**4.7 The pump and the probe laser**

The pump and probe lasers used in our experiments are *Littrow* cavity diode lasers 26 delivering about 50 mW of single longitudinal mode emission near 780 nm at a laser line width of nearly 1 MHz. Each laser was protected with a 60 dB optical isolator 27. The optical isolators were placed inside the laser case after the grating. The use of the optical isolators is essential to obtain a reproducible magneto optical trap as it is very difficult to avoid reflections back into the laser. These reflections can destroy the single mode emission of the lasers.

### **4.8 Description of the Pound Drever Hall method for frequency stability of the pump and probe lasers**

The setup of a cold atom cloud requires fixed cooling and repumping laser frequencies. It is possible to obtain the cloud of cooled atoms without stabilizing the laser but it makes the work more difficult. The Pound Drever Hall method permits the stability of the frequency of the laser frequencies close to the resonances. Fig. 17 shows the optical setup of the Pound Drever Hall detector. A diode laser is collimated by a aspheric lens of short focal distance and its wavelength controlled by a grating that reflects its first diffraction order back into the laser cavity. The wavelength is roughly adjusted by rotating the grating. A piezo electric transducer (PZT) can produce fine angular displacements of the grating and control the frequency of the lasers single mode emission at the MHz level. An optical isolator installed in front of the laser permits to avoid unwanted back reflections into the laser cavity. These reflections could destroy the single mode emission of the laser. Laser exiting the optical isolator is driven to the confocal scanning Fabry Perot interferometer. Two mirrors (2M) lifted the laser to 15 cm from the optical top. The beam was conducted by means of an optical glass divider, a mirror and a pair of mirrors that placed the beam at the level of the interferometers axis. The beam passes a polarizing beam splitter cube, a quarter wave plate

<sup>26</sup> Toptica Photonics, Model DL100

<sup>27</sup> TV-Linos, Model FI-790

172 Quantum Optics and Laser Experiments

earths. The soldering was made by means of thermocouple point soldering device. This uses three 5.1 mF, 350 V electrolytic capacitors in parallel. 70 V is enough to sold the parts.

The pump and probe lasers used in our experiments are *Littrow* cavity diode lasers 26 delivering about 50 mW of single longitudinal mode emission near 780 nm at a laser line width of nearly 1 MHz. Each laser was protected with a 60 dB optical isolator 27. The optical isolators were placed inside the laser case after the grating. The use of the optical isolators is essential to obtain a reproducible magneto optical trap as it is very difficult to avoid reflections back into the laser. These reflections can destroy the single mode emission of the

**4.8 Description of the Pound Drever Hall method for frequency stability of the pump** 

The setup of a cold atom cloud requires fixed cooling and repumping laser frequencies. It is possible to obtain the cloud of cooled atoms without stabilizing the laser but it makes the work more difficult. The Pound Drever Hall method permits the stability of the frequency of the laser frequencies close to the resonances. Fig. 17 shows the optical setup of the Pound Drever Hall detector. A diode laser is collimated by a aspheric lens of short focal distance and its wavelength controlled by a grating that reflects its first diffraction order back into the laser cavity. The wavelength is roughly adjusted by rotating the grating. A piezo electric transducer (PZT) can produce fine angular displacements of the grating and control the frequency of the lasers single mode emission at the MHz level. An optical isolator installed in front of the laser permits to avoid unwanted back reflections into the laser cavity. These reflections could destroy the single mode emission of the laser. Laser exiting the optical isolator is driven to the confocal scanning Fabry Perot interferometer. Two mirrors (2M) lifted the laser to 15 cm from the optical top. The beam was conducted by means of an optical glass divider, a mirror and a pair of mirrors that placed the beam at the level of the interferometers axis. The beam passes a polarizing beam splitter cube, a quarter wave plate

We used only one getter for more than 100 hours and it is still working.

Fig. 16. View of the rubidium getter.

**4.7 The pump and the probe laser** 

lasers.

