Steady state of a low-density ensemble of atoms in a monochromatic field taking into account recoil effects
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Steady State of a LowDensity Ensemble of Atoms in a Monochromatic Field Taking into account Recoil Effects O. N. Prudnikova,b, R. Ya. Il’enkova,b, A. V. Taichenacheva,b, A. M. Tumaikina,b, and V. I. Yudina,b a
Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia email: [email protected] b Institute of Laser Physics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent’eva 13/3, Novosibirsk, 630090 Russia email: [email protected] Received November 15, 2010
Abstract—A method has been developed for obtaining the steadystate solution of a quantum kinetic equa tion for the atomic density matrix in an arbitrarily polarized monochromatic field with the complete inclusion of recoil effects and degeneracy of atomic levels in the projection of the angular momentum. This method makes it possible to obtain the most general solution beyond the previously accepted approximations (semi classical approximation, secular approximation, etc.). In particular, it has been shown that the laser cooling temperature is a function of not only the depth of the optical potential (as was previously thought), but also the mass of an atom. DOI: 10.1134/S1063776111050189
1. INTRODUCTION The laser cooling of neutral atoms is one of the highpriority fields of the development of atomic and laser physics. Cold atoms are used in atomic spectros copy, newgeneration frequency standards, experi ments with a Bose–Einstein condensate of neutral atoms, etc. The main difficulty of theoretical descrip tion is that the kinetics of neutral atoms in polarized light fields is described by a quantum kinetic equation for the atomic density matrix including all atomic lev els, coherence between them, and recoil effects in the processes of absorption and emission of photons. To qualitatively describe kinetic effects, a semiclassical approximation was first developed (see, e.g., [1]), where the equations for the density matrix are reduced to a Fokker–Plancktype equation for the Wigner dis tribution function in the phase space. One of the main applicability conditions of the semiclassical approxi mation is the smallness of the recoil parameter ωR/γ, where γ is the spontaneous decay rate and ωR = 2k2/M is the recoil energy obtained by an atom with the rest mass M emitting or absorbing a photon with the momentum k. Another necessary condition is the smallness of the momentum of photons of the light field as compared to the width of the momentum dis tribution of atoms, k/Δp 1. In the framework of this approach, the expressions for the force and diffu sion coefficients were obtained, which allow the approximate description of cooling effects and the dynamics of atoms in light fields, including the effects of the Doppler and subDoppler cooling of atoms. More recently, quantum methods were developed to analyze the kinetics of atoms beyond the semiclassical
approximation [2–4]. However, the developed quan tum approaches also have a number of limitations. In particular, for the quantum description of
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