Double, triple, and quadruple magic wavelengths for cesium ground, excited, and Rydberg states

Dynamic polarizabilities of cesium Rydberg states, explicitly nS1/2, nP1/2, nP3/2, nD3/2, and nD5/2, where the principal quantum number n is $40$ to $70$, are presented for linearly polarized light. The dynamic polarizability is calculated using the sum-over-states approach. We identify double magic wavelengths in the range of $1,000-2,000$~nm for simultaneous trapping of the ground state and a Rydberg state, which are, respectively, red-detuned and blue-detuned with respect to a low-lying excited auxiliary state. Based on calculations of the radiative lifetime, blackbody radiation induced transitions, and population transfer out of the Rydberg and auxiliary states (estimated within two-state as well as master equation models), we conclude that magic wavelength trapping is particularly promising experimentally for the nDJ,|MJ| Rydberg series with angular momentum $J=3/2$ and projection quantum numbers MJ=± 1/2 (auxiliary state 8P1/2) and MJ=± 3/2 (auxiliary state 8P3/2), using trap depths as large as $10$~μK. Moreover, by tuning the angle between the quantization axis and the polarization vector of the light, we identify triple and quadruple magic wavelengths, for which the polarizabilities of the ground state, a Rydberg state, and, respectively, one and two low-lying excited states are equal. Our comprehensive theoretical study provides much needed guidance for on-going experimental efforts on cesium Rydberg-state based quantum simulations that operate on time scales up to several μs.