Quantum theory of resonant scattering of atoms by a pulsed field under coherent population trapping conditions

Abstract

We develop an entirely quantum mechanical analytical description of scattering of atoms with angular momenta j g →j→j e =j (j is an integer) by a pulsed σ+−σ− field. In the stationary-atom approximation with exact accounting for recoil effects, we solve the problem of the change in the distribution of atoms among the internal and translational degrees of freedom initiated by a single pulse for j g =1, 2. We find in analytical form recurrence formulas that make it possible to calculate the distribution of the atoms after an arbitrary sequence of pulses has acted on the system. We show that for discrete (resonant) values of the time interval between the pulses, the action of N pulses leads to effective formation and narrowing of peaks at discrete points in momentum space and to a broadening of the envelope of these peaks. In the case of a broad initial momentum distribution we derive explicit formulas for the peaks and the envelope and study their asymptotic behavior for N≫1. Finally, in the weak-field limit we study numerically the dependence of the contrast of the scattering diagram on pulse length.