ikuta R, Kobayashi T, Kawakami T, Miki S, Yabuno M, Yamashita T, et al. Polarization insensitive frequency conversion for an atom-photon entanglement distribution via a telecom network. Nature Communications. 2018;**9**:1997. DOI: 10.1038/ s41467-018-04338-x

[104] Bock M, Eich P, Kucera S, Kreis M, Lenhard A, Becher C, et al. High-fidelity entanglement between a trapped ion and a telecom photon via quantum frequency conversion. Nature Communications. 2018;**9**:1998. DOI: 10.1038/s41467-018-04341-2

[105] Dréau A, Tchebotareva A, Mahdaoui AE, Bonato C, Hanson R. Quantum frequency conversion of single photons from a nitrogen-vacancy center in diamond to telecommunication wavelengths. Physical Review Applied. 2018;**9**:064031. DOI: 10.1103/ PhysRevApplied.9.064031

[106] Shentu GL, Pelc JS, Wang XD, Sun QC, Zheng MY, Fejer MM, et al. Ultralow noise up-conversion detector and spectrometer for the telecom band. Optics Express. 2013;**21**:13986-13991. DOI: 10.1364/OE.21.013986

[107] Liu SL, Zhou Q, Zhou ZY, Liu SK, Li Y, Li YH, et al. Multiplexing heralded single photons in orbital angular momentum space. Physical Review A. 2019;**100**:013833. DOI: 10.1103/PhysRevA.100.013833

[108] Migdall AL, Branning D, Castelletto S. Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source. Physical Review A. 2002;**66**:053805. DOI: 10.1103/PhysRevA.66.053805

[109] Collins MJ, Xiong C, Rey IH, Vo TD, He J, Shahnia S, et al. Integrated spatial multiplexing of heralded single-photon sources. Nature Communications. 2013;**4**:2582. DOI: 10.1038/ncomms3582

[110] Kaneda F, Christensen BG, Wong JJ, Park HS, McCusker KT, Kwiat PG. Time-multiplexed heralded single-photon source. Optica. 2015;**2**:1010-1013. DOI: 10.1364/ OPTICA.2.001010

[111] Puigibert MG, Aguilar GH, Zhou Q, Marsili F, Shaw MD, Verma VB, et al. Heralded single photons based on spectral multiplexing and feedforward control. Physical Review Letters. 2017;**119**:083601. DOI: 10.1103/ PhysRevLett.119.083601

[112] Joshi C, Farsi A, Clemmen S, Ramelow S, Gaeta AL. Frequency multiplexing for quasi-deterministic heralded single-photon sources. Nature Communications. 2018;**9**:847. DOI: 10.1038/s41467-018-03254-4

[113] Nasr MB, Carrasco S, Saleh BEA, Sergienko AV, Teich MC, Torres JP, et al. Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion. Physical

Review Letters. 2008;**100**:183601. DOI: 10.1103/PhysRevLett.100.183601

**Chapter 4**

**Abstract**

and networks.

down-conversion

**1. Introduction**

**57**

Single-Photon Frequency

*Yuanhua Li and Xianfeng Chen*

Conversion for Quantum Interface

Single-photon frequency conversion for quantum interface plays an important role in quantum communications and networks, which is crucial for the realization of quantum memory, faithful entanglement swapping and quantum teleportation. In this chapter, we will present our recent experiments about single-photon frequency conversion based on quadratic nonlinear processes. Firstly, we demonstrated spectrum compression of broadband single photons at the telecom wavelength to the near-visible window, marking a critical step towards coherent photonic interface. Secondly, we demonstrated the nonlinear interaction between two chirped broadband single-photon-level coherent states, which may be utilized to achieve heralding entanglement at a distance. Finally, we theoretically introduced and experimentally demonstrated single-photon frequency conversion in the telecom band, enabling switching of single photons between dense wavelengthdivision multiplexing channels. Moreover, quantum entanglement between the photon pair is maintained after the frequency conversion. Our researches have realized three significant quantum interfaces via single-photon frequency conversion, which hold great promise for the development of quantum communications

**Keywords:** quantum interface, quantum network, single-photon frequency conversion, periodically poled lithium niobate waveguide, sum frequency generation, cascaded nonlinear process, spectrum compression, spontaneous

In recent years, nonlinear quantum optics has developed rapidly, such as quantum communication [1], quantum computation [2], quantum memory [3], quantum network [4], and so on. In order to realize these quantum applications, coherent quantum interface is a significant quantum device as it is capable of frequency and bandwidth in the telecom band is converted simultaneously. Quantum network is an important platform to study quantum communication, quantum computation, and quantum memory. Quantum network consists of many nodes and the quantum communication channels of the connected nodes, and the quantum communication channels of different connected nodes need to be connected by a quantum interface. Any node in a quantum network has the capability of quantum communication, quantum memory, quantum entanglement swapping, and generation of single photon sources. When the quantum channel of different nodes

[114] Kues M, Reimer C, Roztocki P, Cortés LR, Sciara S, Wetzel B, et al. On-chip generation of high-dimensional entangled quantum states and their coherent control. Nature. 2017;**546**:622. DOI: 10.1038/nature22986

[115] Liu SL, Zhou ZY, Liu SK, Li YH, Li Y, Yang C, et al. Coherent manipulation of a three-dimensional maximally entangled state. Physical Review A. 2018;**98**:062316. DOI: 10.1103/PhysRevA.98.062316

[116] Kovlakov EV, Straupe SS, Kulik SP. Quantum state engineering with twisted photons via adaptive shaping of the pump beam. Physical Review A. 2018;**98**:060301. DOI: 10.1103/PhysRevA.98.060301

[117] Liu SL, Yang C, Xu ZH, Liu SK, Li Y, Li YH, et al. A high-dimensional quantum frequency converter. arXiv:1908.10569 [quant-ph]

[118] Wang JW, Paesani S, Dong YH, Santagati R, Skrzypczyk P, Salavrakos A, et al. Multidimensional quantum entanglement with largescale integrated optics. Science. 2018;**360**:285-291. DOI: 10.1126/science. aar7053

[119] Qiang X, Zhou X, Wang J, Wilkes CM, Loke T, O'Gara S, et al. Large-scale silicon quantum photonics implementing arbitrary two-qubit processing. Nature Photonics. 2018;**12**:534-539. DOI: 10.1038/ s41566-018-0236-y

## **Chapter 4**

*Single Photon Manipulation*

DOI: 10.1364/OE.21.013986

[107] Liu SL, Zhou Q, Zhou ZY, Liu SK, Li Y, Li YH, et al. Multiplexing heralded single photons in orbital angular momentum space. Physical Review A. 2019;**100**:013833. DOI: 10.1103/PhysRevA.100.013833

[108] Migdall AL, Branning D,

Castelletto S. Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source. Physical Review A. 2002;**66**:053805. DOI: 10.1103/PhysRevA.66.053805

[109] Collins MJ, Xiong C, Rey IH, Vo TD, He J, Shahnia S, et al. Integrated spatial multiplexing of heralded single-photon sources. Nature Communications. 2013;**4**:2582. DOI:

[110] Kaneda F, Christensen BG, Wong JJ, Park HS, McCusker KT, Kwiat PG. Time-multiplexed heralded

single-photon source. Optica. 2015;**2**:1010-1013. DOI: 10.1364/

[111] Puigibert MG, Aguilar GH, Zhou Q, Marsili F, Shaw MD, Verma VB, et al. Heralded single photons based on spectral multiplexing and feedforward control. Physical Review Letters. 2017;**119**:083601. DOI: 10.1103/

10.1038/ncomms3582

OPTICA.2.001010

PhysRevLett.119.083601

[112] Joshi C, Farsi A, Clemmen S, Ramelow S, Gaeta AL. Frequency multiplexing for quasi-deterministic heralded single-photon sources. Nature Communications. 2018;**9**:847. DOI: 10.1038/s41467-018-03254-4

[113] Nasr MB, Carrasco S, Saleh BEA, Sergienko AV, Teich MC, Torres JP, et al. Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion. Physical

and spectrometer for the telecom band. Optics Express. 2013;**21**:13986-13991.

Review Letters. 2008;**100**:183601. DOI: 10.1103/PhysRevLett.100.183601

[114] Kues M, Reimer C, Roztocki P, Cortés LR, Sciara S, Wetzel B, et al. On-chip generation of high-dimensional entangled quantum states and their coherent control. Nature. 2017;**546**:622.

DOI: 10.1038/nature22986

[115] Liu SL, Zhou ZY, Liu SK, Li YH, Li Y, Yang C, et al. Coherent manipulation of a three-dimensional maximally entangled state. Physical Review A. 2018;**98**:062316. DOI: 10.1103/PhysRevA.98.062316

[116] Kovlakov EV, Straupe SS, Kulik SP. Quantum state engineering with twisted photons via adaptive shaping of the pump beam. Physical Review A. 2018;**98**:060301. DOI: 10.1103/PhysRevA.98.060301

[117] Liu SL, Yang C, Xu ZH, Liu SK, Li Y, Li YH, et al. A high-dimensional quantum frequency converter. arXiv:1908.10569 [quant-ph]

Dong YH, Santagati R, Skrzypczyk P, Salavrakos A, et al. Multidimensional quantum entanglement with largescale integrated optics. Science.

2018;**360**:285-291. DOI: 10.1126/science.

[119] Qiang X, Zhou X, Wang J, Wilkes CM, Loke T, O'Gara S, et al. Large-scale silicon quantum photonics implementing arbitrary two-qubit processing. Nature Photonics. 2018;**12**:534-539. DOI: 10.1038/

s41566-018-0236-y

[118] Wang JW, Paesani S,

aar7053

**56**

## Single-Photon Frequency Conversion for Quantum Interface

*Yuanhua Li and Xianfeng Chen*

## **Abstract**

Single-photon frequency conversion for quantum interface plays an important role in quantum communications and networks, which is crucial for the realization of quantum memory, faithful entanglement swapping and quantum teleportation. In this chapter, we will present our recent experiments about single-photon frequency conversion based on quadratic nonlinear processes. Firstly, we demonstrated spectrum compression of broadband single photons at the telecom wavelength to the near-visible window, marking a critical step towards coherent photonic interface. Secondly, we demonstrated the nonlinear interaction between two chirped broadband single-photon-level coherent states, which may be utilized to achieve heralding entanglement at a distance. Finally, we theoretically introduced and experimentally demonstrated single-photon frequency conversion in the telecom band, enabling switching of single photons between dense wavelengthdivision multiplexing channels. Moreover, quantum entanglement between the photon pair is maintained after the frequency conversion. Our researches have realized three significant quantum interfaces via single-photon frequency conversion, which hold great promise for the development of quantum communications and networks.

**Keywords:** quantum interface, quantum network, single-photon frequency conversion, periodically poled lithium niobate waveguide, sum frequency generation, cascaded nonlinear process, spectrum compression, spontaneous down-conversion

## **1. Introduction**

In recent years, nonlinear quantum optics has developed rapidly, such as quantum communication [1], quantum computation [2], quantum memory [3], quantum network [4], and so on. In order to realize these quantum applications, coherent quantum interface is a significant quantum device as it is capable of frequency and bandwidth in the telecom band is converted simultaneously. Quantum network is an important platform to study quantum communication, quantum computation, and quantum memory. Quantum network consists of many nodes and the quantum communication channels of the connected nodes, and the quantum communication channels of different connected nodes need to be connected by a quantum interface. Any node in a quantum network has the capability of quantum communication, quantum memory, quantum entanglement swapping, and generation of single photon sources. When the quantum channel of different nodes

performs the conversion of quantum communication and quantum memory, a quantum interface is needed, which can simultaneously realize spectral compression and frequency conversion because the bandwidth and the center frequency of the single photon used in quantum communication and quantum memory are different. When two broadband photons of different nodes' quantum channels are connected by quantum entanglement swapping, the connected quantum interface can efficiently couple the two broadband photons and simultaneously realize the nonlinear frequency conversion of the two broadband photons. The nonlinear upconversion of two broadband photons in nonlinear crystals can be converted into a high frequency narrowband photon, which provides a basis for implementing different types of quantum interfaces.

easily detected by a silicon avalanche photodiode (APD). Many theoretical schemes have been proposed to achieve the pulse compression or the frequency conversion. For instance, the 1550-nm photons can be converted into the near-infrared window through the nonlinear processes, such as the SFG. As theoretical schemes are diverse, they can be characterized by one common shortage, namely realizing only one operation. Therefore, it is highly expected that an optical technology is capable of simultaneously performing spectrum compression and frequency conversion in

In our experiment, spectral compression of single-photon-level laser pulse is generated by SFG between a positively chirped single-photon-level laser pulse and a negatively chirped classical laser pulse. As known, a laser pulse can be expressed as the frequency-dependent electric field *<sup>E</sup>*ð Þ¼ *<sup>ν</sup> <sup>U</sup>*ð Þ*<sup>ν</sup> <sup>e</sup>iϕ ν*ð Þ, where *<sup>U</sup>*ð Þ*<sup>ν</sup>* and *ϕ ν*ð Þ represent the amplitude information and phase information of the laser pulse, respectively. Obviously, we can obtain a chirp result when a transform-limited

2

, where *A* is a constant

*,* (1)

laser pulse is subject to a quadratic phase *ϕ ν*ð Þ ≈ *A*ð Þ *ν* � *ν*<sup>0</sup>

*Single-Photon Frequency Conversion for Quantum Interface*

*DOI: http://dx.doi.org/10.5772/intechopen.88867*

*dϕ ν*ð Þ*=dν* ¼ 2*πt* ¼ 2*A*ð Þ *ν* � *ν*<sup>0</sup> ; thus, *ν* ¼ *ν*<sup>0</sup> þ *πt=A* is realized.

*ΔνTH*

*SFG* <sup>≈</sup> ln 4 *A*

the PPLN waveguide, i.e., *Δν* ¼ *Δν*^*=L*, where *Δν*^ ¼ 4200 GHz � cm is the

the mode-locked optical-fiber laser pulse source generates 500-fs pulses at 1551.54 nm center wavelength, about 6.4 nm spectral bandwidth (6.4 nm is the FWHM of the spectral intensity distribution), 59.98 MHz repetition rate, and 45.2 MW average power. We split the laser pulse source into two replicas using a 50:50 beam splitter (BS), and then one of the two replicas of laser pulse is sent to a broadband fiber Bragg grating 1 (FBG1); at the same time, the other laser pulse is coupled into the FBG2. The parameters of FBG1 and FBG2 are exactly the same (1547 nm center wavelength, 39 nm FWHM bandwidth, and 5 nm/cm chirp rate).

used in the waveguide, the maximum SFG efficiency is guaranteed.

