Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics B Atomic Molecular and Optical Physics

Momentum diffusion of atoms moving in laser fields

K Berg-Sorenson, Yvan Castin, Ejvind Bonderup, Klaus Mølmer

Published Oct 28, 1992• 37 citations
Publisher

Abstract

The momentum diffusion coefficient, as a function of position and velocity, is discussed for two-state atoms travelling through a standing-wave laser field. Equations leading to the force and diffusion coefficient have been obtained by Minogin. The authors present an alternative derivation, based on moments of the Wigner function and give numerical solutions in terms of matrix continued fractions. In strong fields, the discussion is supplemented by a derivation of the diffusion coefficient within the dressed-atom basis, and a picture of the diffusion mechanism emerges which is quite different from the one at low intensities. Calculated forces and diffusion coefficients are used in a Fokker-Planck equation to obtain stationary atomic velocity distributions.

DOI
10.1088/0953-4075/25/20/016

Related papers

Correlation-function approach to the momentum diffusion of atoms moving in standing waves

G. S. Agarwal, Klaus Mølmer

We consider the momentum diffusion of atoms moving in a standing-wave laser field. We show how the correlation-function approach as originally applied to atoms at rest can be generalized to derive the velocity dependence of the momentum diffusion coefficient in standing waves, and that it gives results in agreement with the transport-equation approach to laser cooling. As an example we apply our calculations to determine the achievements of laser cooling in intense fields where cooling may occur around a nonvanishing velocity. Here we obtain temperatures which are 30% lower than the corresponding minimum obtained around zero velocity. Our explicit calculations involve usage of the optical Bloch equations, the quantum regression theorem, and the matrix continued-fraction method.

Physical Review A•Jun 1, 1993•13 citations

Atomic motion in a high-intensity standing wave laser field

L.F. Saez Ramdohr

This work discusses the effect of a high-intensity standing wave laser field on the motion of neutral atoms moving with a relatively high velocity. The analysis involves a detailed calculation of the force acting on the atoms and the calculation of the diffusion tensor associated with the fluctuations of the quantum force operator. The high-intensity laser field limit corresponds to a Rabi frequency much greater than the natural rate of the atom. The general results are valid for any atomic velocity. Results are then specialized to the case of slow and fast atoms where the Doppler shift of the laser frequency due to the atomic motion is either smaller or larger than the natural decay rate of the atom. The results obtained for the force and diffusion tensor are applied to a particular ideal experiment that studies the evolution of a fast atomic beam crossing a high-intensity laser beam. The theories developed previously, for a similar laser configuration, discuss only the low atomic velocities case and not the more realistic case of fast atoms. Here, an approximate solution of the equation for the distribution is obtained. Starting from the approximate distribution function, the deflection angle and dispersion angle for themore » atomic beam with respect to the free motion are calculated.« less

•Jan 1, 1987•0 citations

Evolution of the velocity distribution of atoms under the action of the bichromatic force

V. I. Romanenko, Леонід Петрович Яценко

We study numerically the evolution of the velocity distribution of atoms under the action of the bichromatic force. The comparison of the time dependencies of the distribution width and the average acceleration of atoms reveals the correlation of these quantities. We show that the estimation of the momentum diffusion coefficient on the basis of the analogy between the interaction of atoms with the counterpropagating bichromatic waves and the interaction of atoms with the counterpropagating sequences of the $\ensuremath{\pi}$ pulses roughly corresponds to the results of numerical calculations. To separate the influence of the momentum diffusion on the evolution of atomic momentum distribution from the influence of the time-dependent Doppler shift, we study the motion of a ``heavy'' atom, for which the velocity change during the interaction of an atom with the field can be neglected. Provided that the parameters of the atom-field interaction are optimal, we show that the momentum diffusion coefficient is proportional to the intensity of the laser radiation. We used the Monte Carlo wave-function method for the numerical simulation of the atomic motion.

arXiv:2011.11312•Physical Review A•Apr 9, 2021•3 citations

Radiation Pressure on Atoms: Laser Cooling and Intense Field Effects.