26 Toptica Photonics, Model DL100 27 TV-Linos, Model FI-790

**and probe lasers** 

and was focused with an *f* = 200 mm lens to the interferometer. The light reflected from the interferometer becomes horizontally polarized after passing twice the quarter wave plate and was reflected by the polarizing beam splitter cube into a fast photodiode 28.

Fig. 17. Optical setup for Pound Drever Hall stabilization method.

The reflected electric field from a Fabry Perot interferometer is given by

$$E\_r = \frac{\left(1 - e^{i\delta}\right)\sqrt{R}}{1 - R\,\mathrm{e}^{i\delta}} E\_i \tag{23}$$

where *R* is the mirror reflectivity and FSR 2 / . The laser is modulated at a frequency / 2 20 MHz . The incident laser amplitude can be written as a carrier with two weak sidebands as

$$\mathcal{I}(\alpha) = \int\_0^2 (\beta) \mathcal{L}(\alpha; \alpha\_0) + \sum\_{n=1}^\infty f\_n^2(\beta) \left[ \mathcal{L}(\alpha; \alpha\_0 + n\Omega) + \mathcal{L}(\alpha; \alpha\_0 - n\Omega) \right] \tag{24}$$

where is the modulation amplitude,

$$L(w) = \frac{1}{\pi} \frac{\frac{1}{2}\Gamma}{\left(\rho - \alpha\_0\right)^2 + \left(\frac{1}{2}\Gamma\right)^2} \tag{25}$$

is a Lorentzian function, and the laser linewidth. A modulated spectra for / 2 20 MHz modulation frequency and laser linewidth 10 MHz is depicted in Fig.18.

<sup>28</sup> Thorlabs, Model PDA10-EC

Cold Atoms Experiments: Influence of Laser Intensity Imbalance on Cloud Formation 175

rotating mounts 31 but in our case we used fixed mounts constructed by us. Multiple order wave plates require specification of the used wavelength. In our case the required wavelength was 780 nm. A linear polarized beam incident on a multiple order quarter wave plate produces circular polarized light when the electrical field of the incident laser is oriented at 45 degrees with respect to the optical axis of the quarter wave plate. One of the vector components of the *E*- field is parallel to the optical axis and the other perpendicular. A good method to check the orientation of optical axis of a quarter wave plate is to construct

Fig. 20. Optical isolator. PBSC = polarizing beam splitter cube, M = mirror.

PBSC PBSC

, the electrical field rotates at an angle 2

windings per sheet. To drive the coils we used two 5A variable current supplies.

Incident light coming from the left side with its polarization vector parallel to the plane of the paper passes the polarizing beam splitter cube and continues through the quarter wave plate. When the optical axis of the plate is rotated in 45º respect to the electrical field the wave becomes circular. The reflected light turns into perpendicular to the plane of the paper and becomes fully reflected by the polarizing beam splitter cube. With the aid of a photodiode it is possible to find the largest reflected signal by rotating the quarter wave plate slightly back and forth. The optical axis of the half wave plate can be found using the linear incident laser light and a polarizing beam splitter cube. When this plate is rotated a 45º relative to the incident field, the field rotates 90º. In general when the half wave plate is

QWP QWP incident light reflected light

transmission of 0.4 and reflectivity of 0.6. This is correct but the transmitted *E*-fields are

The force acting on the atoms in the magneto optical trap is position space dependant being larger for atoms that are more distant from the center of the trap. The MOT coils are two copper solenoids with same dimensions and number of windings. The coils are disposed in anti Helmholtz configuration one over the other. Fig. 21 shows a diagram of the coils. The current in one coil flows in opposite direction with respect to the other coil. It is recommended (Wieman, 1995) to have a variable magnetic field gradient with a maximum of 0.2 T/m. We used normally between 0.10 and 0.15 T/m. We used a 1.15 mm diameter (AWG 17), enameled copper wire. Each coil has 196 windings ordered in 14 sheets with 14

M M

. This can be used to obtain a

an optical isolator as shown in Fig. 20.

rotated at an angle

slightly rotated to vertical or horizontal.

