Resonance frequency shift of a two-level atom in a pulsed optical trap

We consider the effect of a periodic pulsed perturbation on the shift of resonance frequency for a Rabi oscillation. Unlike a continuous perturbation, where the frequency shift is proportional to the perturbation strength, the shift under a pulsed perturbation shows periodic behavior. In fact, when the pulse height and the pulse duration are set such that a fictitious spin completes a 2π precession around the principal quantization axis, there is no frequency shift. This phenomenon can be used for optical frequency metrology by trapping reference atoms in a properly controlled pulsed optical trap. We estimate the residual systematic shift and line broadening due to practical limits from pulse energy fluctuation, atomic motion, and finite pulse duration and find that it is on the order of 100 Hz.