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Physical Review A

Cooling or heating of atoms by radiatively assisted inelastic collisions

Arturo Bambini

Published Sep 1, 1993• 2 citations
Publisher

Abstract

The transfer of energy from the translational to the internal degrees of freedom or vice versa is analyzed for radiatively assisted inelastic collisions among atoms in a gas. For a specific atomic-level configuration, it is shown that the absorption of a laser photon may induce a transition between two levels that are displaced by the collisional interaction (a dipole-dipole potential in this treatment) if a fraction of the kinetic energy of the atomic relative motion is simultaneously absorbed. The process thus results in a cooling of the atomic kinetic temperature. In other level configurations, energy goes in the opposite direction, with a heating of the kinetic temperature. This mechanism is described by means of the Wigner-function formalism, which allows a passing to the quasiclassical limit for the atomic motion in a simple way.

DOI
10.1103/physreva.48.2161

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The transfer of energy from the translational to the internal degrees of freedom or vice versa is analyzed for radiatively assisted inelastic collisions among atoms in a gas. For a specific atomic-level configuration, it is shown that the absorption of a laser photon may induce a transition between two levels that are displaced by the collisional interaction (a dipole-dipole potential in this treatment) if a fraction of the kinetic energy of the atomic relative motion is simultaneously absorbed. The process thus results in a cooling of the atomic kinetic temperature. In other level configurations, energy goes in the opposite direction, with a heating of the kinetic temperature. This mechanism is described by means of the Wigner-function formalism, which allows a passing to the quasiclassical limit for the atomic motion in a simple way.
The authors introduce a model for radiative collisions which allows one to obtain a simple analytical expression for the transition probability. This model basically consists of an improvement to the Landau-Zener model, in order to obtain a more realistic representation of the Hamiltonian of the system throughout the collision. They apply the results to the problem of radiative collisions when the dipole-dipole interaction is responsible for the energy transfer and obtain an analytical expression for the cross section as a function of the frequency and intensity of the laser field. Their results are compared with experimental results and reasonable agreement is obtained.
We simulate collisions between two atoms, which move in an optical lattice under the dipole-dipole interaction. The model describes simultaneously the two basic dynamical processes, namely the Sisyphus cooling of single atoms, and the light-induced inelastic collisions between them. We consider the $J=1/\stackrel{\ensuremath{\rightarrow}}{2}J=3/2$ laser cooling transition for Cs and Na. We find that the hotter atoms in a thermal sample are selectively lost or heated by the collisions, which modifies the steady-state distribution of atomic velocities, reminiscent of the evaporative cooling process.
In this paper we derive the Fokker-Planck equation that describes the motion of a charged particle, trapped in a static harmonic potential and cooled by radiation pressure forces exerted by a laser beam. This equation is then discussed in both the classical and quantum regimes. The model adopted here is a simple one, in which one-dimensional motion and a two-level atom are assumed, and the time evolution of the system is described in the quasiclassical limit, in which the quantum nature of the photon exchanged between the particle and the field plays no role. We report relevant graphs for the loss of kinetic energy suffered by the particle in the cooling process and estimates of the lowest kinetic temperature that can be reached in these experiments.
A theoretical analysis of one-dimensional cooling of atoms is presented. The method of cooling is based on velocity-selective coherent population trapping. Both internal and translational degrees of freedom of the atoms are treated quantum mechanically. The analytic expression for atomic density matrix is obtained in the limit of large interaction time and small kinetic momentum of atom. It is demonstrated that: (i) there is a limit on the lowest temperature that can be achieved by such a method and it is determined by the small but finite rate of decay of the coherence between two low-lying states in the three-level Lambda -configuration; (ii) the fraction of atoms involved in the cooling process decreases to zero as the atom-field interaction time increases, because of the presence of such a relaxation which always takes place in real experimental systems.
When an atom or a molecule interacts with a light beam, the light emitted or absorbed carries valuable information about the atomic or molecular structure. This phenomenon underlies the whole field of spectroscopy. But the interaction of a photon with an atom can be used to manipulate the atom as well as to probe its structure. For example, in an approach called optical pumping, invented by Alfred Kastler, one can use the resonant exchange of angular momentum between atoms and polarized photons to align or orient the spins of atoms or to put them in nonequilibrium situations. In his original 1950 paper Kastler also proposed using optical pumping to cool and to heat the internal degrees of freedom, calling the phenomena the “effet luminofrigorique” and the “effet luminocalorique.” Another famous example of the use of photon-atom interaction to control atoms is laser cooling. This technique relies on resonant exchange of linear momentum between photons and atoms to control their external degrees of freedom and thus to reduce their kinetic energy. Laser cooling was suggested independently by Theodor Hänsch and Arthur Schawlow for neutral atoms and by David Wineland and Hans Dehmelt for trapped ions. In an article written three years ago for PHYSICS TODAY (June 1987, page 34), Wineland and Wayne Itano presented the principle of laser cooling and the potential applications of cold atoms to fields of physics such as ultrahigh resolution spectroscopy, atomic clocks, collisions, surface physics and collective quantum effects. At that time laser cooling had brought temperatures down to a few hundred microkelvin, but unexpected improvements during the last three years have dramatically lowered those temperatures to only a few microkelvin. We now feel we understand the new physical mechanisms responsible for these very low temperatures.