Effect of scattered radiation on sub-Doppler cooling

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Abstract
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.