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

Dynamic polarizabilities of cesium Rydberg states, explicitly $n{S}_{1/2}, n{P}_{1/2}, n{P}_{3/2}, n{D}_{3/2}$, and $n{D}_{5/2}$, where the principal quantum number $n$ is 40--70, are presented for linearly polarized light. The dynamic polarizability is calculated using the sum-over-state approach. We identify double magic wavelengths in the range of $1000--2000$ nm for simultaneous trapping of the ground state and a Rydberg state, which are red detuned and blue detuned, respectively, 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 and master-equation models), we conclude that magic wavelength trapping is particularly promising experimentally for the $n{D}_{J,|{M}_{J}|}$ Rydberg series with angular momentum $J=3/2$ and projection quantum numbers ${M}_{J}=\ifmmode\pm\else\textpm\fi{}1/2$ (auxiliary state $8{P}_{1/2}$) and ${M}_{J}=\ifmmode\pm\else\textpm\fi{}3/2$ (auxiliary state $8{P}_{3/2}$), using trap depths as large as $10\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{K}$. 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 ongoing experimental efforts on cesium Rydberg-state-based quantum simulations that operate on timescales up to several microseconds.