Quantum theory of cooling of atoms below the one-photon recoil energy by a pulsed field

Abstract

A completely quantum-analytical description of the cooling of atoms with angular momenta jg=1→je=1 by a pulsed σ1−σ− field is developed. The problem of the change produced in the distribution of the atoms over the internal and translational degrees of freedom by a single field pulse is solved exactly with respect to recoil effects. Recurrence formulas for the distribution after the action of an arbitrary sequence of pulses are found in analytical form. It is shown that N field pulses result in the formation and narrowing of peaks at discrete points in momentum space as well as broadening of the envelope of these peaks. Explicit formulas are obtained for the peaks and envelopes in the case of a wide initial momentum distribution, and their asymptotic behavior for N≫1 is investigated.