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 *Δν*<sup>2</sup> *P* þ 1 *Δν*<sup>2</sup> *Q*

s

where *Δν<sup>P</sup>* and *Δν<sup>Q</sup>* are the bandwidths (FWHM). The FWHM bandwidth *Δν* is limited by group velocity dispersion, and decreases linearly with the length of

spectral acceptance of the waveguide. When the full FWHM bandwidths of positively chirped single-photon-level laser pulse and negatively chirped classical laser pulse are

A schematic of our experimental setup is shown in **Figure 1**. In our experiment,

and *ν*<sup>0</sup> is the center frequency. In terms of *dϕ ν*ð Þ*=dν* ¼ 2*πt*, one can obtain

The negatively chirped classical laser pulse of frequency with *ν*0*,P* increases linearly in time *t*1, i.e., *ν*0*,P*ð Þ¼ *t*<sup>1</sup> *ν*0*,P* þ *πt*1*=A,* and the positively chirped singlephoton-level pulse frequency with *ν*0*,Q* decreases linearly in time *t*2, *ν*0*,Q* ð Þ¼ *t*<sup>2</sup> *ν*0*,Q* � *πt*2*=A:* Here, *A* is the chirp rate, *ν*0*,P* and *ν*0*,Q* are the center frequency of these two laser pulse sources, and Δ*t* ¼ *t*<sup>1</sup> � *t*<sup>2</sup> is a relative time delay between the negatively chirped classical laser pulse and positively chirped single-photon-level laser pulse. In our work, *ν*0*,P* and *ν*0*,Q* are equal as chirped laser pulse and negatively laser pulse are two replicas of the laser source. When the positively chirped singlephoton-level laser pulse and negatively classical laser pulse simultaneously reach the PPLN waveguide chip, a blue-shifted frequency component of negatively classical laser pulse (*ν*0*,P* þ *πt*1*=A*) would match a red-shifted frequency component of positively chirped single-photon-level laser pulse (*ν*0*,Q* � *πt*2*=A*) with the relative time delay Δ*t*, and all frequency components of these two laser pulses would sum to a new narrow frequency with *ν*0*,SFG*ð Þ¼ Δ*t ν*0*,P* þ *ν*0*,Q* þ *π*Δ*t=A*. The expected (TH) intensity bandwidth (FWHM) of the SFG photon is given by the following

the telecom band.

equation [8]:

**59**

Periodically polarized lithium niobate (PPLN) waveguides have higher secondorder nonlinear coefficients than other nonlinear crystals. PPLN waveguide not only transmits a wide spectrum but is also easily integrated and processed into PPLN waveguide chips. It also can preserve the quantum properties of photons. The nonlinear effect of PPLN waveguide chip can realize the up-conversion and down-conversion of nonlinear frequencies of different wavelength photons. Therefore, PPLN waveguide chip is ideal for implementing different types of quantum interfaces.

In our work, we utilized PPLN waveguide chip to realize several kinds of different functions of single-photon frequency conversion for coherent quantum interface. First, we have demonstrated the generated coherent quantum interface suitable for quantum communication at 1550 nm and quantum memory in the near-visible window. We exploit a positively chirped single-photon-level laser pulse and a negatively chirped classical laser pulse by sum frequency generation (SFG) process to compress the bandwidth of the positively chirped single-photon-level laser pulse in a PPLN waveguide chip—from 800 to 13.7 GHz—which is approaching the bandwidth regime of some quantum memories. In the same time, one can flexibly convert the 1550-nm telecom-band photons into the nearinfrared window [5]. Second, we have experimentally demonstrated the SFG between two broadband single-photon-level coherent states by using a highefficiency PPLN waveguide chip. The SFG efficiency of 1*:*<sup>06</sup> <sup>10</sup><sup>7</sup> is realized, which provides potentially feasible quantum applications, such as faithful entanglement swapping without post-selection and nonlinear interaction between single photons with an integrated device at room temperature. What's more, longdistance quantum communication can be achieved by broadband single photons generated in a spontaneous parametric down conversion (SPDC) source [6]. Finally, we have realized the core quantum interface for fiber quantum networks. We report single-photon frequency conversion in a telecommunication band based on cascaded quadratic nonlinearity, i.e., SFG and difference frequency generation (DFG), in a PPLN waveguide. It shows that the frequency of single photons can be precisely converted to a DFG with continuous adjustability in a wide telecommunication band and their quantum characteristics are protected after the single-photon frequency conversion [7].

## **2. Methodology and result**

#### **2.1 Spectral compression of single-photon-level laser pulse**

Photons at 1550 nm are critical to all quantum information tasks via an opticalfiber network. Nevertheless, the narrowband photons in the near-visible wavelength regime possess the most efficient quantum memories and an ability of being *Single-Photon Frequency Conversion for Quantum Interface DOI: http://dx.doi.org/10.5772/intechopen.88867*

performs the conversion of quantum communication and quantum memory, a quantum interface is needed, which can simultaneously realize spectral compression and frequency conversion because the bandwidth and the center frequency of the single photon used in quantum communication and quantum memory are different. When two broadband photons of different nodes' quantum channels are connected by quantum entanglement swapping, the connected quantum interface can efficiently couple the two broadband photons and simultaneously realize the nonlinear frequency conversion of the two broadband photons. The nonlinear upconversion of two broadband photons in nonlinear crystals can be converted into a high frequency narrowband photon, which provides a basis for implementing dif-

Periodically polarized lithium niobate (PPLN) waveguides have higher secondorder nonlinear coefficients than other nonlinear crystals. PPLN waveguide not only transmits a wide spectrum but is also easily integrated and processed into PPLN waveguide chips. It also can preserve the quantum properties of photons. The nonlinear effect of PPLN waveguide chip can realize the up-conversion and down-conversion of nonlinear frequencies of different wavelength photons. Therefore, PPLN waveguide chip is ideal for implementing different types of

In our work, we utilized PPLN waveguide chip to realize several kinds of different functions of single-photon frequency conversion for coherent quantum interface. First, we have demonstrated the generated coherent quantum interface suitable for quantum communication at 1550 nm and quantum memory in the near-visible window. We exploit a positively chirped single-photon-level laser pulse and a negatively chirped classical laser pulse by sum frequency generation (SFG) process to compress the bandwidth of the positively chirped single-photon-level

laser pulse in a PPLN waveguide chip—from 800 to 13.7 GHz—which is

be precisely converted to a DFG with continuous adjustability in a wide

**2.1 Spectral compression of single-photon-level laser pulse**

single-photon frequency conversion [7].

**2. Methodology and result**

**58**

telecommunication band and their quantum characteristics are protected after the

Photons at 1550 nm are critical to all quantum information tasks via an opticalfiber network. Nevertheless, the narrowband photons in the near-visible wavelength regime possess the most efficient quantum memories and an ability of being

one can flexibly convert the 1550-nm telecom-band photons into the nearinfrared window [5]. Second, we have experimentally demonstrated the SFG between two broadband single-photon-level coherent states by using a highefficiency PPLN waveguide chip. The SFG efficiency of 1*:*<sup>06</sup> <sup>10</sup><sup>7</sup> is realized, which provides potentially feasible quantum applications, such as faithful entanglement swapping without post-selection and nonlinear interaction between single photons with an integrated device at room temperature. What's more, longdistance quantum communication can be achieved by broadband single photons generated in a spontaneous parametric down conversion (SPDC) source [6]. Finally, we have realized the core quantum interface for fiber quantum networks. We report single-photon frequency conversion in a telecommunication band based on cascaded quadratic nonlinearity, i.e., SFG and difference frequency generation (DFG), in a PPLN waveguide. It shows that the frequency of single photons can

approaching the bandwidth regime of some quantum memories. In the same time,

ferent types of quantum interfaces.

*Single Photon Manipulation*

quantum interfaces.

easily detected by a silicon avalanche photodiode (APD). Many theoretical schemes have been proposed to achieve the pulse compression or the frequency conversion. For instance, the 1550-nm photons can be converted into the near-infrared window through the nonlinear processes, such as the SFG. As theoretical schemes are diverse, they can be characterized by one common shortage, namely realizing only one operation. Therefore, it is highly expected that an optical technology is capable of simultaneously performing spectrum compression and frequency conversion in the telecom band.

In our experiment, spectral compression of single-photon-level laser pulse is generated by SFG between a positively chirped single-photon-level laser pulse and a negatively chirped classical laser pulse. As known, a laser pulse can be expressed as the frequency-dependent electric field *<sup>E</sup>*ð Þ¼ *<sup>ν</sup> <sup>U</sup>*ð Þ*<sup>ν</sup> <sup>e</sup>iϕ ν*ð Þ, where *<sup>U</sup>*ð Þ*<sup>ν</sup>* and *ϕ ν*ð Þ represent the amplitude information and phase information of the laser pulse, respectively. Obviously, we can obtain a chirp result when a transform-limited laser pulse is subject to a quadratic phase *ϕ ν*ð Þ ≈ *A*ð Þ *ν* � *ν*<sup>0</sup> 2 , where *A* is a constant and *ν*<sup>0</sup> is the center frequency. In terms of *dϕ ν*ð Þ*=dν* ¼ 2*πt*, one can obtain *dϕ ν*ð Þ*=dν* ¼ 2*πt* ¼ 2*A*ð Þ *ν* � *ν*<sup>0</sup> ; thus, *ν* ¼ *ν*<sup>0</sup> þ *πt=A* is realized.

The negatively chirped classical laser pulse of frequency with *ν*0*,P* increases linearly in time *t*1, i.e., *ν*0*,P*ð Þ¼ *t*<sup>1</sup> *ν*0*,P* þ *πt*1*=A,* and the positively chirped singlephoton-level pulse frequency with *ν*0*,Q* decreases linearly in time *t*2, *ν*0*,Q* ð Þ¼ *t*<sup>2</sup> *ν*0*,Q* � *πt*2*=A:* Here, *A* is the chirp rate, *ν*0*,P* and *ν*0*,Q* are the center frequency of these two laser pulse sources, and Δ*t* ¼ *t*<sup>1</sup> � *t*<sup>2</sup> is a relative time delay between the negatively chirped classical laser pulse and positively chirped single-photon-level laser pulse. In our work, *ν*0*,P* and *ν*0*,Q* are equal as chirped laser pulse and negatively laser pulse are two replicas of the laser source. When the positively chirped singlephoton-level laser pulse and negatively classical laser pulse simultaneously reach the PPLN waveguide chip, a blue-shifted frequency component of negatively classical laser pulse (*ν*0*,P* þ *πt*1*=A*) would match a red-shifted frequency component of positively chirped single-photon-level laser pulse (*ν*0*,Q* � *πt*2*=A*) with the relative time delay Δ*t*, and all frequency components of these two laser pulses would sum to a new narrow frequency with *ν*0*,SFG*ð Þ¼ Δ*t ν*0*,P* þ *ν*0*,Q* þ *π*Δ*t=A*. The expected (TH) intensity bandwidth (FWHM) of the SFG photon is given by the following equation [8]:

$$
\Delta\nu\_{\rm SFG}^{\rm TH} \approx \frac{\ln 4}{A} \sqrt{\frac{1}{\Delta\nu\_P^2} + \frac{1}{\Delta\nu\_Q^2}}\tag{1}
$$

where *Δν<sup>P</sup>* and *Δν<sup>Q</sup>* are the bandwidths (FWHM). The FWHM bandwidth *Δν* is limited by group velocity dispersion, and decreases linearly with the length of the PPLN waveguide, i.e., *Δν* ¼ *Δν*^*=L*, where *Δν*^ ¼ 4200 GHz � cm is the spectral acceptance of the waveguide. When the full FWHM bandwidths of positively chirped single-photon-level laser pulse and negatively chirped classical laser pulse are used in the waveguide, the maximum SFG efficiency is guaranteed.

A schematic of our experimental setup is shown in **Figure 1**. In our experiment, the mode-locked optical-fiber laser pulse source generates 500-fs pulses at 1551.54 nm center wavelength, about 6.4 nm spectral bandwidth (6.4 nm is the FWHM of the spectral intensity distribution), 59.98 MHz repetition rate, and 45.2 MW average power. We split the laser pulse source into two replicas using a 50:50 beam splitter (BS), and then one of the two replicas of laser pulse is sent to a broadband fiber Bragg grating 1 (FBG1); at the same time, the other laser pulse is coupled into the FBG2. The parameters of FBG1 and FBG2 are exactly the same (1547 nm center wavelength, 39 nm FWHM bandwidth, and 5 nm/cm chirp rate).

We first obtain the spectrum of the positively chirped laser pulse by using an optical-fiber-coupled spectrometer and find a width 800 � 20 GHz FWHM centered at 1551.54 nm (shown in red). The positively chirped laser pulse is then coupled through an optical fiber and superposed with the negatively chirped classical laser pulse (790 � 20GHz, centered at 1551.54 nm) in the PPLN waveguide chip for SFG. The SFG photons, after IF, are sent to a single-mode optical fiber and coupled into the optical-fiber-coupled spectrometer. Here, the FWHM bandwidths of both negatively and positively chirped laser pulses are smaller than the spectral acceptance of the PPLN waveguide chip (*Δν* ¼ *Δν*^*=L* ¼ 807 GHz). Thus, the full FWHM bandwidths of positively and negatively chirped laser pulses are used in the PPLN waveguide chip, as expected. As shown in **Figure 2(a)**, we measure significant spectral compression of the positively chirped laser pulse. The initial bandwidth of the positively chirped laser pulse is 800 GHz centered at 1551.54 nm (shown in red). When the quadratic phase is applied and the two laser pulses are up-converted, the bandwidth of laser pulse generated reduces to 33 � 1GHz (FWHM) centered at 775.77 nm (shown in black), where the relative time delay

*Single-Photon Frequency Conversion for Quantum Interface*

*DOI: http://dx.doi.org/10.5772/intechopen.88867*

Taking the resolution of our spectrometer into account, Δ*ν<sup>R</sup>* ¼ 30 � 1 GHz (FWHM), the actual bandwidth of the SFG photons after deconvolution is

malized intensities and, for the up-converted case, correspond to the average of 10 consecutive scans of 15 min acquisition time. This result agrees closely with theory,

*SFG* ¼ 9*:*8 � 0*:*7 GHz (FWHM) from Eq. (1), using the expected chirp parameter *<sup>A</sup>* ¼ �ð Þ <sup>2</sup>*:*<sup>52</sup> � <sup>0</sup>*:*<sup>01</sup> <sup>∗</sup> 108*fs*<sup>2</sup> given by the geometry of our FBG. Therefore, a bandwidth compression ratio of 58:1 is achieved in the positively chirped laser pulse

The center wavelength of the SFG photons can be controlled by adjusting the relative delay Δ*t* between the input pulses at the PPLN waveguide chip. The SFG spectrum of the created laser pulse could be given by a function of the delay time, with the fitted center wavelengths shown in **Figure 3**. The experimental results show that the wavelength depends linearly on the delay time, as expected. The linear fit gives a slope of �0*:*0247 � 0*:*001 nm/ps. In terms of the slope data, we

agreement with the chirp parameter *<sup>A</sup>* ¼ �ð Þ <sup>2</sup>*:*<sup>52</sup> � <sup>0</sup>*:*<sup>01</sup> <sup>∗</sup> 108*fs*<sup>2</sup> of the FBG1. It is also shown that the bandwidth compression ratio independent of the optical relative delay Δ*t*, which agrees closely with the theoretical result from the above Eq. (1).

