2. High precision excitation and manipulation of a localized single atom to a highly excited Rydberg state

In this section, the theory of the three-step axial Doppler-free GGLG excitation of an alkali atom (e.g., Rb) from the ground state to the desired Rydberg state at the level of a single atomic excitation which is crucial for applications to quantum information processing is presented. The Rydberg excitation process is based on faroff resonance dipole-dipole-quadrupole transition. The quadrupole Rydberg transition in the last step is via LG-polarized laser beam. The Rydberg atom is localized at the dark center of structured beam, where the effect of atomic vibrations as well as AC-Stark shift is completely disappeared. The geometry of excitation as well as unique properties of LG-Rydberg excitation beam provides qudit of quantum memory in less disrupting effects such as motional heating effect, spontaneous emission due to high power, AC-Stark and Doppler, and recoil shift at the center of the trap which guarantee the high-fidelity gate.
