We have studied the temperature scaling laws for the conditions under which a cloud of trapped atoms in the configuration makes the transition from the temperature-limited regime to the multiple-scattering regime. Our experimental technique for measuring temperature relies on measuring the ballistic expansion of the cloud after turning off the confining forces and imaging the cloud size as a function of time with two CCD cameras. In the transition regime, the temperature T is shown to depend on the number of atoms N and the peak density n as and as , in a manner consistent with theoretical predictions. Here is defined as the equilibrium temperature of a low-density optical molasses. In the multiple-scattering regime we find that , where Ω and δ are the Rabi frequency and the detuning of the trapping laser, respectively, and Γ is the natural linewidth of the cycling transition. We have also measured the ratio of temperatures along the axial and radial directions of the magnetic field gradient coils and find that the temperature is isotropic only if the intensities of the three orthogonal trapping beams are equal, and that the ratio is generally independent of trapping laser intensity and magnetic field gradient. Finally we demonstrate a measurement of the gravitational acceleration precise to by tracking the center of the cloud during ballistic expansion.
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