*The positively chirped pulse spectrum and up-converted laser pulse spectrum (a) and relative frequency (b) [5].*

, in good

measure the negatively chirp parameter of *<sup>A</sup>* ¼ �ð Þ <sup>2</sup>*:*<sup>55</sup> � <sup>0</sup>*:*<sup>01</sup> <sup>∗</sup> 108*fs*<sup>2</sup>

<sup>p</sup> <sup>¼</sup> <sup>13</sup>*:*<sup>7</sup> � <sup>4</sup>*:*2 GHz (FWHM). The spectra are given by nor-

Δ*t* ¼ 0.

Δ*ν EXP*

Δ*νTH*

**Figure 2.**

**61**

(**Figure 2(b)**).

*SFG* <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Δ*ν*<sup>2</sup>

*<sup>M</sup>* � <sup>Δ</sup>*ν*<sup>2</sup> *R*

#### **Figure 1.**

*Experimental set-up. ATT, variable optical attenuator; BS, beam splitter (50:50); Circulators, optical fiber circulators; PC, polarization controller; FBG, fiber Bragg grating; Delay Fiber, optical adjustable delay fiber; SPBS, single mode polarization beam splitter (single mode to polarization maintaining); SBS, single mode beam splitter (single mode to polarization maintaining); PPLN-WG, PPLN waveguide chip; IF, interference filter; SAPD, silicon APD [5].*

It is known that FBG can be used for up-chirping and down-chirping, depending on the choice of the side from which the laser pulse is reflected. Thus, the two different chirp laser pulses after FBG1 and FBG2 are the same but with the opposite sign. It means that the positively chirped and negatively laser pulses have an equal and opposite chirp, �*A*. A positively chirped laser pulse is generated through FBG1 to introduce a linear chirp by group velocity dispersion. The other laser pulse is negative after a broadband FBG2. A variable optical attenuator (ATT1) is used to create a positively chirped single-photon-level laser pulse, and the other variable optical attenuator (ATT2) is used to control the energy of negatively chirped classical laser pulse for this experiment.

Then, the positively chirped single-photon-level laser pulse and the negatively chirped classical laser pulse are combined by a 1550/1550 nm 50:50 single-mode beam splitter (SBS) and couple into the z-cut PPLN waveguide chip through the optical-fiber pigtail. Two single-mode polarization beam splitters (SPBS (200:1)) and two polarization controllers (PCs) are used for controlling the positively chirped single-photon-level laser pulse and the negatively chirped classical laser pulse to the TM mode; it is known that the PPLN waveguide chip only supports Type-0 (*ee* ! *e*) phase matching in our work. A temperature controller (TC) is used for adjusting the PPLN waveguide chip's temperature to keep the QPM of the SFG process. The spectrally narrowed SFG photon pulse can be obtained in the PPLN waveguide chip, after interference filter (IF) with a nominal bandwidth of 20 nm (FWHM) centered around 780 nm (loss is about 1.2 dB), and then coupled into an optical-fiber-coupled spectrometer. Finally, the SFG photons are detected by a SAPD, whose detection efficiency is up to 60% at 775 nm and dark count rate is 26 Hz. In our experiment, a superconducting single photon detector (SSPD) is used to calibrate and monitor the counts of photons of positively chirped single-photon-level laser pulse, whose detection efficiency is up to 10% at 1551 nm and dark count rate is 600 Hz. Using the IF, any residue of the positively or negatively chirped photons have to be filtered out from the SFG photons by a factor of 10�18.

The reverse-proton-exchange PPLN waveguide chip is 52-mm long and QPM to perform the SFG process 1551 nm + 1551 nm ! 775.5 nm. It is poled through the quasi-phase-matching period of 19.6 μm. Moreover, one has a total fiber-to-outputfacet throughput of approximately �1.5 dB for the telecom band. The PPLN waveguide chip is antireflection coated to prevent interference fringes and enhance the system efficiency.

*Single-Photon Frequency Conversion for Quantum Interface DOI: http://dx.doi.org/10.5772/intechopen.88867*

We first obtain the spectrum of the positively chirped laser pulse by using an optical-fiber-coupled spectrometer and find a width 800 � 20 GHz FWHM centered at 1551.54 nm (shown in red). The positively chirped laser pulse is then coupled through an optical fiber and superposed with the negatively chirped classical laser pulse (790 � 20GHz, centered at 1551.54 nm) in the PPLN waveguide chip for SFG. The SFG photons, after IF, are sent to a single-mode optical fiber and coupled into the optical-fiber-coupled spectrometer. Here, the FWHM bandwidths of both negatively and positively chirped laser pulses are smaller than the spectral acceptance of the PPLN waveguide chip (*Δν* ¼ *Δν*^*=L* ¼ 807 GHz). Thus, the full FWHM bandwidths of positively and negatively chirped laser pulses are used in the PPLN waveguide chip, as expected. As shown in **Figure 2(a)**, we measure significant spectral compression of the positively chirped laser pulse. The initial bandwidth of the positively chirped laser pulse is 800 GHz centered at 1551.54 nm (shown in red). When the quadratic phase is applied and the two laser pulses are up-converted, the bandwidth of laser pulse generated reduces to 33 � 1GHz (FWHM) centered at 775.77 nm (shown in black), where the relative time delay Δ*t* ¼ 0.

Taking the resolution of our spectrometer into account, Δ*ν<sup>R</sup>* ¼ 30 � 1 GHz (FWHM), the actual bandwidth of the SFG photons after deconvolution is Δ*ν EXP SFG* <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Δ*ν*<sup>2</sup> *<sup>M</sup>* � <sup>Δ</sup>*ν*<sup>2</sup> *R* <sup>p</sup> <sup>¼</sup> <sup>13</sup>*:*<sup>7</sup> � <sup>4</sup>*:*2 GHz (FWHM). The spectra are given by normalized intensities and, for the up-converted case, correspond to the average of 10 consecutive scans of 15 min acquisition time. This result agrees closely with theory, Δ*νTH SFG* ¼ 9*:*8 � 0*:*7 GHz (FWHM) from Eq. (1), using the expected chirp parameter *<sup>A</sup>* ¼ �ð Þ <sup>2</sup>*:*<sup>52</sup> � <sup>0</sup>*:*<sup>01</sup> <sup>∗</sup> 108*fs*<sup>2</sup> given by the geometry of our FBG. Therefore, a bandwidth compression ratio of 58:1 is achieved in the positively chirped laser pulse (**Figure 2(b)**).

The center wavelength of the SFG photons can be controlled by adjusting the relative delay Δ*t* between the input pulses at the PPLN waveguide chip. The SFG spectrum of the created laser pulse could be given by a function of the delay time, with the fitted center wavelengths shown in **Figure 3**. The experimental results show that the wavelength depends linearly on the delay time, as expected. The linear fit gives a slope of �0*:*0247 � 0*:*001 nm/ps. In terms of the slope data, we measure the negatively chirp parameter of *<sup>A</sup>* ¼ �ð Þ <sup>2</sup>*:*<sup>55</sup> � <sup>0</sup>*:*<sup>01</sup> <sup>∗</sup> 108*fs*<sup>2</sup> , in good agreement with the chirp parameter *<sup>A</sup>* ¼ �ð Þ <sup>2</sup>*:*<sup>52</sup> � <sup>0</sup>*:*<sup>01</sup> <sup>∗</sup> 108*fs*<sup>2</sup> of the FBG1. It is also shown that the bandwidth compression ratio independent of the optical relative delay Δ*t*, which agrees closely with the theoretical result from the above Eq. (1).

**Figure 2.** *The positively chirped pulse spectrum and up-converted laser pulse spectrum (a) and relative frequency (b) [5].*

It is known that FBG can be used for up-chirping and down-chirping, depending

Then, the positively chirped single-photon-level laser pulse and the negatively chirped classical laser pulse are combined by a 1550/1550 nm 50:50 single-mode beam splitter (SBS) and couple into the z-cut PPLN waveguide chip through the optical-fiber pigtail. Two single-mode polarization beam splitters (SPBS (200:1)) and two polarization controllers (PCs) are used for controlling the positively chirped single-photon-level laser pulse and the negatively chirped classical laser pulse to the TM mode; it is known that the PPLN waveguide chip only supports Type-0 (*ee* ! *e*) phase matching in our work. A temperature controller (TC) is used for adjusting the PPLN waveguide chip's temperature to keep the QPM of the SFG process. The spectrally narrowed SFG photon pulse can be obtained in the PPLN waveguide chip, after interference filter (IF) with a nominal bandwidth of 20 nm (FWHM) centered around 780 nm (loss is about 1.2 dB), and then coupled into an optical-fiber-coupled spectrometer. Finally, the SFG photons are detected by a SAPD, whose detection efficiency is up to 60% at 775 nm and dark count rate is 26 Hz. In our experiment, a superconducting single photon detector (SSPD) is used to calibrate and monitor the counts of photons of positively chirped single-photon-level laser pulse, whose detection efficiency is up to 10% at

1551 nm and dark count rate is 600 Hz. Using the IF, any residue of the positively or negatively chirped photons have to be filtered out from the SFG photons by a

The reverse-proton-exchange PPLN waveguide chip is 52-mm long and QPM to perform the SFG process 1551 nm + 1551 nm ! 775.5 nm. It is poled through the quasi-phase-matching period of 19.6 μm. Moreover, one has a total fiber-to-outputfacet throughput of approximately �1.5 dB for the telecom band. The PPLN waveguide chip is antireflection coated to prevent interference fringes and enhance the

on the choice of the side from which the laser pulse is reflected. Thus, the two different chirp laser pulses after FBG1 and FBG2 are the same but with the opposite sign. It means that the positively chirped and negatively laser pulses have an equal and opposite chirp, �*A*. A positively chirped laser pulse is generated through FBG1 to introduce a linear chirp by group velocity dispersion. The other laser pulse is negative after a broadband FBG2. A variable optical attenuator (ATT1) is used to create a positively chirped single-photon-level laser pulse, and the other variable optical attenuator (ATT2) is used to control the energy of negatively chirped clas-

*Experimental set-up. ATT, variable optical attenuator; BS, beam splitter (50:50); Circulators, optical fiber circulators; PC, polarization controller; FBG, fiber Bragg grating; Delay Fiber, optical adjustable delay fiber; SPBS, single mode polarization beam splitter (single mode to polarization maintaining); SBS, single mode beam splitter (single mode to polarization maintaining); PPLN-WG, PPLN waveguide chip; IF, interference*

sical laser pulse for this experiment.

**Figure 1.**

*filter; SAPD, silicon APD [5].*

*Single Photon Manipulation*

factor of 10�18.

system efficiency.

**60**

been considered, such as the coupling loss of 0.7 dB, reflection loss of 1.2 dB, total fiber-to-output-facet loss of 1.5 dB, and detection efficiency of 60% (see **Figure 4**). The lower SFG signal for single photons required longer times than for the intense photons states. Thus, all the data are measured within a day to reduce the effects of drift. The results show that the SFG efficiency increases with increasing

It is found that the SFG efficiency decreases with reducing the photons of negatively chirped laser pulse, and the efficiency of SFG also increases with increasing input power of the positively and negatively chirped laser pulse. Next, we obtain the efficiency of SFG in two ways: one, by controlling the photons of the negatively chirped laser pulse with the ATT1 and ATT2; the other by increasing the power of positively and negatively chirped laser pulse with the ATT1 and ATT2. **Figure 5** depicts the results of these two measurements. The SFG efficiencies, SFG photons, the power of produced harmonics, and error bars of them are accounted,

As shown in **Figure 5(a)**, when the negatively chirped laser pulse (10 photons per pulse) and the positively chirped single-photon-level laser pulse (0.933 photons per pulse) are simultaneously sent to the PPLN waveguide chip, the maximum SFG efficiency of 4*:*<sup>58</sup> � <sup>10</sup>�<sup>7</sup> is obtained, where the relative time delay <sup>Δ</sup>*<sup>t</sup>* <sup>¼</sup> 0. In **Figure 5(b)**, we use the ATT1 and ATT2 to keep the input power of positively and negatively chirped laser pulse at 203.1 and 202.8 μW, respectively. The power of produced harmonics *Ei*ð Þ *i* ¼ 0*;* 1*;* 2 can be measured, where *E*<sup>0</sup> is the total power of SFG and SHG of the positively and negatively chirped laser pulse, *E*<sup>1</sup> is the power of

SHG of the positively chirped laser pulse, and *E*<sup>2</sup> is the power of SHG of the negatively chirped laser pulse. When the relative time delay Δ*t* ¼ 0, the power of SHG generated is *E*<sup>0</sup> ¼ 21*:*62 *μW*, which is obtained from SHG of the positively chirped laser pulse (*E*<sup>1</sup> ¼ 0*:*28 *μW*), SHG of the negatively chirped laser pulse (*E*<sup>2</sup> ¼ 0*:*01 *μW*), and SFG photons (*ESFG* ¼ *E*<sup>0</sup> � *E*<sup>1</sup> � *E*<sup>2</sup> ¼ 21*:*33 *μW*). In the case, the maximum SFG efficiency of 20% is obtained, where the relative time delay Δ*t* ¼ 0. Here, the total losses have been taken into account. We also find that the rate of SFG photons generated is 73 times of the rate of SHG photons generated of

In our scheme, although both the negatively and positively chirped laser pulses are at the same center wavelength, the power of SHG from each is kept below the power of SFG (see **Figure 5(b)**). At the same time, the SHG photons from the two independent laser pulses are also lower than the SFG photons when the bandwidth of positively chirped single-photon-level laser pulse is compressed

*SFG photons and SFG efficiencies (a), SFG efficiencies and the energy of generated SHG photons (b). The abscissa is a variable optical relative time delay between the negatively and positively chirped laser pulses at the*

the average of photons of the positively chirped pulse (see **Figure 4**).

where the dark counts (3.5 Hz) are subtracted.

