We report our experimental measurements and theoretical analysis of the position response function of a cloud of cold atoms residing in the viscous medium of an optical molasses and confined by a magneto-optical trap (MOT). We measure the position response function by applying a transient homogeneous magnetic field as a perturbing force. We observe a transition from a damped oscillatory motion to an over-damped relaxation, stemming from a competition between the viscous drag provided by the optical molasses and the restoring force of the MOT. Our observations are in both qualitative and quantitative agreement with the predictions of a theoretical model based on the Langevin equation. As a consistency check, and as a prototype for future experiments, we also study the free diffusive spreading of the atomic cloud in our optical molasses with the confining magnetic field of the MOT turned off. We find that the measured value of the diffusion coefficient agrees with the value predicted by our Langevin model, using the damping coefficient. The damping coefficient was deduced from our measurements of the position response function at the same temperature.
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