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Physical Review A

Atomic-beam cooling: A simulation approach

R. Blatt, Wolfgang A. Ertmer, P. Zoller, J. L. Hall

Published Oct 1, 1986• 31 citations
Publisher

Abstract

Laser cooling af atoms in an atomic beam is studied theoretically by using a simulation approach derived from a pure-state analysis of resonant radiation pressure. Detailed numerical results are presented discussing the form of the atomic velocity distribution (and its minimum achievable width) and effects due to the spatial (focusing) and frequency variation of a Gaussian laser beam. A comparison of these results with recent experiments is given.

DOI
10.1103/physreva.34.3022

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Laser cooling af atoms in an atomic beam is studied theoretically by using a simulation approach derived from a pure-state analysis of resonant radiation pressure. Detailed numerical results are presented discussing the form of the atomic velocity distribution (and its minimum achievable width) and effects due to the spatial (focusing) and frequency variation of a Gaussian laser beam. A comparison of these results with recent experiments is given.
The present state of research on the cooling of atomic ensembles by means of laser radiation pressure is discussed. First the basic theory of resonance radiation pressure is reviewed. The effect of recoil on the drift and fluctuations of the momentum of an atom interacting with resonance radiation is examined. There is an analysis of the forces acting on an atom in some simple light fields: a traveling plane wave, a Gaussian beam, and counterpropagating Gaussian beams. The review then focuses on the monochromatization of atoms by resonance radiation pressure and related methods for laser cooling of atoms. The roles played by the radiation pressure force and by momentum diffusion in shaping the narrow velocity distributions of the ensemble of atoms are analyzed. The lowest temperature obtainable in the radiation cooling of atoms is estimated. The basic experimental methods for laser cooling of atomic beams are described. Problems of the three-dimensional cooling of atomic ensembles and problems of localizing cold atoms in light fields, steady-state magnetic fields, and electrostatic fields are discussed. The review concludes with a discussion of some applications of cold atoms in high-precision spectroscopy, frequency standards, and atomic physics.
Recent advances in experimental laser cooling have shown the possibility of stopping an atomic beam using the light pressure force of a counter-propagating laser wave. As an application to laser cooling, it is proposed to build a single frequency cesium laser that has a narrow linewidth. Laser cooling techniques are used to cool an atomic beam of cesium to an average velocity of 5 m/s, corresponding to a temperature of 0.2°K. Expressions of the basic forces that a laser wave exerts on atoms are derived according to a semi-classical approach. The experimental problems and methods of avoiding these problems are treated in detail. A computer Monte-Carlo simulation is used to discuss the feasibility of building the proposed laser. This simulation was done for an ensemble of 10,000 atoms of cesium, and it included the effects of the gravitational force and the related experimental variables. The possibility of building single frequency lasers that use a cooled medium of noble gases, and many other applications of laser cooling are briefly discussed at the end of this work.
We propose an efficient method of cooling atoms in a strong Gaussian standing wave. The steep gradients of the atomic potential energy give rise to large dipole forces, which can be much stronger than the maximum radiation pressure force and can therefore stop atoms in a much shorter distance. We have simulated the cooling process using a semi-classical Monte- Carlo method, which includes the radial motion, in addition to the motion along the beams. Both motions are calculated directly without separation the dynamics into force and diffusion terms. To cool a large range of atomic velocities the frame in which the standing wave is at rest was swept by changing the frequencies of the counter-propagating beams, in a similar way to the well-known chirp cooling technique using the radiation pressure force. If the curvature of Gaussian beams far from beam waist is employed the radial motion and velocities can be reduced even for the blue detuning comparing to the near waist case. The simulations show that it is possible to stop caesium atoms in a distance of several centimeters (the exact value depends on the laser power, beam waist radius and acceptable chirping force) starting from the most probable velocity at room temperature. Narrower radial and wider axial velocity distribution was obtained for red detuning comparing with the blue one.
The theory of the resonance radiation force is studied as it applies to the slowing of a two-level atom using a swept frequency laser. The theory is developed in detail for this case. A single partial differential equation called the Fokker-Planck equation is found to describe the atomic motion for many cases. This equation is solved numerically for a one dimensional geometry. Results from this numerical solution are found to be within 10% of experimental results. Analysis of this problem in one dimension leads to the prediction that for fixed amounts of frequency sweeping, a faster scan rate will yield smaller full width at half maximum (FWHM) spread in the velocity distribution for the atomic beam. This program also predicts that the atoms can be slowed arbitrarily close to 0 m/sec using this technique. The program used for this analysis is included. Keywords: Resonance radiation force; Slowing an atomic beam; Laser cooling of atoms; Fokker Planck equation; Thesis.