*Single-Photon Frequency Conversion for Quantum Interface*

*DOI: http://dx.doi.org/10.5772/intechopen.88867*

these two independent laser pulses.

**Figure 5.**

**63**

*PPLN waveguide chip [5].*

**Figure 3.**

*The SFG spectrum of the created laser pulse (a), central wavelength and compression ratio of the output pulses versus the optical relative delay (b). Error bars are smaller than the data points [5].*

In our experiment, it is verified that any SFG photons detected by the SAPD is the result of the SFG process, and not a SHG of the positively or negatively chirped photons. Moreover, any residue of photons the positively or negatively chirped laser pulse has to be filtered out from SFG photons by a factor of 10�18. Once the number of positively chirped laser pulse is controlled to single-photon level, the detected SHG counts from the positively chirped laser pulse drop to its dark counts (3.5 Hz). When the input power of the negatively chirped laser pulse is less than 0.6 nW, the SHG photons are also equal to the dark counts. The efficiency of SFG is then given by *ηSFG* ¼ *PSFG=βN*, where *PSFG* is the number of SFG photons per second, *β* is the repetition rate of seed laser, and *N* is average of photons per second of positively chirped laser pulse.

As shown in **Figure 4**, the power of the negatively chirped laser pulse is keeping at 0.6 nW. The SFG photons and SFG efficiencies are measured. The average of photons per second (*N*<sup>1</sup> ¼ 0*:*933 and *N*<sup>2</sup> ¼ 0*:*302) of positively chirped laser pulse can be obtained with the ATT2. By adjusting the relative delay Δ*t*, SFG photons and SFG efficiencies of different situations are measured (like **Figure 3(b)**). At the same time, it is found that the overall conversion efficiency of SFG varies with the relative delay Δ*t*. When the relative time delay Δ*t* ¼ 0, the maximum SFG efficiency is 7*:*<sup>82</sup> � <sup>10</sup>�<sup>6</sup> with the average of photons of positively chirped laser pulse (0.933), where the dark counts (3.5 Hz) are subtracted. Here, the total losses have

#### **Figure 4.**

*SFG photons (top) and SFG efficiencies (bottom). The abscissa is a variable optical relative delay between the negatively and positively chirped laser pulses at the PPLN waveguide chip [5].*

#### *Single-Photon Frequency Conversion for Quantum Interface DOI: http://dx.doi.org/10.5772/intechopen.88867*

been considered, such as the coupling loss of 0.7 dB, reflection loss of 1.2 dB, total fiber-to-output-facet loss of 1.5 dB, and detection efficiency of 60% (see **Figure 4**).

The lower SFG signal for single photons required longer times than for the intense photons states. Thus, all the data are measured within a day to reduce the effects of drift. The results show that the SFG efficiency increases with increasing the average of photons of the positively chirped pulse (see **Figure 4**).

It is found that the SFG efficiency decreases with reducing the photons of negatively chirped laser pulse, and the efficiency of SFG also increases with increasing input power of the positively and negatively chirped laser pulse. Next, we obtain the efficiency of SFG in two ways: one, by controlling the photons of the negatively chirped laser pulse with the ATT1 and ATT2; the other by increasing the power of positively and negatively chirped laser pulse with the ATT1 and ATT2. **Figure 5** depicts the results of these two measurements. The SFG efficiencies, SFG photons, the power of produced harmonics, and error bars of them are accounted, where the dark counts (3.5 Hz) are subtracted.

As shown in **Figure 5(a)**, when the negatively chirped laser pulse (10 photons per pulse) and the positively chirped single-photon-level laser pulse (0.933 photons per pulse) are simultaneously sent to the PPLN waveguide chip, the maximum SFG efficiency of 4*:*<sup>58</sup> � <sup>10</sup>�<sup>7</sup> is obtained, where the relative time delay <sup>Δ</sup>*<sup>t</sup>* <sup>¼</sup> 0. In **Figure 5(b)**, we use the ATT1 and ATT2 to keep the input power of positively and negatively chirped laser pulse at 203.1 and 202.8 μW, respectively. The power of produced harmonics *Ei*ð Þ *i* ¼ 0*;* 1*;* 2 can be measured, where *E*<sup>0</sup> is the total power of SFG and SHG of the positively and negatively chirped laser pulse, *E*<sup>1</sup> is the power of SHG of the positively chirped laser pulse, and *E*<sup>2</sup> is the power of SHG of the negatively chirped laser pulse. When the relative time delay Δ*t* ¼ 0, the power of SHG generated is *E*<sup>0</sup> ¼ 21*:*62 *μW*, which is obtained from SHG of the positively chirped laser pulse (*E*<sup>1</sup> ¼ 0*:*28 *μW*), SHG of the negatively chirped laser pulse (*E*<sup>2</sup> ¼ 0*:*01 *μW*), and SFG photons (*ESFG* ¼ *E*<sup>0</sup> � *E*<sup>1</sup> � *E*<sup>2</sup> ¼ 21*:*33 *μW*). In the case, the maximum SFG efficiency of 20% is obtained, where the relative time delay Δ*t* ¼ 0. Here, the total losses have been taken into account. We also find that the rate of SFG photons generated is 73 times of the rate of SHG photons generated of these two independent laser pulses.

In our scheme, although both the negatively and positively chirped laser pulses are at the same center wavelength, the power of SHG from each is kept below the power of SFG (see **Figure 5(b)**). At the same time, the SHG photons from the two independent laser pulses are also lower than the SFG photons when the bandwidth of positively chirped single-photon-level laser pulse is compressed

#### **Figure 5.**

*SFG photons and SFG efficiencies (a), SFG efficiencies and the energy of generated SHG photons (b). The abscissa is a variable optical relative time delay between the negatively and positively chirped laser pulses at the PPLN waveguide chip [5].*

In our experiment, it is verified that any SFG photons detected by the SAPD is the result of the SFG process, and not a SHG of the positively or negatively chirped photons. Moreover, any residue of photons the positively or negatively chirped laser pulse has to be filtered out from SFG photons by a factor of 10�18. Once the number of positively chirped laser pulse is controlled to single-photon level, the detected SHG counts from the positively chirped laser pulse drop to its dark counts (3.5 Hz). When the input power of the negatively chirped laser pulse is less than 0.6 nW, the SHG photons are also equal to the dark counts. The efficiency of SFG is then given by *ηSFG* ¼ *PSFG=βN*, where *PSFG* is the number of SFG photons per second, *β* is the repetition rate of seed laser, and *N* is average of photons per second of positively

*The SFG spectrum of the created laser pulse (a), central wavelength and compression ratio of the output pulses*

*versus the optical relative delay (b). Error bars are smaller than the data points [5].*

As shown in **Figure 4**, the power of the negatively chirped laser pulse is keeping at 0.6 nW. The SFG photons and SFG efficiencies are measured. The average of photons per second (*N*<sup>1</sup> ¼ 0*:*933 and *N*<sup>2</sup> ¼ 0*:*302) of positively chirped laser pulse can be obtained with the ATT2. By adjusting the relative delay Δ*t*, SFG photons and SFG efficiencies of different situations are measured (like **Figure 3(b)**). At the same time, it is found that the overall conversion efficiency of SFG varies with the relative delay Δ*t*. When the relative time delay Δ*t* ¼ 0, the maximum SFG efficiency is 7*:*<sup>82</sup> � <sup>10</sup>�<sup>6</sup> with the average of photons of positively chirped laser pulse (0.933), where the dark counts (3.5 Hz) are subtracted. Here, the total losses have

*SFG photons (top) and SFG efficiencies (bottom). The abscissa is a variable optical relative delay between the*

*negatively and positively chirped laser pulses at the PPLN waveguide chip [5].*

chirped laser pulse.

**Figure 4.**

**62**

**Figure 3.**

*Single Photon Manipulation*

(see **Figures 4** and **5(a)**). We can also confirm that by controlling the power of the negatively chirped laser pulse, considering a positively chirped single-photon-level laser pulse (0.933 photons per pulse). **Figure 6** depicts the results of experimental and theoretical SFG and SHG.

*EN*1*ES*

*EN*<sup>1</sup> ≤5*:*2 nJ is realized. This result agrees closely with experiment, as shown in

power of the negatively chirped laser pulse must be very low. Thus, the SFG efficiency is limited. The way to improve SFG efficiency is to filter out the photons of wavelengths centered at 1551.54 nm of the negatively chirped laser pulse.

In order to reduce the number of SHG photons to the dark counts (3.5 Hz), the

Furthermore, our results may provide potential application in standard decoystate quantum key distribution. By considering a fiber attenuation of 0.2 dB/km, the coupling loss of 0.7 dB, the dark counts of 3.5 Hz, total fiber-to-output-facet loss of 1.5 dB, reflection loss of 1.2 dB, detection efficiency of 60%, and laser pulse with a 59.98 MHz repetition rate, the SFG efficiency of 7*:*<sup>82</sup> � <sup>10</sup>�<sup>6</sup> will achieve a rate of

**2.2 Nonlinear interaction between broadband single-photon-level coherent**

It has been demonstrated that parametric interactions hold numerous advanced applications in quantum communication, but strong optical fields are usually used to preserve quantum property [9]. Nonlinear interactions between single photons have been experimentally measured, such as spontaneous down-conversion [10] and cross-phase modulation [11]. Here, we take the next step and report, a SFG between two broadband single-photon-level coherent states. In our experiment, the SFG efficiency of 1*:*<sup>06</sup> � <sup>10</sup>�<sup>7</sup> is realized, which provides potentially feasible quantum applications, such as faithful entanglement swapping without post-selection and nonlinear interaction between single photons with an integrated device at room temperature. What's more, long-distance quantum communication can be achieved by broadband single photons generated in a spontaneous parametric down conver-

In our experiment, a mode-locked optical fiber laser generates 500-fs pulses at 1551 nm with a repetition of 59.98 MHz and is used to generate the two chirped broadband single-photon-level coherent states after FBG1 and FBG2. These two chirped broadband coherent states are combined via a 50:50 SBS and sent to a PPLN waveguide chip. The PPLN waveguide chip length is 52 mm, and its total losses are 2.2 dB including a coupling loss of 0.7 dB and a total fiber-to-output-facet loss of 1.5 dB. The unconverted photons are deterministically separated from the SFG

A schematic of the experimental setup is shown in **Figure 7**. The mode-locked optical fiber laser can generate two copies of the pulses with equal energy with a 50:50 BS. These two copies of the pulses are used to produce two broadband singlephoton-level coherent states with ATT1 and ATT2. One of the two copies of the laser pulses is couple into the FBG1, and the other laser pulse is coupled into the FBG2. Thus, the spectrums of two copies of the photons after FBG1 and FBG2 are the same but with the opposite sign. In our experiment, the positively chirped single-photon-level coherent state is generated with the FBG2, and the other single-photon-level coherent state is the negatively chirped coherent state after

photons after IF, and the SFG photons are coupled into a silicon APD.

In terms of *EN*<sup>1</sup> ¼ *qEN*<sup>2</sup>

about 8 bits/h on a distance of 20 km.

**Figure 6(a)**.

**states**

sion (SPDC) source.

the FBG1.

**65**

coefficient. In our experiment, one has *ES* <sup>¼</sup> <sup>7</sup>*:*<sup>3</sup> � <sup>10</sup>�<sup>3</sup>

*Single-Photon Frequency Conversion for Quantum Interface*

*DOI: http://dx.doi.org/10.5772/intechopen.88867*

*EN*<sup>2</sup> j j<sup>2</sup> <sup>≥</sup>1*:* (2)

nJ and *q* ¼ 26*:*8; thus,

, one can obtain *EN*<sup>1</sup> ≤*q*<sup>2</sup>*ES*, where *q* is proportional

Once the input power of the negatively chirped laser pulse is more than 0.6 nW, the up-converted photons generated consists of SHG photons of the negatively chirped laser pulse, and SFG photons of the negatively chirped laser pulse and the positively chirped single-photon-level laser pulse. In our experiment, up-converted photons cannot be filtered out separately; thus, the SFG photons *PSFG* cannot be measured. Here, we first send the negatively chirped laser pulse to the PPLN waveguide chip alone, and the SHG photons *P*<sup>1</sup> of the negatively chirped laser pulse can be measured. If we simultaneously couple the negatively chirped laser pulse and positively chirped single-photon-level laser pulse together into the PPLN waveguide chip, the photons *P*<sup>0</sup> of SFG and SHG can be obtained. The SFG photons generated are obtained with the equation *PSFG* ¼ *P*<sup>0</sup> � *P*1. When the relative time delay Δ*t* ¼ 0, the SHG and SFG photons of different situations are obtained by controlling the power of the negatively chirped laser pulse (see **Figure 6(a)**). When the power of negatively chirped laser pulse is less than 4.8 nW, we find that SHG photons generated are lower than the SFG photons generated. When *PSFG* ¼ *P*1, the SFG efficiency of 3*:*<sup>12</sup> � <sup>10</sup>�<sup>5</sup> is obtained. The measured results show that the number of SHG photons will be more than the number of SFG photons when the power of negatively chirped laser pulse is more than 4.8 nW.

