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arXiv:1305.5033 · Ukrainian Journal of Physics

Momentum Diffusion of Atoms and Nanoparticles in an Optical Trap Formed by Sequences of Counter-Propagating Light Pulses

V. I. Romanenko, A.V. Romanenko, Ye. G. Udovitskaya, Леонід Петрович Яценко

Published May 1, 2013• 5 citations
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Abstract

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”.

DOI
10.15407/ujpe58.05.0438

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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”.
The analysis of atomic motion in the field formed by sequences of counterpropagating light pulses reveals the conditions when the field creates the trap in which the temperature of trapped atoms drops to the Doppler limit. The atomic state is described by the wave function using the Monte Carlo wave function method, whereas the atomic motion is considered in the framework of classical mechanics. Laser cooling and trapping is achieved only for non-resonant atom–field interaction. The pulse area does not matter for this effect, in contrast to the repetition period. When the motion of a trapped atom is slowed down, it oscillates around the anti-nodes of a non-stationary standing wave formed by the counterpropagating light pulses at the point where they ‘collide’. The discussed trap is also applicable for trapping and cooling of the molecules for which the matrix of Frank–Condon factors is almost diagonal.
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.
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.
A new trap for atoms and small particles based on the interaction between an atom and the field of counter-propagating light pulses that are partially superposed in time has been proposed. A substantial difference from the known analogs consists in that the atom-field interaction is close to the adiabatic one, which allows a considerably higher momentum to be transferred to the atom within the same time interval and makes the trap smaller in size. It has been shown that, owing to the dependence of the light pressure force on the atom velocity, the atomic ensemble is cooled at its interaction with the field.
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.
We discuss a possible one-dimensional trapping and cooling of atoms and molecules due to their nonresonant interaction with counterpropagating light pulse trains. The counterpropagating pulses form a one-dimensional trap for atoms and molecules and a properly chosen carrier frequency detuning from the transition frequency of the atoms or molecules keeps the temperature of the atomic or molecular ensemble close to the Doppler cooling limit. The calculation by the Monte Carlo wave-function method is carried out for the two-level and three-level schemes of the atom's and the molecule's interaction with the field, respectively. The models discussed are applicable to atoms and molecules with almost diagonal Frank-Condon factor arrays. Illustrative calculations are carried out for ensemble-averaged characteristics for sodium atoms and SrF molecules in the trap. The potential for the nanoparticle light pulses's trap formed by counterpropagating light pulse trains is also discussed.