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Japanese Journal of Applied Physics

Velocity Fluctuation of Cold Cs Atoms in a Travelling Plane Electromagnetic Wave

Soo Chang, Jae Heung Jo, Ho Seong Lee

Published Jun 1, 1998• 0 citations
Publisher

Abstract

We theoretically investigated the transverse and longitudinal velocity fluctuations of initially cooled Cs atoms below (or close to) the Doppler limit as the atoms were slowly accelerated in a travelling plane electromagnetic wave. We first derived a kinetic equation describing the atomic motion in the first order rate equation approximation and then numerically solved the equation. Increase or decrease in the longitudinal fluctuation was shown to depend upon the initial atom temperature and the detuning, while the tranverse fluctuation routinely increased with interaction time.

DOI
10.1143/jjap.37.3548

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We theoretically investigated the transverse and longitudinal velocity fluctuations of initially cooled Cs atoms below (or close to) the Doppler limit as the atoms were slowly accelerated in a travelling plane electromagnetic wave. We first derived a kinetic equation describing the atomic motion in the first order rate equation approximation and then numerically solved the equation. Increase or decrease in the longitudinal fluctuation was shown to depend upon the initial atom temperature and the detuning, while the tranverse fluctuation routinely increased with interaction time.
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In this paper we discuss the effect of scattered radiation generated by a gas of cold atoms on the temperature of the gas. We show that by treating the reradiated field of the atoms as a fluctuating background field we can derive a master equation for a single atom where the effect of the surrounding medium is included in an effective relaxation operator. This relaxation operator is of second order in the interaction with the medium and in the binary-collision approximation can be written as the sum of two-body interactions with a correlation time equal to the natural lifetime of the atomic transition. The effect of the medium on the two most important sub-Doppler cooling mechanisms, Sisyphus and motion-induced orientation cooling, is investigated analytically in a one-dimensional model. In this we restrict ourselves to the limit of low saturation, weak background field and take the rate-equation limit for the collision operator. We find that both mechanisms are very sensitive to such a background field and that the temperature increases approximately as the number of atoms to the one-third power.
The effect of field fluctuations on the motion of a two-level atom in resonant laser radiation is investigated theoretically. The internal motion of the atom is treated quantum mechanically (optical Bloch equations); the translational motion, which is coupled to the internal motion, is treated classically (Ehrenfest's theorem); and the fluctuating radiation is treated as a classical electromagnetic wave with stochastic phase (phase-diffusion model). An expression for the radiation force and equations of motion for the ensemble-averaged Bloch vector are derived and used to calculate (i) the radiation force in a plane running wave, (ii) the steady-state radiation force in a general standing wave, and (iii) the dissipative force in a plane standing wave in the limit of strong phase fluctuations. In case (iii) it is found that the atomic velocity is damped when the radiation is tuned above resonance, which is opposite to the case of a weak coherent standing wave, in which damping occurs for radiation tuned below resonance. It is shown that fluctuations have a substantial effect on the radiation force only when the spectral width of the radiation approaches or exceeds the spontaneous emission rate.
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