Next, we carry out the theoretical analysis for SHG and SFG photons. As shown in **Figure 6(b)**, the spectrum of the negatively chirped laser pulse is measured. It is found that the intensity of the negatively chirped laser pulse at 1551.54 nm is very close to zero. When the negatively chirped laser pulse is sent to the PPLN waveguide alone, the number of SHG photons generated is very low. Here, we assume that the power of the negatively chirped laser pulse which can be converted into SHG photons is *EN*<sup>2</sup> (black area), thus, the SHG photons *<sup>P</sup>*<sup>1</sup> <sup>∝</sup> *EN*<sup>2</sup> j j<sup>2</sup> . However, when the negatively and positively chirped laser pulses are simultaneously couple together into the PPLN waveguide chip, photons in all spectrum of the negatively chirped laser pulse can be used to produce the SFG photons. The full power of the negatively chirped laser pulse is *EN*<sup>1</sup> , as shown in **Figure 6(b)**. Thus, the SFG photons *PSFG* ∝*EN*1*ES*, where *ES* is the power of the positively chirped singlephoton-level laser pulse. When *PSFG=P*<sup>1</sup> ≥1, the number of SFG photons generated is more than the number of SHG photons. In the case, we obtain

#### **Figure 6.**

*SHG photons and SFG photons (a), the negatively chirped laser pulse spectrum (b). The dark counts (3.5 Hz) are subtracted, and the error bars are accounted [5].*

*Single-Photon Frequency Conversion for Quantum Interface DOI: http://dx.doi.org/10.5772/intechopen.88867*

(see **Figures 4** and **5(a)**). We can also confirm that by controlling the power of the negatively chirped laser pulse, considering a positively chirped single-photon-level laser pulse (0.933 photons per pulse). **Figure 6** depicts the results of experimental

Once the input power of the negatively chirped laser pulse is more than 0.6 nW,

Next, we carry out the theoretical analysis for SHG and SFG photons. As shown in **Figure 6(b)**, the spectrum of the negatively chirped laser pulse is measured. It is found that the intensity of the negatively chirped laser pulse at 1551.54 nm is very close to zero. When the negatively chirped laser pulse is sent to the PPLN waveguide alone, the number of SHG photons generated is very low. Here, we assume that the power of the negatively chirped laser pulse which can be converted into

. However, when

the up-converted photons generated consists of SHG photons of the negatively chirped laser pulse, and SFG photons of the negatively chirped laser pulse and the positively chirped single-photon-level laser pulse. In our experiment, up-converted photons cannot be filtered out separately; thus, the SFG photons *PSFG* cannot be measured. Here, we first send the negatively chirped laser pulse to the PPLN waveguide chip alone, and the SHG photons *P*<sup>1</sup> of the negatively chirped laser pulse can be measured. If we simultaneously couple the negatively chirped laser pulse and positively chirped single-photon-level laser pulse together into the PPLN waveguide chip, the photons *P*<sup>0</sup> of SFG and SHG can be obtained. The SFG photons generated are obtained with the equation *PSFG* ¼ *P*<sup>0</sup> � *P*1. When the relative time delay Δ*t* ¼ 0, the SHG and SFG photons of different situations are obtained by controlling the power of the negatively chirped laser pulse (see **Figure 6(a)**). When the power of negatively chirped laser pulse is less than 4.8 nW, we find that SHG photons generated are lower than the SFG photons generated. When *PSFG* ¼ *P*1, the SFG efficiency of 3*:*<sup>12</sup> � <sup>10</sup>�<sup>5</sup> is obtained. The measured results show that the number of SHG photons will be more than the number of SFG photons when the

power of negatively chirped laser pulse is more than 4.8 nW.

SHG photons is *EN*<sup>2</sup> (black area), thus, the SHG photons *<sup>P</sup>*<sup>1</sup> <sup>∝</sup> *EN*<sup>2</sup> j j<sup>2</sup>

is more than the number of SHG photons. In the case, we obtain

**Figure 6.**

**64**

*are subtracted, and the error bars are accounted [5].*

the negatively and positively chirped laser pulses are simultaneously couple together into the PPLN waveguide chip, photons in all spectrum of the negatively chirped laser pulse can be used to produce the SFG photons. The full power of the negatively chirped laser pulse is *EN*<sup>1</sup> , as shown in **Figure 6(b)**. Thus, the SFG photons *PSFG* ∝*EN*1*ES*, where *ES* is the power of the positively chirped singlephoton-level laser pulse. When *PSFG=P*<sup>1</sup> ≥1, the number of SFG photons generated

*SHG photons and SFG photons (a), the negatively chirped laser pulse spectrum (b). The dark counts (3.5 Hz)*

and theoretical SFG and SHG.

*Single Photon Manipulation*

$$\frac{E\_{N\_1} E\_S}{\left| E\_{N\_2} \right|^2} \ge 1. \tag{2}$$

In terms of *EN*<sup>1</sup> ¼ *qEN*<sup>2</sup> , one can obtain *EN*<sup>1</sup> ≤*q*<sup>2</sup>*ES*, where *q* is proportional coefficient. In our experiment, one has *ES* <sup>¼</sup> <sup>7</sup>*:*<sup>3</sup> � <sup>10</sup>�<sup>3</sup> nJ and *q* ¼ 26*:*8; thus, *EN*<sup>1</sup> ≤5*:*2 nJ is realized. This result agrees closely with experiment, as shown in **Figure 6(a)**.

In order to reduce the number of SHG photons to the dark counts (3.5 Hz), the power of the negatively chirped laser pulse must be very low. Thus, the SFG efficiency is limited. The way to improve SFG efficiency is to filter out the photons of wavelengths centered at 1551.54 nm of the negatively chirped laser pulse.

Furthermore, our results may provide potential application in standard decoystate quantum key distribution. By considering a fiber attenuation of 0.2 dB/km, the coupling loss of 0.7 dB, the dark counts of 3.5 Hz, total fiber-to-output-facet loss of 1.5 dB, reflection loss of 1.2 dB, detection efficiency of 60%, and laser pulse with a 59.98 MHz repetition rate, the SFG efficiency of 7*:*<sup>82</sup> � <sup>10</sup>�<sup>6</sup> will achieve a rate of about 8 bits/h on a distance of 20 km.

## **2.2 Nonlinear interaction between broadband single-photon-level coherent states**

It has been demonstrated that parametric interactions hold numerous advanced applications in quantum communication, but strong optical fields are usually used to preserve quantum property [9]. Nonlinear interactions between single photons have been experimentally measured, such as spontaneous down-conversion [10] and cross-phase modulation [11]. Here, we take the next step and report, a SFG between two broadband single-photon-level coherent states. In our experiment, the SFG efficiency of 1*:*<sup>06</sup> � <sup>10</sup>�<sup>7</sup> is realized, which provides potentially feasible quantum applications, such as faithful entanglement swapping without post-selection and nonlinear interaction between single photons with an integrated device at room temperature. What's more, long-distance quantum communication can be achieved by broadband single photons generated in a spontaneous parametric down conversion (SPDC) source.

In our experiment, a mode-locked optical fiber laser generates 500-fs pulses at 1551 nm with a repetition of 59.98 MHz and is used to generate the two chirped broadband single-photon-level coherent states after FBG1 and FBG2. These two chirped broadband coherent states are combined via a 50:50 SBS and sent to a PPLN waveguide chip. The PPLN waveguide chip length is 52 mm, and its total losses are 2.2 dB including a coupling loss of 0.7 dB and a total fiber-to-output-facet loss of 1.5 dB. The unconverted photons are deterministically separated from the SFG photons after IF, and the SFG photons are coupled into a silicon APD.

A schematic of the experimental setup is shown in **Figure 7**. The mode-locked optical fiber laser can generate two copies of the pulses with equal energy with a 50:50 BS. These two copies of the pulses are used to produce two broadband singlephoton-level coherent states with ATT1 and ATT2. One of the two copies of the laser pulses is couple into the FBG1, and the other laser pulse is coupled into the FBG2. Thus, the spectrums of two copies of the photons after FBG1 and FBG2 are the same but with the opposite sign. In our experiment, the positively chirped single-photon-level coherent state is generated with the FBG2, and the other single-photon-level coherent state is the negatively chirped coherent state after the FBG1.

#### **Figure 7.**

*Experimental set-up. ATT, variable optical attenuator; BS, beam splitter (50:50); Circulators, optical fiber circulators; PC, polarization controller; FBG, fiber Bragg grating; Delay Fiber, optical adjustable delay fiber; SPBS, single mode polarization beam splitter (single mode to polarization maintaining); SBS, single mode beam splitter (single mode to polarization maintaining); PPLN-WG, PPLN waveguide chip; IF, interference filter; SAPD, silicon APD [6].*

The FBG can be used to produce the up-chirping and down-chirping, depending on the choice of the side from which the laser pulse is reflected. As the two copies of the laser pulses are from the same seed laser, they have the same initially center frequency *ω*0. When two copies of the laser pulses with instantaneous frequencies described as *ω*1ðÞ¼ *t ω*<sup>0</sup> þ *At* and *ω*2ðÞ¼ *t ω*<sup>0</sup> � *At* (where *A* is the linear chirp parameter) undergo SFG, the frequency of the laser pulse generated is constant ð Þ *ω*1ð Þþ*t ω*2ðÞ¼ *t* 2*ω*<sup>0</sup> ; thus, the high frequency long narrowband laser pulse can be realized.

Subsequently, the positively and negatively chirped coherent states are sent to the PPLN waveguide chip by the fiber pigtail. The PPLN waveguide chip is a reverse-proton-exchange waveguide that is QPM to perform the SFG process 1551 nm + 1551 nm ! 775.5 nm. The PPLN waveguide chip has a QPM period of 19.6 μm. Two SPBS (200:1) and two PCs are used for controlling the positively and negatively chirped single-photon-level coherent states to the TM mode. A SSPD is used to calibrate and monitor the counts of the positively and negatively chirped single-photon-level photons, whose detection efficiency is up to 10% at 1551 nm and dark count rate of 600 Hz. A stable TC is used to keep at 27° to maintain the QPM condition of the SFG process. The long narrowed SFG photons of higher frequency are generated after the IF, with 20 nm FWHM bandwidth and 780 nm center wavelength (about 1.2 dB loss). Finally, the SFG photons are detected with a SAPD. The SFG photons and the laser clock signal are recorded using a TDC.

photons *NSFG* cannot be measured. First, the pump light is sent to the PPLN waveguide chip alone, and the number of SHG photons *N*<sup>1</sup> can be obtained. Similarly, the number of SHG photons *N*<sup>2</sup> of signal light is obtained when only the signal light is sent to the PPLN waveguide chip alone. When we simultaneously couple the pump and signal laser pulses together into the PPLN waveguide chip, we can obtain the number of photons *N*<sup>0</sup> of SFG and SHG. Therefore, the number of SFG photons is obtained with the equation *NSFG* ¼ *N*<sup>0</sup> � *N*<sup>1</sup> � *N*2. For the SFG photons to be measured distinctly, any residue of pump and signal light has to be filtered out from up-

*Pump and signal light spectrums (a), and the spectrums of up-converted light (SFG and SHG), SHG of signal*

*ηSFG* ¼ *NSFG=NA*, where *NA* is the number of photons per second of the signal light. For instance, the input power of the signal and pump light is keeping at 200.2

conversion photons in this work. Here, the efficiency of SFG is given by

**Figure 8.**

**67**

*light, SHG of pump light (b) [6].*

*Single-Photon Frequency Conversion for Quantum Interface*

*DOI: http://dx.doi.org/10.5772/intechopen.88867*

and 200.4 μW, respectively. When they are simultaneously sent to the PPLN waveguide chip, the FWHM bandwidth and power of the created up-conversion light can be measured. If pump light (or signal light) is sent to the PPLN waveguide chip alone, the bandwidth and power of SHG of pump light (or signal light) can be obtained. When the PPLN waveguide chip's temperature is kept at 27°, as shown in **Figure 8(b)**, the FWHM bandwidth of the created up-conversion light is about 0.07 nm, centered at 775.78 nm. In this case, the power of up-conversion light is 20.9 μW (involving the SFG and SHG), which is obtained from SHG of signal light (0.25 μW), SHG of pump light (0.01 μJ), and SFG of pump light and signal light (20.54 μW). The maximum SFG efficiency of 5% is obtained, which is used for

We first measure the spectrums of the negatively chirped laser pulse (800 � 20 GHz spectral FWHM bandwidth, and 1551.56 nm center wavelength) and the positively chirped laser pulse (790 � 20 GHz FWHM, and 1551.56 nm center wavelength) by using a spectrometer, which are shown in **Figure 8(a)**. The pump light (the negatively chirped laser pulse) and the signal light (the positively chirped laser pulse) are simultaneously sent to the PPLN waveguide chip. By using an IF, the generated SFG photons are sent into the spectrometer.

In our experiment, when the classical pump and signal laser pulses are coupled into the PPLN waveguide chip, the up-converted photons consist of SHG of pump light, SHG of signal light, and SFG of pump light and signal light. In our experiment, up-converted photons cannot be filtered out separately; thus, the SFG

*Single-Photon Frequency Conversion for Quantum Interface DOI: http://dx.doi.org/10.5772/intechopen.88867*

#### **Figure 8.**

The FBG can be used to produce the up-chirping and down-chirping, depending on the choice of the side from which the laser pulse is reflected. As the two copies of the laser pulses are from the same seed laser, they have the same initially center frequency *ω*0. When two copies of the laser pulses with instantaneous frequencies described as *ω*1ðÞ¼ *t ω*<sup>0</sup> þ *At* and *ω*2ðÞ¼ *t ω*<sup>0</sup> � *At* (where *A* is the linear chirp parameter) undergo SFG, the frequency of the laser pulse generated is constant ð Þ *ω*1ð Þþ*t ω*2ðÞ¼ *t* 2*ω*<sup>0</sup> ; thus, the high frequency long narrowband laser pulse can

*Experimental set-up. ATT, variable optical attenuator; BS, beam splitter (50:50); Circulators, optical fiber circulators; PC, polarization controller; FBG, fiber Bragg grating; Delay Fiber, optical adjustable delay fiber; SPBS, single mode polarization beam splitter (single mode to polarization maintaining); SBS, single mode beam splitter (single mode to polarization maintaining); PPLN-WG, PPLN waveguide chip; IF, interference*

Subsequently, the positively and negatively chirped coherent states are sent to

We first measure the spectrums of the negatively chirped laser pulse (800 � 20 GHz spectral FWHM bandwidth, and 1551.56 nm center wavelength) and the positively chirped laser pulse (790 � 20 GHz FWHM, and 1551.56 nm center wavelength) by using a spectrometer, which are shown in **Figure 8(a)**. The pump light (the negatively chirped laser pulse) and the signal light (the positively chirped laser pulse) are simultaneously sent to the PPLN waveguide chip. By using an IF, the

In our experiment, when the classical pump and signal laser pulses are coupled into the PPLN waveguide chip, the up-converted photons consist of SHG of pump light, SHG of signal light, and SFG of pump light and signal light. In our experiment, up-converted photons cannot be filtered out separately; thus, the SFG

generated SFG photons are sent into the spectrometer.

the PPLN waveguide chip by the fiber pigtail. The PPLN waveguide chip is a reverse-proton-exchange waveguide that is QPM to perform the SFG process 1551 nm + 1551 nm ! 775.5 nm. The PPLN waveguide chip has a QPM period of 19.6 μm. Two SPBS (200:1) and two PCs are used for controlling the positively and negatively chirped single-photon-level coherent states to the TM mode. A SSPD is used to calibrate and monitor the counts of the positively and negatively chirped single-photon-level photons, whose detection efficiency is up to 10% at 1551 nm and dark count rate of 600 Hz. A stable TC is used to keep at 27° to maintain the QPM condition of the SFG process. The long narrowed SFG photons of higher frequency are generated after the IF, with 20 nm FWHM bandwidth and 780 nm center wavelength (about 1.2 dB loss). Finally, the SFG photons are detected with a SAPD. The SFG photons and the laser clock signal are recorded using a TDC.

be realized.