30 CVI - Melles Griot, Model QWPM-780-10-2

31 Thorlabs, Model RSP1

**4.10 Anti Helmholtz coils: magneto optical trap** 

Fig. 18. Laser modulated with 20 MHz sinusoidal function. Sidebands can be seen at both sides of the central feature.

Two sidebands can be found on each side of the central feature. The signal produced by the fast photodiode is mixed with the modulation sinusoidal signal. The error function (Fig.19) is obtained when the product of these two functions is passed through a low pass filter.

Fig. 19. Error function considering a FSR = 1GHz, finesse = 500 and 20 MHz modulation.

#### **4.9 Polarizing optics: left and right circulating light**

Laser beams with opposite helicity polarizations impinge on an atom from opposite directions. Magnetic levels of the atoms are shifted by the magnetic field. The net result is a position-dependent force that pushes the atoms into the center of the magneto optical trap.

In our experiment we used 1 inch diameter multiple order quarter wave plates 29 and 1 inch diameter multiple order half wave plates 30. The wave plates can be installed in optical

<sup>29</sup> CVI - Melles Griot, Model QWPM-780-10-4

174 Quantum Optics and Laser Experiments


Two sidebands can be found on each side of the central feature. The signal produced by the fast photodiode is mixed with the modulation sinusoidal signal. The error function (Fig.19) is obtained when the product of these two functions is passed through a low pass filter.

> -40 -20 0 20 40 relative frequency (MHz)

Laser beams with opposite helicity polarizations impinge on an atom from opposite directions. Magnetic levels of the atoms are shifted by the magnetic field. The net result is a position-dependent force that pushes the atoms into the center of the magneto optical trap. In our experiment we used 1 inch diameter multiple order quarter wave plates 29 and 1 inch diameter multiple order half wave plates 30. The wave plates can be installed in optical

Fig. 19. Error function considering a FSR = 1GHz, finesse = 500 and 20 MHz modulation.

Fig. 18. Laser modulated with 20 MHz sinusoidal function. Sidebands can be seen at both

intensity (a.u.)

sides of the central feature.

error signal (a.u.)

**4.9 Polarizing optics: left and right circulating light** 

29 CVI - Melles Griot, Model QWPM-780-10-4

rotating mounts 31 but in our case we used fixed mounts constructed by us. Multiple order wave plates require specification of the used wavelength. In our case the required wavelength was 780 nm. A linear polarized beam incident on a multiple order quarter wave plate produces circular polarized light when the electrical field of the incident laser is oriented at 45 degrees with respect to the optical axis of the quarter wave plate. One of the vector components of the *E*- field is parallel to the optical axis and the other perpendicular. A good method to check the orientation of optical axis of a quarter wave plate is to construct an optical isolator as shown in Fig. 20.

Fig. 20. Optical isolator. PBSC = polarizing beam splitter cube, M = mirror.

Incident light coming from the left side with its polarization vector parallel to the plane of the paper passes the polarizing beam splitter cube and continues through the quarter wave plate. When the optical axis of the plate is rotated in 45º respect to the electrical field the wave becomes circular. The reflected light turns into perpendicular to the plane of the paper

and becomes fully reflected by the polarizing beam splitter cube. With the aid of a photodiode it is possible to find the largest reflected signal by rotating the quarter wave plate slightly back and forth. The optical axis of the half wave plate can be found using the linear incident laser light and a polarizing beam splitter cube. When this plate is rotated a 45º relative to the incident field, the field rotates 90º. In general when the half wave plate is rotated at an angle , the electrical field rotates at an angle 2 . This can be used to obtain a transmission of 0.4 and reflectivity of 0.6. This is correct but the transmitted *E*-fields are slightly rotated to vertical or horizontal.