Michael S. Lubell, Marvin H. Mittleman, Kenneth H. Rubin

It is conventional to describe the motion of an atom in a laser field (and other D.C fields) by a Fokker-Planck equation which is characterized by a force and a diffusion coefficient. Gordon and Ashkin have obtained a result for the diffusion coefficient in a spherically symmetric approximation. We have recently treated it as a second order tensor and have gotten a different result. The tensor has three terms. The leading term arises from the recoil of the atom during fluorescence, the second comes from gradients of the laser intensity and the D.C. fields and the last comes from a combination of the recoil term and gradients. The trace of our leading term agrees with the result of Gordon and Ashkin but there is no agreement at all with the other terms. The calculation was performed for a traveling wave laser and is being extended now to a standing wave laser by a graduate student. The experiment being undertaken here will use a swept laser frequency to compensate for the change in resonance frequency (due to the Doppler effect) of the atom as it slows down.

Progress Report•May 21, 1984•0 citations

The light pressure force and the friction and diffusion coefficients for atoms in a resonant nonuniformly polarized laser field

A. V. Bezverbnyĭ, Прудников Олег Николаевич, А. В. Тайченачев +2 more

The motion of slow atoms with degenerate energy levels in a resonant, nonuniformly polarized laser field is described by the Fokker-Planck equation for the atomic distribution function in phase space in terms of the semiclassical approach. Field gradient expansions are used for the spatially nonuniform coefficients of the equation. For closed atomic transitions J g =J→J e =J+1 (J g and J e are the total angular momenta of the ground and excited states, respectively), new analytical results are presented for the light pressure force and the friction and diffusion coefficients in momentum space. These results allow the kinetic effects (laser cooling, localization in optical potential wells, etc.) in a field of arbitrary one-, two-, or three-dimensional configuration to be investigated. In several cases, the new contributions to the friction coefficient are interpreted qualitatively.

Journal of Experimental and Theoretical Physics•Mar 1, 2003•20 citations

Atomic Momentum Diffusion in the Field of Counter-Propagating Stochastic Light Waves

V. I. Romanenko, O. G. Udovytska, V. M. Khodakovskii +1 more

The momentum diffusion of atoms in the field of two counter-propagating stochastic waves, one of which reproduces the other one with a certain time delay, has been studied. It is shown that the parameters of atom-field interaction, at which the light pressure force is maximum, correspond to the increasing momentum diffusion coefficient. In the case of high-intensity field described by the stochastic field model, the momentum diffusion coefficient was found to be proportional to the square root of the field autocorrelation time. The wave function describing the inner state of atoms is modeled, by using the Monte-Carlo method. Numerical calculations are carried out for cesium atoms.

