Spectroscopy and coherent control of Rydberg-Rydberg transitions with a modulated optical lattice

We discuss recent experimental progress involving the use of a 1064-nm, intensity-modulated optical lattice to drive Doppler-free Rydberg-Rydberg transitions with spatial selectivity at the order of the lattice period. Permitted by the A●A-term of the minimal coupling Hamiltonian, this drive provides a first-order coupling between two Rydberg states that is free of the usual l-selection rules. We discuss lattice-modulation spectroscopy of Rydberg nS_1/2-nP_1/2 transitions that inhibit on-resonant excitation due to a rotary-echo-like effect from the Rydberg-atom trajectory within the ponderomotive potential, while permitting excitations at vibrational sidebands. We further drive the nS_1/2-(n+1)S_1/2 transition by simultaneous application of a lattice modulation and a microwave field. In this case, the net transition amplitude is a coherent sum of both the A●A and the A●p interactions in the minimal coupling Hamiltonian. Experimental and numerical data are provided for both discussions.