**66**

**Figure 7.**

*filter; SAPD, silicon APD [6].*

*Single Photon Manipulation*

*Pump and signal light spectrums (a), and the spectrums of up-converted light (SFG and SHG), SHG of signal light, SHG of pump light (b) [6].*

photons *NSFG* cannot be measured. First, the pump light is sent to the PPLN waveguide chip alone, and the number of SHG photons *N*<sup>1</sup> can be obtained. Similarly, the number of SHG photons *N*<sup>2</sup> of signal light is obtained when only the signal light is sent to the PPLN waveguide chip alone. When we simultaneously couple the pump and signal laser pulses together into the PPLN waveguide chip, we can obtain the number of photons *N*<sup>0</sup> of SFG and SHG. Therefore, the number of SFG photons is obtained with the equation *NSFG* ¼ *N*<sup>0</sup> � *N*<sup>1</sup> � *N*2. For the SFG photons to be measured distinctly, any residue of pump and signal light has to be filtered out from upconversion photons in this work. Here, the efficiency of SFG is given by *ηSFG* ¼ *NSFG=NA*, where *NA* is the number of photons per second of the signal light.

For instance, the input power of the signal and pump light is keeping at 200.2 and 200.4 μW, respectively. When they are simultaneously sent to the PPLN waveguide chip, the FWHM bandwidth and power of the created up-conversion light can be measured. If pump light (or signal light) is sent to the PPLN waveguide chip alone, the bandwidth and power of SHG of pump light (or signal light) can be obtained. When the PPLN waveguide chip's temperature is kept at 27°, as shown in **Figure 8(b)**, the FWHM bandwidth of the created up-conversion light is about 0.07 nm, centered at 775.78 nm. In this case, the power of up-conversion light is 20.9 μW (involving the SFG and SHG), which is obtained from SHG of signal light (0.25 μW), SHG of pump light (0.01 μJ), and SFG of pump light and signal light (20.54 μW). The maximum SFG efficiency of 5% is obtained, which is used for

estimating the efficiency of SFG between two single-photon-level states in our work. As shown in **Figure 9**, the efficiency of SFG depends on the PPLN waveguide chip's temperature. Correcting for all of these losses, the intrinsic device maximum SFG efficiency of 20% is obtained, as expected.

When the number of photons per pulse of pump light and signal light is attenuated to 5.13 and 5.64, respectively, the detected count of SHG of signal light (or pump light) drop to 3.8 Hz (dark count). It can be shown that any photons detected by the SPAD are the SFG photons when the signal and pump light are attenuated to single-photon-per-pulse simultaneously. Therefore, photons of SHG of pump light and signal light are not considered in our scheme.

In our experiment, the number of photons per pulse (equal for pump and signal) are obtained with ATT1 and ATT2, as they can be detected and calibrated by the SSPD. According to our experimental results, the SFG efficiency and SFG photons are shown in **Figure 10**. Here, dark counts of 3.8 Hz and the total losses of about 5.6 dB have been taken into account.

The overall conversion efficiency of SFG is given by *η*<sup>0</sup> *SFG* <sup>¼</sup> *ξ λ*ð Þ*hcΔνL*<sup>2</sup> *=λtbp*, where *ξ λ*ð Þ is the measured up-conversion efficiency of the PPLN waveguide chip, *λ* is the center wavelength of pump light, *tbp* is the time-bandwidth product, *Δν* is the bandwidth of pump light, and *L* is the length of the PPLN waveguide chip. Consider that *ξ λ*ð Þ¼ 5%*<sup>=</sup> <sup>W</sup>* � *cm*<sup>2</sup> ð Þ and *tbp* <sup>¼</sup> <sup>0</sup>*:*4 in our experiment, thus the expected SFG efficiency is *η*<sup>0</sup> *SFG* <sup>≈</sup> <sup>1</sup> � <sup>10</sup>�7. We measure the efficiency of *<sup>η</sup>SFG* <sup>¼</sup> ð Þ� <sup>1</sup>*:*<sup>06</sup> � <sup>0</sup>*:*<sup>23</sup> <sup>10</sup>�7. It is shown that the SFG efficiency is high enough to provide efficient, yet simpler solutions to linear optics based protocols for the heralded creation of maximally entangled pairs or for the implementation of device-

**2.3 Single-photon frequency conversion via cascaded quadratic nonlinear**

In quantum networks, many nodes are needed, which are used to perform quantum information memory/processing tasks. Each node has the ability to generate quantum states and perform quantum Bell-state measurements. All nodes are connected by using optical fibers. Frequency conversion has important applications in fiber quantum networks, and frequency converters are set to light. At the intermediate node of the fiber quantum network, the information transmission mode of the corresponding wavelength is obtained, and the specific wavelength signal carrying the information is transferred to the other wavelength. The development of this technology has greatly improved the transmission capacity of the optical net-

In addition to the frequency conversion between the communication band and the visible band, single-photon frequency conversion between communication bands, like classical fiber networks, has important applications in large-scale quantum networks, as well as between independent sources of different users. Quantum cryptic transmission or quantum key distribution also requires different wavelengths to be converted to coincidence before interference. Therefore, the single photon frequency conversion interface between communication bands is critical in

However, there are not many experiments to achieve single-photon frequency conversion in the communication band. There are only two known solutions and each of these experimental solutions has imperfections. The first solution is to achieve high-precision frequency conversion by optical single sideband modulator (OSSB). This method can eliminate the frequency distinguishability between different single photons, but the frequency conversion range that this scheme can achieve covers only dozens. Gigahertz does not meet the requirements of communication networks. The second scheme is consistent with the four-wave mixing principle of the classical light in the previous section. The third-order nonlinearity of the optical fiber is used to realize the frequency conversion of the communication band, but we know that the third-order nonlinear coefficient is much smaller than 2. The order nonlinear coefficient, thus one must use 750 m long fiber, which is very

In order to make up for the shortcomings of the above two schemes, we use the high second-order nonlinear coefficients of the PPLN waveguide and the wide-band

**processes**

*SFG efficiency and SFG photons [6].*

**Figure 10.**

work and the flexibility of the entire network.

*Single-Photon Frequency Conversion for Quantum Interface*

*DOI: http://dx.doi.org/10.5772/intechopen.88867*

quantum communication.

unfavorable for device integration.

**69**

independent quantum key distribution. For SFG between two single photons, our efficiency of SFG is about eight times of the efficiency of SFG given by Sangouard et al. [12]. When the single-photonlevel pump and signal light are not chirped in our experiment, the SFG photons are zero. This is because the intensity of pump light (or signal light) at 1551.56 nm is very low (see **Figure 8(a)**). However, when the negatively and positively chirped pulses are simultaneously coupled into the PPLN waveguide chip, photons in all spectrums of the negatively and positively chirped light are used to create the SFG photons. Therefore, we can improve the efficiency of SFG between single photons by using the chirped technology.

**Figure 9.** *SFG efficiency. The efficiency of SFG can be controlled by keeping the PPLN-WG chip's temperature [6].*

*Single-Photon Frequency Conversion for Quantum Interface DOI: http://dx.doi.org/10.5772/intechopen.88867*

**Figure 10.** *SFG efficiency and SFG photons [6].*

estimating the efficiency of SFG between two single-photon-level states in our work. As shown in **Figure 9**, the efficiency of SFG depends on the PPLN waveguide chip's temperature. Correcting for all of these losses, the intrinsic device maximum

When the number of photons per pulse of pump light and signal light is attenuated to 5.13 and 5.64, respectively, the detected count of SHG of signal light (or pump light) drop to 3.8 Hz (dark count). It can be shown that any photons detected by the SPAD are the SFG photons when the signal and pump light are attenuated to single-photon-per-pulse simultaneously. Therefore, photons of SHG of pump light

In our experiment, the number of photons per pulse (equal for pump and signal) are obtained with ATT1 and ATT2, as they can be detected and calibrated by the SSPD. According to our experimental results, the SFG efficiency and SFG photons are shown in **Figure 10**. Here, dark counts of 3.8 Hz and the total losses of about

where *ξ λ*ð Þ is the measured up-conversion efficiency of the PPLN waveguide chip, *λ* is the center wavelength of pump light, *tbp* is the time-bandwidth product, *Δν* is the bandwidth of pump light, and *L* is the length of the PPLN waveguide chip. Consider that *ξ λ*ð Þ¼ 5%*<sup>=</sup> <sup>W</sup>* � *cm*<sup>2</sup> ð Þ and *tbp* <sup>¼</sup> <sup>0</sup>*:*4 in our experiment, thus the expected SFG

*<sup>η</sup>SFG* <sup>¼</sup> ð Þ� <sup>1</sup>*:*<sup>06</sup> � <sup>0</sup>*:*<sup>23</sup> <sup>10</sup>�7. It is shown that the SFG efficiency is high enough to provide efficient, yet simpler solutions to linear optics based protocols for the heralded creation of maximally entangled pairs or for the implementation of device-

*SFG efficiency. The efficiency of SFG can be controlled by keeping the PPLN-WG chip's temperature [6].*

For SFG between two single photons, our efficiency of SFG is about eight times of the efficiency of SFG given by Sangouard et al. [12]. When the single-photonlevel pump and signal light are not chirped in our experiment, the SFG photons are zero. This is because the intensity of pump light (or signal light) at 1551.56 nm is very low (see **Figure 8(a)**). However, when the negatively and positively chirped pulses are simultaneously coupled into the PPLN waveguide chip, photons in all spectrums of the negatively and positively chirped light are used to create the SFG photons. Therefore, we can improve the efficiency of SFG between single photons

*SFG* <sup>≈</sup> <sup>1</sup> � <sup>10</sup>�7. We measure the efficiency of

*SFG* <sup>¼</sup> *ξ λ*ð Þ*hcΔνL*<sup>2</sup>

*=λtbp*,

SFG efficiency of 20% is obtained, as expected.

*Single Photon Manipulation*

and signal light are not considered in our scheme.

The overall conversion efficiency of SFG is given by *η*<sup>0</sup>

5.6 dB have been taken into account.

independent quantum key distribution.

by using the chirped technology.

efficiency is *η*<sup>0</sup>

**Figure 9.**

**68**

### **2.3 Single-photon frequency conversion via cascaded quadratic nonlinear processes**

In quantum networks, many nodes are needed, which are used to perform quantum information memory/processing tasks. Each node has the ability to generate quantum states and perform quantum Bell-state measurements. All nodes are connected by using optical fibers. Frequency conversion has important applications in fiber quantum networks, and frequency converters are set to light. At the intermediate node of the fiber quantum network, the information transmission mode of the corresponding wavelength is obtained, and the specific wavelength signal carrying the information is transferred to the other wavelength. The development of this technology has greatly improved the transmission capacity of the optical network and the flexibility of the entire network.

In addition to the frequency conversion between the communication band and the visible band, single-photon frequency conversion between communication bands, like classical fiber networks, has important applications in large-scale quantum networks, as well as between independent sources of different users. Quantum cryptic transmission or quantum key distribution also requires different wavelengths to be converted to coincidence before interference. Therefore, the single photon frequency conversion interface between communication bands is critical in quantum communication.

However, there are not many experiments to achieve single-photon frequency conversion in the communication band. There are only two known solutions and each of these experimental solutions has imperfections. The first solution is to achieve high-precision frequency conversion by optical single sideband modulator (OSSB). This method can eliminate the frequency distinguishability between different single photons, but the frequency conversion range that this scheme can achieve covers only dozens. Gigahertz does not meet the requirements of communication networks. The second scheme is consistent with the four-wave mixing principle of the classical light in the previous section. The third-order nonlinearity of the optical fiber is used to realize the frequency conversion of the communication band, but we know that the third-order nonlinear coefficient is much smaller than 2. The order nonlinear coefficient, thus one must use 750 m long fiber, which is very unfavorable for device integration.

In order to make up for the shortcomings of the above two schemes, we use the high second-order nonlinear coefficients of the PPLN waveguide and the wide-band type-0 quasi-phase matching to realize the single-photon frequency conversion based on the cascaded second-order nonlinear process. In the experiment, we realized the precise frequency conversion between DWDM channels through the cascading process of SFG + DFG. At the same time, we also proved that the quantum characteristics of single photons remain in this process. Our experiment is very suitable for the construction of quantum networks.

