Energy shift and state mixing of Rydberg atoms in ponderomotive optical traps

We present a degenerate perturbation analysis in the spin–orbit coupled basis for Rydberg atoms in an optical trap. The perturbation matrix is found to be nearly the same for two states with the same total angular momentum j, and orbital angular momentum number l differing by 1, The same perturbation matrices result in the same state-mixing and energy shift. We also study the dependence of state mixing and energy shift on the periodicity and symmetry of the ponderomotive potentials induced by different optical traps. State mixing in a one-dimensional lattice formed with two counterpropagating Gaussian beams is studied and yields a statedependent trap depth. We also calculate the state-mixing in an optical trap formed by four parallel, separated and highly focused Gaussian beams.