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Quantum theory of pulsed subrecoil cooling of atoms

A quantum analytic treatment of the resonant scattering of atoms with jg equals j yields je equals j (j is an integer) transitions by a pulsed (sigma) + - (sigma) - field is developed. In the approximation of motionless atoms, the atomic density matrix after action of single light pulse is evaluated with exact consideration of the recoil effects. Recurrent equations, which allow to calculate the distribution after arbitrary pulse sequences are found in the analytic form. It is shown that for discrete pulse frequencies the action of N light pulses leads to the formation and narrowing of peaks in discrete points of the momentum space, and also to the broadening of the envelope of the momentum distribution. In the case of the wide (with respect to the photon momentum) initial distribution the explicit formulae for peaks and envelope are obtained and an asymptotic behavior of the solution is analyzed. In the low-intensity limit a dependence of the scattering pattern contrast on the pulse duration is studied.