The nonlinear process of frequency conversion of a single photon can be described by the following effective Hamiltonian [13]:

$$
\hat{H} = i\hbar \left( \chi\_1 E\_{P1} \hat{a}\_i \hat{a}\_m^\dagger + \chi\_2 E\_{P2} \hat{a}\_m \hat{a}\_t^\dagger - \text{H.c.} \right), \tag{3}
$$

continuous light. WDM with an isolation of 180 dB is used to filter out noise. Finally, the corresponding two channels in signal (1554.13 nm, CH29) and idler

*Experimental setup of (a) the single-photon frequency convertor, (b) photon-pairs preparation, (c) Hong-Ou-Mandel interference, and (d) measurement of time-energy entanglement. DWDM, 100-GHz dense wavelength-division multiplexing; CH25 and CH37 and CH41, DWDM channels with 100-GHz spacing defined by ITU-TG.694.1; Filter, combination of DWDM and band pass filter (200–1540 and 1560– 1800 nm); PC, polarization controller; SPD, single-photon detector (quantum efficiencies, η<sup>d</sup>* ¼ *10:0* � *0:2%; repetition frequency of gate, f = 50 MHz; width of gate, 1 ns; dark count probability per nanosecond, <sup>D</sup>* <sup>¼</sup> *<sup>1</sup>* � *<sup>10</sup>*�*<sup>6</sup>); EDFA, erbium-doped fiber amplifier; WDM, 780–1550-nm wavelength-division multiplexing; TDC, time-to-digital convertor (coincidence time window, t = 1 ns); Delayer, fiber path-length delayer; BS, 50:50 fiber beam splitter; MZI, 1-GHz unbalanced planar lightwave circuit Mach-Zehnder*

conversion. By changing the center wavelength of the auxiliary pump P2, we achieved frequency conversion of the signal photon �12 DWDM channels. In the classic light test, we set the signal power to 1 mW, and both P1 and P2 have a power of 10 mW (because the PPLN waveguide is limited by thermal effects, the maximum total input power of the waveguide we use for conversion is around 20 mW). We can get that the theoretical value is in good agreement with the experimental value, and the conversion efficiency of �12CH is about 0.8%. In theory, the tunable frequency conversion has a full width at half maximum of about 76 nm, which

First, we use classical light to test the conversion efficiency of tunable frequency

In our experiment, the photon-pair generation rate is set to 0.002 per detection gate. The maximum single-photon conversion efficiency in the experiment is that

/gate. When the incident power of both auxiliary pumps is 179.5 mW, 100% conversion efficiency can be obtained. However, there are three main reasons for the reduction in conversion efficiency in actual experiments. The first reason is that the thermal effect of the PPLN waveguide limits the power of the incident light. This limitation is also the most important cause of the drop in conversion efficiency. We know that if a PPLN waveguide doped with MgO is used, the damage threshold

refractive index, and it can withstand the total incident power of 360 mW. Another reason is the phase difference between the two auxiliary pumps P1 and P2, and we get the conversion efficiency proportional to *φ*<sup>1</sup> � *φ*<sup>2</sup> j j. Since there is no synchronous lock between the phase differences between P1 and P2 in our experiments, *φ*<sup>1</sup> � *φ*<sup>2</sup> j j is equal to 0.5 after averaging over time. This reason will directly lead to a 50% reduction in conversion efficiency. The last reason is also the problem that

when PP1 = PP2 = 10 mW, the maximum number of converted photons is

can be greatly improved without changing the scattering properties of its

<sup>5</sup>*:*<sup>5</sup> � <sup>10</sup><sup>4</sup>*=*s, and the conversion efficiency is calculated to be 0.55%. At the same time, we measured that the noise generated by the frequency conversion process is

(1557.36 nm, CH25) DWDM are separated.

*Single-Photon Frequency Conversion for Quantum Interface*

*DOI: http://dx.doi.org/10.5772/intechopen.88867*

covers the entire communication C-band.

10�<sup>7</sup>

**71**

**Figure 11.**

*interferometers [7].*

where *α*^*<sup>i</sup>* a is the annihilation operator for the wave at frequency *ωi*, (*i* ¼ *s; m; t* is signal, mediate, and target photons, respectively). *χ*1*,*<sup>2</sup> are coupling constants that are proportional to the second-order susceptibility *χ*ð Þ<sup>2</sup> of the PPLN waveguide chip, *EP*<sup>1</sup> and *EP*<sup>2</sup> are the electric field amplitudes of pump lasers, and H*:c:* is a Hermitian conjugate. The conversion efficiency *η<sup>c</sup>* can be obtained by using the Heisenberg equation of motion, which is given by the following equation:

$$\eta\_c(L) = \frac{\eta\_1 \eta\_2 P\_{P1} P\_{P2} |\cos\left[2(\rho\_1 - \rho\_2)\right]|}{(\eta\_1 P\_{P1} + \eta\_2 P\_{P2})} \times \left\{1 - \cos\left[\eta\_1 P\_{P1} + \eta\_2 P\_{P2}\right]^{(1/2)} L\right\}^2,\tag{4}$$

where *φ*<sup>1</sup> and *φ*<sup>2</sup> are the phases of the two pumps, respectively. *η*<sup>1</sup> and *η*<sup>2</sup> are the efficiencies of the normalized power, and *<sup>η</sup>*<sup>1</sup> <sup>≈</sup> *<sup>η</sup>*<sup>2</sup> <sup>¼</sup> <sup>1</sup>*:*1*=*W cm2. The efficiency of single-photon frequency conversion is 100% if *PP*<sup>1</sup> <sup>¼</sup> *PP*<sup>2</sup> <sup>¼</sup> *<sup>π</sup>*<sup>2</sup>*<sup>=</sup>* <sup>2</sup>*η*1*L*<sup>2</sup> � �.

It is very challenging for realizing simultaneous phase matching in our work. However, this problem can be easily solved using QPM. In the experiment, we realized the broadband single photon frequency conversion of the communication band by the type-0 cascading SFG/DFG process. A 5-cm-long PPLN waveguide chip is used, and its poling period is 19.0 μm. In addition, the cascaded *χ*ð Þ<sup>2</sup> : *χ*ð Þ<sup>2</sup> processes give rise to a large effective third nonlinearity typically 10<sup>4</sup> � <sup>10</sup><sup>5</sup> times larger than a pure *χ*ð Þ<sup>3</sup> process, which manifests an advantage over its counterpart of FWM, e.g., in fibers.

The experimental setup of the single-photon frequency conversion is shown in **Figure 11(a)**. The center wavelengths of the two auxiliary pumps P1 and P2 are 1547.72 nm (CH37) and 1544.53 nm (CH41), respectively. Both narrow-band continuous lasers increase power through an erbium-doped fiber amplifier (EDFA). A set of DWDMs placed behind the EDFA, using 150 dB of isolation to filter out the noise generated during the EDFA amplification process. Then, we use another set of DWDMs to combine the three signals of signal single photon, P1 and P2 into one beam and couple into the waveguide. The combined light undergoes a cascaded nonlinear process SFG + DFG in the PPLN waveguide, converting the signal photons into target photons. At the output of the waveguide, we use a third set of DWDMs to pick out the target photons, while using 180 dB of isolation to filter out the noise generated during P1, P2, and conversion. In our experimental scheme, frequency-adjustable single-photon frequency conversion can be achieved by adjusting the wavelength of the auxiliary pump light.

For the performance of the converter, we tested the photon pair prepared by SPDC instead of the weak coherent pulse. The photon pair preparation process is shown in **Figure 11(b)**. After a continuous laser with a center wavelength of 1555.8 nm is amplified by EDFA power, a continuous light of 777.9 nm is generated by a frequency doubling process in a PPLN waveguide. The SPDC photon pair is prepared by pumping the second waveguide with the frequency-doubled

*Single-Photon Frequency Conversion for Quantum Interface DOI: http://dx.doi.org/10.5772/intechopen.88867*

#### **Figure 11.**

type-0 quasi-phase matching to realize the single-photon frequency conversion based on the cascaded second-order nonlinear process. In the experiment, we realized the precise frequency conversion between DWDM channels through the cascading process of SFG + DFG. At the same time, we also proved that the quantum characteristics of single photons remain in this process. Our experiment is very

The nonlinear process of frequency conversion of a single photon can be

*<sup>m</sup>* <sup>þ</sup> *<sup>χ</sup>*2*EP*2*α*^*mα*^†

where *α*^*<sup>i</sup>* a is the annihilation operator for the wave at frequency *ωi*, (*i* ¼ *s; m; t* is signal, mediate, and target photons, respectively). *χ*1*,*<sup>2</sup> are coupling constants that are proportional to the second-order susceptibility *χ*ð Þ<sup>2</sup> of the PPLN waveguide chip, *EP*<sup>1</sup> and *EP*<sup>2</sup> are the electric field amplitudes of pump lasers, and H*:c:* is a Hermitian conjugate. The conversion efficiency *η<sup>c</sup>* can be obtained by using the Heisenberg

where *φ*<sup>1</sup> and *φ*<sup>2</sup> are the phases of the two pumps, respectively. *η*<sup>1</sup> and *η*<sup>2</sup> are the efficiencies of the normalized power, and *<sup>η</sup>*<sup>1</sup> <sup>≈</sup> *<sup>η</sup>*<sup>2</sup> <sup>¼</sup> <sup>1</sup>*:*1*=*W cm2. The efficiency of

It is very challenging for realizing simultaneous phase matching in our work. However, this problem can be easily solved using QPM. In the experiment, we realized the broadband single photon frequency conversion of the communication band by the type-0 cascading SFG/DFG process. A 5-cm-long PPLN waveguide chip is used, and its poling period is 19.0 μm. In addition, the cascaded *χ*ð Þ<sup>2</sup> : *χ*ð Þ<sup>2</sup> processes give rise to a large effective third nonlinearity typically 10<sup>4</sup> � <sup>10</sup><sup>5</sup> times larger than a pure *χ*ð Þ<sup>3</sup> process, which manifests an advantage over its counterpart of

The experimental setup of the single-photon frequency conversion is shown in **Figure 11(a)**. The center wavelengths of the two auxiliary pumps P1 and P2 are 1547.72 nm (CH37) and 1544.53 nm (CH41), respectively. Both narrow-band continuous lasers increase power through an erbium-doped fiber amplifier (EDFA). A set of DWDMs placed behind the EDFA, using 150 dB of isolation to filter out the noise generated during the EDFA amplification process. Then, we use another set of DWDMs to combine the three signals of signal single photon, P1 and P2 into one beam and couple into the waveguide. The combined light undergoes a cascaded nonlinear process SFG + DFG in the PPLN waveguide, converting the signal photons into target photons. At the output of the waveguide, we use a third set of DWDMs to pick out the target photons, while using 180 dB of isolation to filter out the noise generated during P1, P2, and conversion. In our experimental scheme, frequency-adjustable single-photon frequency conversion can be achieved by

For the performance of the converter, we tested the photon pair prepared by SPDC instead of the weak coherent pulse. The photon pair preparation process is shown in **Figure 11(b)**. After a continuous laser with a center wavelength of 1555.8 nm is amplified by EDFA power, a continuous light of 777.9 nm is generated by a frequency doubling process in a PPLN waveguide. The SPDC photon pair is prepared by pumping the second waveguide with the frequency-doubled

*<sup>t</sup>* � <sup>H</sup>*:c:* � �*,* (3)

� <sup>1</sup> � cos½ � *<sup>η</sup>*1*PP*<sup>1</sup> <sup>þ</sup> *<sup>η</sup>*2*PP*<sup>2</sup> ð Þ <sup>1</sup>*=*<sup>2</sup> *<sup>L</sup>* n o<sup>2</sup>

*,* (4)

suitable for the construction of quantum networks.

*Single Photon Manipulation*

described by the following effective Hamiltonian [13]:

*<sup>H</sup>*^ <sup>¼</sup> *<sup>i</sup>*<sup>ℏ</sup> *<sup>χ</sup>*1*EP*1*α*^*sα*^†

equation of motion, which is given by the following equation:

single-photon frequency conversion is 100% if *PP*<sup>1</sup> <sup>¼</sup> *PP*<sup>2</sup> <sup>¼</sup> *<sup>π</sup>*<sup>2</sup>*<sup>=</sup>* <sup>2</sup>*η*1*L*<sup>2</sup> � �.

*<sup>η</sup>c*ð Þ¼ *<sup>L</sup> <sup>η</sup>*1*η*2*PP*1*PP*<sup>2</sup> cos 2 *<sup>φ</sup>*<sup>1</sup> � *<sup>φ</sup>*<sup>2</sup> j j ½ � ð Þ

FWM, e.g., in fibers.

**70**

ð Þ *η*1*PP*<sup>1</sup> þ *η*2*PP*<sup>2</sup>

adjusting the wavelength of the auxiliary pump light.

*Experimental setup of (a) the single-photon frequency convertor, (b) photon-pairs preparation, (c) Hong-Ou-Mandel interference, and (d) measurement of time-energy entanglement. DWDM, 100-GHz dense wavelength-division multiplexing; CH25 and CH37 and CH41, DWDM channels with 100-GHz spacing defined by ITU-TG.694.1; Filter, combination of DWDM and band pass filter (200–1540 and 1560– 1800 nm); PC, polarization controller; SPD, single-photon detector (quantum efficiencies, η<sup>d</sup>* ¼ *10:0* � *0:2%; repetition frequency of gate, f = 50 MHz; width of gate, 1 ns; dark count probability per nanosecond, <sup>D</sup>* <sup>¼</sup> *<sup>1</sup>* � *<sup>10</sup>*�*<sup>6</sup>); EDFA, erbium-doped fiber amplifier; WDM, 780–1550-nm wavelength-division multiplexing; TDC, time-to-digital convertor (coincidence time window, t = 1 ns); Delayer, fiber path-length delayer; BS, 50:50 fiber beam splitter; MZI, 1-GHz unbalanced planar lightwave circuit Mach-Zehnder interferometers [7].*

continuous light. WDM with an isolation of 180 dB is used to filter out noise. Finally, the corresponding two channels in signal (1554.13 nm, CH29) and idler (1557.36 nm, CH25) DWDM are separated.

First, we use classical light to test the conversion efficiency of tunable frequency conversion. By changing the center wavelength of the auxiliary pump P2, we achieved frequency conversion of the signal photon �12 DWDM channels. In the classic light test, we set the signal power to 1 mW, and both P1 and P2 have a power of 10 mW (because the PPLN waveguide is limited by thermal effects, the maximum total input power of the waveguide we use for conversion is around 20 mW). We can get that the theoretical value is in good agreement with the experimental value, and the conversion efficiency of �12CH is about 0.8%. In theory, the tunable frequency conversion has a full width at half maximum of about 76 nm, which covers the entire communication C-band.

