2.3.4 Localized Rydberg excitation in dipole-quadrupole potential landscape

Considering red- and blue-far-off resonance detuned first, second, and Rydberg excitation laser beams, respectively, due to the position-dependent AC-Stark shift of ground and Rydberg states as derived in Eq. (19), a position-dependent dipolequadrupole potential landscape is found:

$$U\_{FORQT}(R\_\perp) = U\_{LG3} + U\_{G1\*} \tag{25}$$

where

$$U\_{qLG3} = U\_{03} \left(\frac{d}{d\mathcal{R}\_\perp} f\_{LG3}(\mathcal{R}\_\perp)\right)^2,\tag{26}$$

and

$$U\_{dG1} = -U\_{01} f\_{G1}^2(R\_\perp) \,\tag{27}$$

are the optical quadrupole and dipole potentials, respectively. In these expres- <sup>2</sup> <sup>j</sup>Ω3ð Þ <sup>0</sup> <sup>j</sup> <sup>2</sup> <sup>ℏ</sup> <sup>ℏ</sup> <sup>j</sup>Ω1ð Þ <sup>0</sup> <sup>j</sup> sions <sup>U</sup><sup>03</sup> <sup>¼</sup> and <sup>U</sup><sup>01</sup> <sup>¼</sup> are quadrupole and dipole potential depth. <sup>4</sup> <sup>j</sup>Δ3ðR;VÞj <sup>4</sup> <sup>j</sup>Δ1ðR;VÞj The first and the last excitation parameters are contributing in the self-trapping potential landscape called far-off resonance optical dipole-quadrupole trap (FORDQT), while the second deriving laser with high intensity increases the excitation probability. Turning the trap off also results in mechanical heating and decoherence due to entanglement between the qubit state and the center of mass motion. The far detuning from all atomic resonances substantially reduces the photon scattering rate, and the atom is localized in an almost conservative potential. It can be seen that the magnitude and direction of the force exerted on the atom depend on both the magnitude and sign of the intensity gradient and the detuning which pushes the atom back toward the dark center of the trap. The flexible geometry of the excitation configuration results in the axial Doppler- and recoil-free excitation at the center of the trap. The localized Rydberg excitation in FORDQT potential can pave the way to establish a new record for the length of the time that quantum information can be stored in and retrieved from a localized trapped Rydberg atom.
