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

TL;DR

This paper identifies multiple magic wavelengths for cesium atoms that enable simultaneous trapping of ground, excited, and Rydberg states, facilitating advanced quantum simulation experiments.

Contribution

It introduces the first calculations of double, triple, and quadruple magic wavelengths for cesium Rydberg states, guiding experimental trapping strategies.

Findings

Double magic wavelengths found in 1000-2000 nm range for ground and Rydberg states.

Triple and quadruple magic wavelengths identified by tuning the polarization angle.

Trap depths up to 10 μK are feasible for specific Rydberg series.

Abstract

Dynamic polarizabilities of cesium Rydberg states, explicitly $nS_{1/2}$, $nP_{1/2}$, $nP_{3/2}$, $nD_{3/2}$, and $nD_{5/2}$, 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 $nD_{J,|M_J|}$ Rydberg series with angular momentum $J=3/2$ and projection quantum numbers $M_J=\pm 1/2$ (auxiliary state $8P_{1/2}$) and $M_J=\pm 3/2$ (auxiliary state $8P_{3/2}$), using trap depths as large as $10$~$\mu$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 on-going experimental efforts on cesium Rydberg-state based quantum simulations that operate on time scales up to several $\mu$s.