In our experiment, the photon-pair generation rate is set to 0.002 per detection gate. The maximum single-photon conversion efficiency in the experiment is that when PP1 = PP2 = 10 mW, the maximum number of converted photons is <sup>5</sup>*:*<sup>5</sup> � <sup>10</sup><sup>4</sup>*=*s, and the conversion efficiency is calculated to be 0.55%. At the same time, we measured that the noise generated by the frequency conversion process is 10�<sup>7</sup> /gate. When the incident power of both auxiliary pumps is 179.5 mW, 100% conversion efficiency can be obtained. However, there are three main reasons for the reduction in conversion efficiency in actual experiments. The first reason is that the thermal effect of the PPLN waveguide limits the power of the incident light. This limitation is also the most important cause of the drop in conversion efficiency. We know that if a PPLN waveguide doped with MgO is used, the damage threshold can be greatly improved without changing the scattering properties of its refractive index, and it can withstand the total incident power of 360 mW. Another reason is the phase difference between the two auxiliary pumps P1 and P2, and we get the conversion efficiency proportional to *φ*<sup>1</sup> � *φ*<sup>2</sup> j j. Since there is no synchronous lock between the phase differences between P1 and P2 in our experiments, *φ*<sup>1</sup> � *φ*<sup>2</sup> j j is equal to 0.5 after averaging over time. This reason will directly lead to a 50% reduction in conversion efficiency. The last reason is also the problem that

other frequency conversion methods will encounter, namely, the loss of fiber coupling and the loss caused by the filter. In our experiment, the total propagation and coupling loss in the PPLN waveguide and the filters is only 4.9 dB.

continuous laser (cw-laser) pumping the PPLN waveguide through the SPDC process [15]. Because the coherence time *τ*<sup>1</sup> of cw-laser is extremely long, and the bandwidth of the down-converted photon pair is much larger than the bandwidth of the pump photon, that is, the coherence time *τ*<sup>2</sup> between photon pairs is very

*Single-Photon Frequency Conversion for Quantum Interface*

*DOI: http://dx.doi.org/10.5772/intechopen.88867*

To measure the characteristics of time-energy entanglement and to exploit this entanglement, we use two unbalanced Mach-Zehnder interferometers (MZI) as shown in **Figure 11(d)**, connecting a single photon detector at the output of the MZI, measuring two coincidence count at the output. We define the optical path difference of the two paths of the MZI interferometer as *τ*3. It is assumed that when *τ*<sup>1</sup> ≥ *τ*3>*τ*2, the exit end of MZI does not have a single photon interference image, and the image of two-photon interference can be observed by the coincidence

The MZI used in our experiments is to change the phase difference between the long and short arms by adjusting the temperature. The phase change of 2*π* corresponds to a temperature change of 0.7°. The entangled interference image before single-photon frequency conversion is shown in **Figure 13**. Because it is necessary to observe the interference image under the two non-collinear base vectors, we can prove that the two-photon is entangled, so we set the MZI temperature of the signal

*Two-photon interference pattern (a) before and (b) after the frequency conversion. T*<sup>1</sup> *is the temperature of the MZI in the signal channel, and T*<sup>2</sup> *is the temperature in the idler channel. The integration time for each dot is*

short.

measurement.

**Figure 13.**

**73**

*(a) 15 s and (b) 3000 s [7].*

After measuring the maximum conversion efficiency experimentally, we measured the conversion accuracy of our single-photon frequency converter by HOM interference. The experimental setup for HOM interference is shown in **Figure 11(c)** [14], where i<sup>0</sup> is the idler photon in the photon pair and s<sup>0</sup> represents the converted signal photon. We placed a fiber optic delay in the i-photon beam path (Delayer, Delayer has an adjustment accuracy of 0.02 mm.), Delayer is used to change the optical path difference δx between i and s<sup>0</sup> ; placing polarization control in the s0 photon path (PC), PC is used to change the polarization of the s0 photon to match the polarization of the i-photon, because the HOM interference visibility of the identical particles is best. In our experiments, the ratio of BS transmittance to reflectance used in our experiments was measured as T:R = 49.9:50.1. The single-photon detector used in this experiment is still a pulse gate detection method, but the performance is upgraded. The dark counts of both detectors are *<sup>D</sup>* <sup>¼</sup> <sup>1</sup> � <sup>10</sup>�<sup>6</sup> per gate.

In HOM, we set the photon pair generation rate μ = 0.002 per gate; the single photon conversion efficiency is set to the maximum conversion efficiency under the constraint condition, i.e., 0.55%; and the measurement time of each data point is 1000 s. Under these conditions, the HOM interference curve we measured is shown in **Figure 12**. The calculated HOM interference visibility of the converted photon pair is 80 ð Þ *:*5 � 3*:*5 %, and this contrast is much larger than the classical and nonclassical limit of 50%, which proves that our single photon converter does. We further analyzed the HOM interference gram and found that the full width at half maximum of the interference gram is 0.56 mm, and the corresponding time is 0.28 ps. Our theoretical full width at half maximum is about 0.50 mm; thus, the theoretical and experimental results are more consistent.

In addition to the true conversion of this feature, another important feature of single-photon frequency conversion is the preservation of quantum properties. As with some previous quantum frequency converters, we demonstrate that the quantum properties are not corrupted during the conversion process by measuring the quantum state visibility of the photon pairs before and after the conversion. In our experiments, the signal and idler photon pairs were prepared as time-energy entangled photon pairs. The time-energy entanglement pair is generated by a

#### **Figure 12.**

*Coincidence count as a function of the path-length change of one photon. The standard deviation is calculated by assuming a Poisson distribution of photon counts. The dashed horizontal line at 50% is the dividing line between the classical and nonclassical interference [7].*

*Single-Photon Frequency Conversion for Quantum Interface DOI: http://dx.doi.org/10.5772/intechopen.88867*

other frequency conversion methods will encounter, namely, the loss of fiber coupling and the loss caused by the filter. In our experiment, the total propagation and

After measuring the maximum conversion efficiency experimentally, we measured the conversion accuracy of our single-photon frequency converter by HOM interference. The experimental setup for HOM interference is shown in **Figure 11(c)** [14], where i<sup>0</sup> is the idler photon in the photon pair and s<sup>0</sup> represents the converted signal photon. We placed a fiber optic delay in the i-photon beam path (Delayer, Delayer has an adjustment accuracy of 0.02 mm.), Delayer is used to change the

photon path (PC), PC is used to change the polarization of the s0 photon to match the polarization of the i-photon, because the HOM interference visibility of the identical particles is best. In our experiments, the ratio of BS transmittance to reflectance used in our experiments was measured as T:R = 49.9:50.1. The single-photon detector used in this experiment is still a pulse gate detection method, but the performance is

In HOM, we set the photon pair generation rate μ = 0.002 per gate; the single photon conversion efficiency is set to the maximum conversion efficiency under the constraint condition, i.e., 0.55%; and the measurement time of each data point is 1000 s. Under these conditions, the HOM interference curve we measured is shown in **Figure 12**. The calculated HOM interference visibility of the converted photon pair is 80 ð Þ *:*5 � 3*:*5 %, and this contrast is much larger than the classical and nonclassical limit of 50%, which proves that our single photon converter does. We further analyzed the HOM interference gram and found that the full width at half maximum of the interference gram is 0.56 mm, and the corresponding time is 0.28 ps. Our theoretical full width at half maximum is about 0.50 mm; thus, the

In addition to the true conversion of this feature, another important feature of single-photon frequency conversion is the preservation of quantum properties. As with some previous quantum frequency converters, we demonstrate that the quantum properties are not corrupted during the conversion process by measuring the quantum state visibility of the photon pairs before and after the conversion. In our experiments, the signal and idler photon pairs were prepared as time-energy entangled photon pairs. The time-energy entanglement pair is generated by a

*Coincidence count as a function of the path-length change of one photon. The standard deviation is calculated by assuming a Poisson distribution of photon counts. The dashed horizontal line at 50% is the dividing line*

; placing polarization control in the s0

coupling loss in the PPLN waveguide and the filters is only 4.9 dB.

upgraded. The dark counts of both detectors are *<sup>D</sup>* <sup>¼</sup> <sup>1</sup> � <sup>10</sup>�<sup>6</sup> per gate.

theoretical and experimental results are more consistent.

**Figure 12.**

**72**

*between the classical and nonclassical interference [7].*

optical path difference δx between i and s<sup>0</sup>

*Single Photon Manipulation*

continuous laser (cw-laser) pumping the PPLN waveguide through the SPDC process [15]. Because the coherence time *τ*<sup>1</sup> of cw-laser is extremely long, and the bandwidth of the down-converted photon pair is much larger than the bandwidth of the pump photon, that is, the coherence time *τ*<sup>2</sup> between photon pairs is very short.

To measure the characteristics of time-energy entanglement and to exploit this entanglement, we use two unbalanced Mach-Zehnder interferometers (MZI) as shown in **Figure 11(d)**, connecting a single photon detector at the output of the MZI, measuring two coincidence count at the output. We define the optical path difference of the two paths of the MZI interferometer as *τ*3. It is assumed that when *τ*<sup>1</sup> ≥ *τ*3>*τ*2, the exit end of MZI does not have a single photon interference image, and the image of two-photon interference can be observed by the coincidence measurement.

The MZI used in our experiments is to change the phase difference between the long and short arms by adjusting the temperature. The phase change of 2*π* corresponds to a temperature change of 0.7°. The entangled interference image before single-photon frequency conversion is shown in **Figure 13**. Because it is necessary to observe the interference image under the two non-collinear base vectors, we can prove that the two-photon is entangled, so we set the MZI temperature of the signal

#### **Figure 13.**

*Two-photon interference pattern (a) before and (b) after the frequency conversion. T*<sup>1</sup> *is the temperature of the MZI in the signal channel, and T*<sup>2</sup> *is the temperature in the idler channel. The integration time for each dot is (a) 15 s and (b) 3000 s [7].*

channel to 23.0 and 24.0°, respectively. The collinear base vector is measured. From **Figure 13(a)**, we calculated the average pre-conversion entanglement visibility as *V* ¼ ð Þ 93*:*8 � 1*:*6 %.

After the single photon frequency conversion, we again measure the entanglement visibility of the converted photon pair, as shown in **Figure 13(b)**. It is calculated that the converted entanglement visibility is *V* ¼ ð Þ 88*:*2 � 5*:*1 %, and this visibility can still break the 71% visibility of Bell's inequality. Therefore, the 88.2% visibility after conversion proves that our single-photon frequency converter maintains the quantum properties of photons with a theoretical visibility of 91%. Since the converted count efficiency is low, the measurement time is extended from 15 s before conversion to 1000 s. The result convincingly shows that quantum entanglement is well preserved during the frequency conversion. Thus, the photon pairs can still be used for quantum communication tasks. We expect that our scheme may have applications in quantum systems, such as quantum communication on multiuser fiber quantum networks and quantum cryptography with independent single photon sources.

## **3. Conclusion**

We have demonstrated three kinds of quantum interfaces with different functions. First, we have experimentally demonstrated that the spectrum of singlephoton-level laser pulse was compressed by a factor of 58 in a PPLN waveguide chip, where a chirped single-photon-level laser pulse and an antichirped laser pulse by fiber Bragg gratings are used to achieve a pulse with new frequency through SFG. Our results have demonstrated the potentially application for PPLN waveguide chip as an integrated platform for spectrum compressing and frequency conversing in the telecom band, such as coherent photonic interfaces between quantum communication at 1550 nm and quantum memory in the near-visible window. Second, we have realized high efficiency SFG between two broadband single-photon-level coherent states by using a high-efficiency PPLN waveguide chip. The result is already competitive with methods based on linear optics, and offers new possibilities such as heralding entanglement at a distance. This technique in our proposal marks a critical step toward the implementation of DI-QKD. Final, we have demonstrated single-photon frequency conversion using a cascaded quadratic nonlinearity in PPLN waveguides chip. The clear HOM dip observed in our experiment shows that the frequency has been precisely switched between DWDM channels. Moreover, the time-energy entanglement is well preserved during the frequency conversion. All works above are of great significance to the development of quantum optics.

**Author details**

Shanghai, China

**75**

\* and Xianfeng Chen<sup>2</sup>

*Single-Photon Frequency Conversion for Quantum Interface*

*DOI: http://dx.doi.org/10.5772/intechopen.88867*

\*Address all correspondence to: lyhua1984@163.com

provided the original work is properly cited.

1 Department of Physics, Jiangxi Normal University, Nanchang, China

2 State Key Laboratory of Advanced Optical Communication Systems and

Networks, Department of Physics and Astronomy, Shanghai Jiao Tong University,

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

Yuanhua Li<sup>1</sup>

## **Conflict of interest**

The authors declare no conflict of interest.

*Single-Photon Frequency Conversion for Quantum Interface DOI: http://dx.doi.org/10.5772/intechopen.88867*

channel to 23.0 and 24.0°, respectively. The collinear base vector is measured. From **Figure 13(a)**, we calculated the average pre-conversion entanglement visibility as

After the single photon frequency conversion, we again measure the entanglement visibility of the converted photon pair, as shown in **Figure 13(b)**. It is calculated that the converted entanglement visibility is *V* ¼ ð Þ 88*:*2 � 5*:*1 %, and this visibility can still break the 71% visibility of Bell's inequality. Therefore, the 88.2% visibility after conversion proves that our single-photon frequency converter maintains the quantum properties of photons with a theoretical visibility of 91%. Since the converted count efficiency is low, the measurement time is extended from 15 s before conversion to 1000 s. The result convincingly shows that quantum entanglement is well preserved during the frequency conversion. Thus, the photon pairs can still be used for quantum communication tasks. We expect that our

scheme may have applications in quantum systems, such as quantum

with independent single photon sources.

communication on multiuser fiber quantum networks and quantum cryptography

We have demonstrated three kinds of quantum interfaces with different functions. First, we have experimentally demonstrated that the spectrum of singlephoton-level laser pulse was compressed by a factor of 58 in a PPLN waveguide chip, where a chirped single-photon-level laser pulse and an antichirped laser pulse by fiber Bragg gratings are used to achieve a pulse with new frequency through SFG. Our results have demonstrated the potentially application for PPLN waveguide chip as an integrated platform for spectrum compressing and frequency conversing in the telecom band, such as coherent photonic interfaces between quantum communication at 1550 nm and quantum memory in the near-visible window. Second, we have realized high efficiency SFG between two broadband single-photon-level coherent states by using a high-efficiency PPLN waveguide chip. The result is already competitive with methods based on linear optics, and offers new possibilities such as heralding entanglement at a distance. This technique in our proposal marks a critical step toward the implementation of DI-QKD. Final, we have demonstrated single-photon frequency conversion using a cascaded quadratic nonlinearity in PPLN waveguides chip. The clear HOM dip observed in our experiment shows that the frequency has been precisely switched between DWDM channels. Moreover, the time-energy entanglement is well preserved during the frequency conversion. All works above are of great significance to the development

*V* ¼ ð Þ 93*:*8 � 1*:*6 %.

*Single Photon Manipulation*

**3. Conclusion**

of quantum optics.

**Conflict of interest**

**74**

The authors declare no conflict of interest.

## **Author details**

Yuanhua Li<sup>1</sup> \* and Xianfeng Chen<sup>2</sup>

1 Department of Physics, Jiangxi Normal University, Nanchang, China

2 State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China

\*Address all correspondence to: lyhua1984@163.com

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Section 3

Nonreciprocal Control

**77**

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## Section 3