Ukrainian Journal of Physics•Aug 2, 2018•2 citations
The momentum diffusion coefficient, as a function of position and velocity, is discussed for two-state atoms travelling through a standing-wave laser field. Equations leading to the force and diffusion coefficient have been obtained by Minogin. The authors present an alternative derivation, based on moments of the Wigner function and give numerical solutions in terms of matrix continued fractions. In strong fields, the discussion is supplemented by a derivation of the diffusion coefficient within the dressed-atom basis, and a picture of the diffusion mechanism emerges which is quite different from the one at low intensities. Calculated forces and diffusion coefficients are used in a Fokker-Planck equation to obtain stationary atomic velocity distributions.
We consider the momentum diffusion of atoms moving in a standing-wave laser field. We show how the correlation-function approach as originally applied to atoms at rest can be generalized to derive the velocity dependence of the momentum diffusion coefficient in standing waves, and that it gives results in agreement with the transport-equation approach to laser cooling. As an example we apply our calculations to determine the achievements of laser cooling in intense fields where cooling may occur around a nonvanishing velocity. Here we obtain temperatures which are 30% lower than the corresponding minimum obtained around zero velocity. Our explicit calculations involve usage of the optical Bloch equations, the quantum regression theorem, and the matrix continued-fraction method.
This work discusses the effect of a high-intensity standing wave laser field on the motion of neutral atoms moving with a relatively high velocity. The analysis involves a detailed calculation of the force acting on the atoms and the calculation of the diffusion tensor associated with the fluctuations of the quantum force operator. The high-intensity laser field limit corresponds to a Rabi frequency much greater than the natural rate of the atom. The general results are valid for any atomic velocity. Results are then specialized to the case of slow and fast atoms where the Doppler shift of the laser frequency due to the atomic motion is either smaller or larger than the natural decay rate of the atom. The results obtained for the force and diffusion tensor are applied to a particular ideal experiment that studies the evolution of a fast atomic beam crossing a high-intensity laser beam. The theories developed previously, for a similar laser configuration, discuss only the low atomic velocities case and not the more realistic case of fast atoms. Here, an approximate solution of the equation for the distribution is obtained. Starting from the approximate distribution function, the deflection angle and dispersion angle for themore » atomic beam with respect to the free motion are calculated.« less
We study numerically the evolution of the velocity distribution of atoms under the action of the bichromatic force. The comparison of the time dependencies of the distribution width and the average acceleration of atoms reveals the correlation of these quantities. We show that the estimation of the momentum diffusion coefficient on the basis of the analogy between the interaction of atoms with the counterpropagating bichromatic waves and the interaction of atoms with the counterpropagating sequences of the $\ensuremath{\pi}$ pulses roughly corresponds to the results of numerical calculations. To separate the influence of the momentum diffusion on the evolution of atomic momentum distribution from the influence of the time-dependent Doppler shift, we study the motion of a ``heavy'' atom, for which the velocity change during the interaction of an atom with the field can be neglected. Provided that the parameters of the atom-field interaction are optimal, we show that the momentum diffusion coefficient is proportional to the intensity of the laser radiation. We used the Monte Carlo wave-function method for the numerical simulation of the atomic motion.
It is conventional to describe the motion of an atom in a laser field (and other D.C fields) by a Fokker-Planck equation which is characterized by a force and a diffusion coefficient. Gordon and Ashkin have obtained a result for the diffusion coefficient in a spherically symmetric approximation. We have recently treated it as a second order tensor and have gotten a different result. The tensor has three terms. The leading term arises from the recoil of the atom during fluorescence, the second comes from gradients of the laser intensity and the D.C. fields and the last comes from a combination of the recoil term and gradients. The trace of our leading term agrees with the result of Gordon and Ashkin but there is no agreement at all with the other terms. The calculation was performed for a traveling wave laser and is being extended now to a standing wave laser by a graduate student. The experiment being undertaken here will use a swept laser frequency to compensate for the change in resonance frequency (due to the Doppler effect) of the atom as it slows down.
The motion of slow atoms with degenerate energy levels in a resonant, nonuniformly polarized laser field is described by the Fokker-Planck equation for the atomic distribution function in phase space in terms of the semiclassical approach. Field gradient expansions are used for the spatially nonuniform coefficients of the equation. For closed atomic transitions J g =J→J e =J+1 (J g and J e are the total angular momenta of the ground and excited states, respectively), new analytical results are presented for the light pressure force and the friction and diffusion coefficients in momentum space. These results allow the kinetic effects (laser cooling, localization in optical potential wells, etc.) in a field of arbitrary one-, two-, or three-dimensional configuration to be investigated. In several cases, the new contributions to the friction coefficient are interpreted qualitatively.
The momentum diffusion of atoms in the field of two counter-propagating stochastic waves, one of which reproduces the other one with a certain time delay, has been studied. It is shown that the parameters of atom-field interaction, at which the light pressure force is maximum, correspond to the increasing momentum diffusion coefficient. In the case of high-intensity field described by the stochastic field model, the momentum diffusion coefficient was found to be proportional to the square root of the field autocorrelation time. The wave function describing the inner state of atoms is modeled, by using the Monte-Carlo method. Numerical calculations are carried out for cesium atoms.