1.4 Rydberg excitation

The excitation of a trapped neutral atom to a highly excited Rydberg state with long coherent time of ground-Rydberg transition is a promising platform for fast multi-qubit gates. The Rydberg state lifetime must be taken into account since the Rydberg state needs to be populated in order to implement two-qubit logical operations. The elementary operations necessary with Rydberg atoms in quantum information rely on the ability to coherently excite a Rydberg state and then returning them back to the ground state in controlled way so that the Rydberg atom is available for further processing. The lack of widely tunable frequency-stabilized ultraviolet wavelength diode lasers required for the direct excitation from the ground state to Rydberg states as well as weak direct excitation cross section has led to the use of multistep processes involving visible and near-infrared wavelengths [62–64]. To limit the spontaneous emission from the intermediate states in multistep excitation, which destroys the coherence, the population of the intermediate states can be manipulated by enlarging the detuning of the excitation laser frequency from the respective resonance frequency compared to the Rabi frequency of single-photon excitation. For large enough detunings, the intermediate states can be eliminated and a four-level system can be approximated to a two-level system with a total coupling strength. In this case, to obtain coherent coupling between the ground state and the Rydberg state, it is necessary to achieve an effective Rabi-frequency Ω well larger than the linewidth of the Rydberg state or of the driving laser fields. The coherent excitation of individual atoms trapped in tight optical dipole using two-photon excitation process has recently been described [65–68]. Also in order to cancel Doppler and recoil effects in Rydberg excitation, which limit the fidelity of the quantum gate [69], three-photon Rydberg excitation configuration is already proposed [70]. However, selectively localized and coherent excitation of atom to a highly excited Rydberg state and creation of a perfect blockade are still challenging [3, 71]. Firstly, the common red-detuned dipole traps can store atoms in the ground state with low decoherence, but they do not trap Rydberg states, and moreover, an atom in the Rydberg state moves in different optical potential than that experienced by the ground state. Secondly, the photoionization near the core due to the red-detuned trapping light, the sensitivity to the stray fields because of the large electron orbit and large polarizability that scales as ∝ n7 [72], and the motional-induced dephasing presents crucial limits to the usable spectrum. Thirdly, although the intermediate state detuning reduces spontaneous

Localized Excitation of Single Atom to a Rydberg State with Structured Laser Beam for Quantum… DOI: http://dx.doi.org/10.5772/intechopen.82319

emission, however, the small spontaneous emission besides of atomic motion and collisions [73] can limit storage times and therefore the ground-Rydberg atomic coherence time. Fourthly, the weak oscillator strength between ground and highly excited Rydberg state and very large electric dipole requires high laser excitation intensity to achieve the required signal-to-noise ratio. Fifthly, in most implementations using lattices or trap arrays generated with diffractive optics, it is relatively difficult to control the trap intensity and avoid perturbation of the atomic energy levels induced by inhomogeneous light distributions. Finally, in highly excited state, the energy separation is very small so that the selective excitation of the atom to a highly excited Rydberg state requires experimental technique with extremely high resolution.

To reduce errors in Rydberg excitation experiments, one solution is turning off the trapping system before the Rydberg excitation. However, it can cause problem for implementations with many qubits and creates unwanted Doppler shifts. This can be addressed by choosing a trap that works for both ground and Rydberg state of the atom. On the other hand, for the implementation of Rydberg-based quantum computing protocols with neutral atoms [3, 74–76], one can use a magic wavelength at which two atomic states (ground and Rydberg states) experience the same AC-Stark shift in a light field. In this chapter, a four-level Rydberg atom as a quantum memory in far-off resonance optical dipole-quadrupole trap is introduced. The controlling of the quantum state of localized Rydberg atom by tuning the excitation parameters is presented. It is shown that the ability to control the quantum state of Rydberg atom opens some interesting prospects for advances in quantum information processing.
