We have studied the temperature scaling laws for the conditions under which a cloud of trapped 85 Rb 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 ͑T − T o ͒ ϰ N 1/3 and as ͑T − T o ͒ ϰ n 2/3 , in a manner consistent with theoretical predictions. Here T o is defined as the equilibrium temperature of a low-density optical molasses. In the multiple-scattering regime we find that T ϰ⍀ 2 / ͑␦⌫͒, where ⍀ and ␦ are the Rabi frequency and the detuning of the trapping laser, respectively, and ⌫ 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 Ϸ0.1% by tracking the center of the cloud during ballistic expansion.

We describe an inexpensive lock-in amplifier that can be built using discrete off-the-shelf RF components and home-built analog circuits. This lock-in has been used in a feedback loop to lock the frequency of a laser to an atomic transition. The frequency stability was tested by trapping rubidium atoms. The feedback loop involves obtaining a modulated saturated absorption signal from a vapor cell using an acousto-optic modulator to modulate the laser frequency. The absorption signal is sent to the lock-in to generate an error signal, proportional to the first derivative of the absorption, which is fed back to the laser to complete the feedback loop. We also demonstrate a simplified optical setup for viewing the saturated absorption spectrum. In this case, the signal consists of narrow saturated absorption spectra riding on top of a Doppler-broadened pedestal. We show that it is possible to greatly reduce the effect of this background and lock the laser to the atomic resonance by modifying the home-built lock-in to generate an error signal proportional to the third derivative of the absorption. The results of this work can be adapted for advanced undergraduate laboratory work.PACS Nos.: 01.50Pa, 07.50.–e, 42.62Fi, 42.60Fc

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Abstract:We determine the absolute density of a sample of laser-cooled atoms in a twolevel system by recording the absorption spectrum of the 85 Rb 5S 1/2 (F = 3, m f = 3) → 5P 3/2 (F = 4, m f = 4) transition. Trapped atoms were prepared in the (F = 3, m f = 3) ground state through optical-pumping techniques. We compare our results with an independent measure of the density that relies on a direct measurement of the number of atoms and size of the atomic sample. We also study the contributions of power broadening, laser line width, and Doppler broadening to the measured absorption spectrum. Our studies suggest that the natural line width (∼6 MHz) can be measured to a precision of less than ∼50 kHz if the laser line width is measured in real-time with a high-finesse Fabry-Perot cavity.