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Ukrainian Journal of Physics

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

V. I. Romanenko, O. G. Udovytska, V. M. Khodakovskii, Леонід Петрович Яценко

Published Aug 2, 2018• 2 citations
Publisher

Abstract

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.

DOI
10.15407/ujpe63.7.616

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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 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 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.
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 apply Monte Carlo wave function method and classical mechanics to description of the atomic motion in the field of laser radiation. Simultaneous use of quantum and classical mechanics for description of inner and translational motion avoids quantization of the translational degrees of freedom. The calculation are carried out for the example of atomic motion in the field of counter-propagating laser waves, one of which repeats the other. It is shown that such scheme of the atom-field interaction leads to confinement of atoms and their cooling by the same laser beams for proper the atom-field interaction parameters. The cases of laser pulses, bichromatic waves and stochastic field (the model of coloured noise) are analyzed.
We present both analytical results and numerical simulations that describe the light pressure on atoms in the fields of counterpropagating waves whose amplitudes and phases are described as stochastic processes. We show that, just as with the light pressure exerted in the field of two counterpropagating bichromatic waves, the light pressure on an atom in counterpropagating stochastic waves may considerably exceed the pressure exerted in the field of a single running wave, when one of them repeats the other with some delay, We also discuss the interaction of an atom with two counterpropagating waves when one of them is monochromatic and the other one has a stochastic phase.
In relation to the newly discovered laser cooling mechanisms, the authors have studied the momentum diffusion of an atom with a j (ground)-j+1 (excited) state transition (j not=0), interacting with two counterpropagating sigma +- sigma - plane waves. A correlation between successive photon absorptions via the multi-sublevel internal atomic structure leads to a large increase of the momentum diffusion coefficient. In a simple probabilistic picture this enhanced diffusion is interpreted as a random walk with effective steps much larger than the one-photon recoil momentum k. For j=1 the authors report the results of a complete calculation (i.e. with a quantum description of the internal atomic state) showing a marked dependence upon the velocity of the atom as well as on the parameters of the laser field (detuning and power).