See-saw protocol for Doppler cooling of multilevel systems with coherent pulse trains

We consider decelerating and cooling an ensemble of multilevel atoms and molecules with a coherent train of ultrashort laser pulses. In the frequency domain such trains form frequency combs. We propose a novel see-saw scheme of Doppler cooling of multilevel atoms and molecules. In this scheme the teeth of the frequency comb are periodically moved in and out of resonance with the allowed transitions. The see-saw cooling may be carried out in practice by switching carrier-envelope phase offset between predefined values. We study the performance of the see-saw scheme for the simplest prototype three-level $\Lambda$ system and demonstrate its advantage. For these systems we demonstrate a procedure for determining optimal train parameters, and see-saw switching period. We also illustrate the performance of the protocol by numerically simulating time evolution of velocity distribution.