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Journal of Experimental and Theoretical Physics Letters

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

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

Published May 1, 1997• 4 citations
Publisher

Abstract

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.

DOI
10.1134/1.567426

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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.
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.
We present a theoretical analysis of a new one-dimensional laser-cooling scheme that was recently demonstrated on a beam of metastable 4He atoms. Both internal and translational degrees of freedom are treated quantum mechanically. Unlike semiclassical approaches, such a treatment can be applied to situations in which the atomic coherence length is of the same order of or larger than the laser wavelength, which is the case for atoms cooled below the one-photon recoil energy. We introduce families of states that are closed with respect to absorption and stimulated emission, and we establish the generalized optical Bloch equations that are satisfied by the corresponding matrix elements. The existence of velocity-selective trapping states that are linear combinations of states with different internal and translational quantum numbers is demonstrated, and the mechanism of accumulation of atoms in these trapping states by fluorescence cycles is analyzed. From a numerical solution of the generalized optical Bloch equations, we study in detail how the final atomic-momentum distribution depends on the various physical parameters: interaction time, width of the initial distribution, laser detuning, laser power, and imbalance between the two counterpropagating waves. We show that the final temperature decreases when the interaction time increases, so that there is no fundamental limit to the lowest temperature that can be achieved by such a method. Finally, possible extensions of this method to two-dimensional cooling are presented.
The setting time of the stationary distribution over translational degrees of freedom of two-level atoms in the field of a one-dimensional standing light wave is studied. The dependences of this time on the problem parameters such as the light wave intensity, frequency detuning, and atom mass are obtained. Calculations are performed on the basis of the quantum-mechanical equation for the atomic density matrix taking completely into account the recoil and spatial localization effects in an arbitrarily intense light field.
Abstract The efficiency of the polarisation mechanisms of laser cooling of atoms is analysed using narrow optical transitions for which the recoil energy is greater than or comparable to the natural line width. By the example of atoms with the J g = 1 → J e = 2 optical transition (J g and J e are the total angular momenta of the ground and excited states) in the resonant light fields of σ + – σ – and lin⊥lin configurations, the analysis of the minimum achievable energies of laser-cooled atoms is performed. It is shown that the polarisation mechanisms of laser cooling under conditions of a significant influence of recoil effects become less efficient and do not lead to average kinetic energies of an ensemble of atoms below the Doppler limit.