2.3.5 Optimization of the system by tuning the excitation parameters

The probability of coherent writing and reading a quantum state into and out of Rydberg atom as a long-lived memory depends on coherence time and strength of coupling between ground and Rydberg state. Substituting the Rabi frequencies defined in Eqs. (22)–(24) into Eqs. (19), (20) and (25), Δeff, Ωeff, and UFORDQT can be interpreted in terms of key parameters of excitation: the orientation of the excitation beams with respect to the quantum axis (θi), the intensity of laser excitation beams (Ii), the detuning from intermediate states (Δi), the laser polarization azimuthal angle (φi), and the orbital angular momentum and the beam waist of the Rydberg excitation LG beam. By adjusting θ<sup>i</sup> the geometry of excitation can be constructed for a Doppler- and recoil-free excitation. The clever choice of φ<sup>i</sup> results in the excitation to a desirable state. While Δ<sup>i</sup> fulfills the far-off resonance condition, the intensity I<sup>i</sup> can be adjusted to boost the effective quadrupole excitation with less effect of AC-Stark shift. Finally, the proper choice of excitation laser beam waists can result in a great reduction of trapping size. In the GGLG excitation

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

Figure 3.

(a) The far-off resonance optical dipole-quadrupole trapping potential normalized to the quadrupole potential versus transversal position of center of mass of the Rydberg atom, for the case Ω<sup>1</sup> = Ω3, |Δ1|=|Δ3|, and ω<sup>01</sup> = ω<sup>02</sup> = 0.2 ω<sup>03</sup> (blue line) [77].

process, the Rydberg atom confines in the FORDQT potential, which is sensitive to the Rydberg atom position with respect to the transversal variations of the intensity of the excitation lasers which keeps the Rydberg atom at the minimum noise position of the trapping center and thus controls localized qudit state in longer coherent time reasonable for quantum information processing. Comparing to the Rydberg dipole excitation via LG beam, the Rydberg GGLG excitation system localizes the atom in a much smaller region. According to Figure 3, if the LG beam is focused into some micron waist, then in this self-trapping excitation system, the atom can be excited to a Rydberg state while tightly confined and controlled to submicron dimensions. Consequently, in a high-dimensional quantum information experiments via Rydberg excitation, care should be taken to relative control over all these parameters.
