Quantized motion of Rydberg atoms in an amplitude-modulated lattice potential

We present a model description of the spectroscopic line shape of Rydberg transitions in an amplitude-modulated Rydberg-atom lattice taking into account the quantization of the center-of-mass motion. In our model, the wave function of both ground and excited states are subject to the periodic potentials that arise from the optical-lattice fields. In contrast to other spectroscopic scheme, in our work the coupling (the effective Rabi frequency) is also periodic as function of the translational coordinate, and it is perfectly phase-locked to the lattice trapping potential. By solving the time-dependent Schr\"odinger equation in momentum representation we obtain the spectrum of the excited-state population. The numerical results for the momentum components of the ground and excited wave functions are averaged over the thermal momentum distribution of the Rydberg atoms. The effect of the lattice parameters and the interaction strength on the line shape of the Rydberg transitions is discussed.