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arXiv:2011.11312 · Physical Review A

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

V. I. Romanenko, Леонід Петрович Яценко

Published Apr 9, 2021• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.103.043104

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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 \ensuremathπ\ensuremath{\pi}\ensuremathπ 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.
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.
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.
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
The motion of atoms and nanoparticles in a trap formed by sequences of counter-propagating light pulses has been analyzed. The atomic state is described by a wave function constructed with the use of the Monte Carlo method, whereas the atomic motion is considered in the framework of classical mechanics. The effects of the momentum diffusion associated with the spontaneous radiation emission by excited atoms and the pulsed character of the atom-to-field interaction on the motion of a trapped atom or nanoparticle are estimated. The motion of a trapped atom is shown to be slowed down for properly chosen parameters of the atom-to-field interaction, so that the atom oscillates around the antinodes of a non-stationary standing wave formed by counter-propagating light pulses at the point where they “collide”.
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.
In quantum optical problems involving the interaction of atoms with laser fields, the atoms are usually considered being stationary during the interaction. Since every photon has a momentum, the atomic momentum (motion) can be changed in the process of absorption and emission of photons. This may force a stationary atom to move or to change momentum of an already moving atom. Therefore, the dynamical behaviour of atoms can be varied by the interaction with a radiation field. For a weak driving field, the influence of this field on the atomic motion can be neglected. However, the intensities of laser fields are generally very strong, and then the motion of the atoms can be considerably changed by the laser field. Here, we discuss this aspect, especially the effect of a driving field on the motion of atoms and the atomic momentum distribution. In particular, we will consider diffraction of atoms by a standing-wave laser field due to an exchange of momentum with the photons of the wave, and radiation force on atoms driven by a running-or standing-wave laser field.