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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum theory of pulsed subrecoil cooling of atoms

А. В. Тайченачев, Anatolii M Tumaikin, Valeriy I. Yudin

Published Oct 21, 1998• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.328229

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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.
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.
A completely quantum-analytical description of the cooling of atoms with angular momenta j g =1→j e =1 by a pulsed σ 1−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.
We experimentally study the motion of atoms interacting with a periodically pulsed near resonant standing wave with a polarization gradient. The atoms are cooled to a comblike momentum distribution. The peaks have widths of $\ensuremath{\approx}0.3\ensuremath{\Elzxh}k$ and a spacing which is an integer multiple of the recoil momentum $\ensuremath{\Elzxh}k$. The atomic population is accumulated in ground states which periodically evolve to dark states each time the standing wave is switched on. These light pulse synchronously recurring dark states exist for discrete pulse frequencies, even if no stationary dark states are present.
Subrecoil cooling can be achieved in three-level \ensuremath{\Lambda}-type atoms subject to counterpropagating laser beams via velocity-selective coherent population trapping [A. Aspect et al., J. Opt. Soc. Am. B 6, 2112 (1989)]. This process leads to narrow peaks in the ground but a flat structure in the excited atomic momentum distributions. By taking advantage of this difference, we construct several analytical functions from which the main cooling features (with the exception of the scaling law about the fraction of subrecoil cooled atoms) can be approximated under arbitrary parameters. This method allows us to generalize the peak-momentum width from symmetric to arbitrary degenerate \ensuremath{\Lambda} systems, and to discuss analytically the small dependence of the momentum distributions on the laser detuning near the two-photon resonance.
We derive an exact and analytical form for the cold-atom momentum distribution after a large number of one-dimensional (1D) Raman cooling cycles has been applied. Our result shows that one can select pulse profiles and lengths rather freely in order to obtain efficient cooling. Our approach takes into account optical pumping (resonant excitation followed by spontaneous emission) as an intergral part of the process, and it is noted that it does not affect the final momentum distribution. Thus subrecoil cooling is possible in general, and not just for carefully selected combinations of pulse forms and durations.
Laser cooling dynamics of neutral atoms with a closed optical transition Jg → Je in light fields with nonuniform polarization formed by counterpropagating waves with linear, circular or elliptical polarization was considered. For the case of finite interaction time of atoms with light field both mechanisms of Doppler and Sub-Doppler laser cooling affected on atoms in ensemble having different velocities were taken into account. We get qualitative relations on a base of numerical analysis in a frame of quasiclassical treatment of laser cooling. These relations allow to define optimal parameters of cooling waves, i.e. polarization, detuning from atomic resonance and intensity of light waves for the most rapid and dip laser cooling from initially wide momentum distribution for finite interaction time of atoms with laser field