Doppler cooling with coherent trains of laser pulses and a tunable velocity comb

We explore the possibility of decelerating and Doppler cooling an ensemble of two-level atoms by a coherent train of short, nonoverlapping laser pulses. We derive analytical expressions for mechanical force exerted by the train. In frequency space the force pattern reflects the underlying frequency comb structure. The pattern depends strongly on the ratio of the atomic lifetime to the repetition time between the pulses and pulse area. For example, in the limit of short lifetimes, the frequency-space peaks of the optical force wash out. We propose to tune the carrier-envelope offset frequency to follow the Doppler-shifted detuning as atoms decelerate; this leads to compression of atomic velocity distribution about comb teeth and results in a “velocity comb”—a series of narrow equidistant peaks in the velocity space.