Magic-wavelength optical traps for Rydberg atoms

We propose blue-detuned optical traps that are suitable for trapping of both ground-state and Rydberg excited atoms. The addition of a background compensation field or a suitable choice of the trap geometry provides a magic trapping condition for ground-state and Rydberg atoms at the trap center. Deviations from the magic condition at finite temperature are calculated. Designs that achieve less than 200-kHz differential trap shift between Cs ground states and $125s$ Rydberg states for 10 $\mu \mathrm{K}$ Cs atoms are presented. Consideration of the trapping potential and photoionization rates suggests that these traps will be useful for quantum-information experiments with atomic qubits.

Figure 1

Scalar polarizability of ground states and Rydberg states of Rb and Cs (solid lines) and vector polarizability of the ground-state (dashed lines).

Figure 2

Setup of blue-detuned dipole traps: (a) Gaussian interference BBT [13], (b) crossed vortex BBT [12], and (c) Gaussian lattice.

Figure 3

Trapping depth of blue-detuned dipole traps in the $x$-$y$ (left column) and $x$-$z$ (right column) planes for Cs 6$s$, $\lambda =780$ nm, $\alpha =-235\times {10}^{-24}$ cm${}^3$, power $P=50$ mW for (a) Gaussian interference BBT, $w_1=2$ $\mu$m and $w_2=3.78$ $\mu$m; (b) crossed vortex BBT, $w=3$ $\mu$m and $\theta ={8.6}^{\circ }$; and (c) Gaussian lattice trap, $w=1.5$ $\mu$m and $d=4$ $\mu$m.

Figure 4

Potential energy of Cs ground-state and $ns$ Rydberg states with $n=100$, 125, 150 in (a) Gaussian interference BBT, (b) vortex BBT, and (c) Gaussian lattice BBT. Trap parameters the same as in Fig. 3.

Figure 5

Energy shift compensation for the crossed vortex BBT with a plane wave of intensity $I_m=128$ $\mu$W$/\mu$m${}^2$, $w=3$ $\mu$m, $\theta =8.6$${}^{\circ }$, and $P=50$ mW.

Figure 6

Trapping potential (top row) and shift difference (bottom row) between Cs $6s$ and $125s$ for a self-magic Gaussian lattice trap with $\lambda =780$ nm, $d=4$ $\mu$m, $w=1.57$ $\mu$m, and $P=50$ mW.

Figure 7

Average transition shift between ground states and $125s$ states of Cs in Gaussian lattice trap with $d=4$ $\mu$m, $w=1.57$ $\mu$m, $P=50$ mW, and $U_{\mathrm{trap}}=k_B\times 300$ $\mu$K.

Figure 8

Photoionization rate for $125s$ Cs in a 780-nm self-magic Gaussian lattice dipole trap, $w=1.57$ $\mu$m, $d=4$ $\mu$m, $P=50$ mW, and $U_{\mathrm{trap}}=k_B\times 300$ $\mu$K.