Frequency-dependent trapping of Rydberg states of cesium

When a highly excited atomic state with a large principal quantum number is occupied by a valence electron, the state is referred to as a Rydberg state. Rydberg states have intriguing and intrinsic features, such as large size, transition dipole moment, polarizability, and long lifetime, which have applications in various branches of physics. Here we present dynamic polarizabilities of Rydberg states of cesium, explicitly $nS_{1/2}$, $nP_{1/2,3/2}$, and $nD_{3/2,5/2}$, where the principal quantum number $n$ goes from $40$ to 70. The dynamic polarizability is calculated by using the sum-over-states approach. We characterize the impact of the room temperature blackbody radiation on the radiative lifetime. We find a set of magic wavelengths for simultaneous trapping of each Rydberg state and the ground state. Based on the Rabi frequency and maximum population transfer between the Rydberg and auxiliary states, we demonstrate the experimental feasibility of the presented magic wavelengths for various depths of the trap. The magic wavelengths for the Rydberg states are blue-detuned to the auxiliary states, which are different low-lying excited states. Moreover, we find triple magic conditions, for which the polarizabilities of the ground, Rydberg, and low-lying excited states intersect at a particular wavelength of the light, by tuning the angle between the quantization axis and the polarization vector.