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Journal of the Optical Society of America B

Measurements of temperature scaling laws in an optically dense magneto-optical trap

Andrejs Vorozcovs, M. Weel, Scott Beattie, S. Cauchi, Anantharaman Kumarakrishnan

Published May 1, 2005• 41 citations

Abstract

We have studied the temperature scaling laws for the conditions under which a cloud of trapped ^85Rb atoms in the sigma+/sigma- 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_0) proportional N^1/3 and as (T-T_0) proportional n^2/3, in a manner consistent with theoretical predictions. Here T_0 is defined as the equilibrium temperature of a low-density optical molasses. In the multiple-scattering regime we find that T proportional Omega^2/(delta Gamma), where Omega and delta are the Rabi frequency and the detuning of the trapping laser, respectively, and Gamma 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 approximately 0.1% by tracking the center of the cloud during ballistic expansion.

DOI: 10.1364/josab.22.000943

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We have studied the temperature scaling laws for the conditions under which a cloud of trapped ^85Rb atoms in the sigma+/sigma- 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_0) proportional N^1/3 and as (T-T_0) proportional n^2/3, in a manner consistent with theoretical predictions. Here T_0 is defined as the equilibrium temperature of a low-density optical molasses. In the multiple-scattering regime we find that T proportional Omega^2/(delta Gamma), where Omega and delta are the Rabi frequency and the detuning of the trapping laser, respectively, and Gamma 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 approximately 0.1% by tracking the center of the cloud during ballistic expansion.

We discuss a simple time of flight technique for measurement of temperature of a cold cloud in a magneto-optical trap (MOT). The technique is based on spatiotemporal fluorescence imaging of the cloud that is allowed to undergo one-dimensional expansion in the presence of the orthogonal two-dimensional configuration of laser beams by temporal modulation of a pair of counterpropagating trapping beams in the MOT. We show that, in the time scale 0< or =t<5 ms, the expansion of the cloud is ballistic and the temperature can be extracted from the time variation of the rms size of the cloud in the expansion direction. The reliability of the technique has been established by comparing the results with release and recapture method, and also by fitting them to the known temperature scaling law.

A cloud of ultracold atoms confined in a magneto-optical trap (MOT) has a temperature greater than that of a low-density vapour in the same light field. It has been observed (Drewsen M. et al., Appl. Phys. B , 59 (1994) 283) that this temperature excess is proportional to the cube root of the total number of trapped atoms ( N 1/3 ). We present an explanation for this effect in terms of the scattering which arises when photons spontaneously emitted by atoms have an appreciable probability of being reabsorbed within the cloud. This hypothesis has been tested by time-of-flight measurements of the temperature of clouds of atoms released from a MOT into 1-dimensional and 3-dimensional optical molasses in the σ + -σ - and lin ⊥ lin configuration.

We have measured the low-density characteristics of a magneto-optical trap for both isotopes of rubidium. Trapped-atom temperatures are measured by the time-of-flight technique and are similar to temperatures in optical molasses. They are below the Doppler limit in most cases and increase linearly with the ratio of laser intensity to laser detuning. A slight difference between the two isotopes is observed. The data agree well with three-dimensional, multistate, semiclassical simulations. Spring constants of the trap are inferred from careful measurements of the size of the trapped-atom cloud. The spring constant is seen to increase with intensity at low intensity, becoming independent of intensity at high intensity. This trend is consistent with sub-Doppler cooling mechanisms.

We present an investigation of the cesium magneto-optical trap, with particular regard to the best combination of atomic density and temperature that can be produced. Conditions in the trap depend on four independent parameters: the detuning and intensity of the light, the gradient of the magnetic field, and the number of atoms trapped. We have varied all these parameters and measured the temperature and density distribution of the trapped cloud. Both the nonlinear variation with position of the restoring force and the reabsorption of photons scattered in the cloud limit the maximum density, and we present an empirical model that takes this into account. This in turn limits the density in phase space \ensuremath{\rho} (defined as the number of atoms in a box with sides of one thermal de Broglie wavelength). We have observed a maximum \ensuremath{\rho}=(1.5\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$, with a spatial density of about 2\ifmmode\times\else\texttimes\fi{}

{10}^{11}

atoms/

{\mathrm{cm}}^{3}

.

Temperatures of rubidium atoms confined in a magneto-optical trap have been measured using time-of-flight. By varying the parameters of the trap, we find that lower temperatures are obtained with lower laser intensities, larger laser detunings, lower atomic densities, and with the 85 vs. the 87 isotope. Temperatures are below the Doppler limit (140 {mu}K for Rb) in most cases. By measuring the size of the trapped cloud as well as the temperature, we can infer the spring constant of the trap. For comparison purposes, we can measure temperatures in optical molasses by turning off the magnetic field of the trap.

This thesis presents the study of atomic cloud density and temperature in a magneto-optical trap (MOT). The purpose is to find the method in obtaining the densest and coldest cloud the setup can produce. In steady state trap, the highest atomic density possible is that of a cloud in multiple scattering regime where a repulsive force between atoms sets a limit to the density. The number of atoms loaded into the trap is controlled by the trapping beam intensity which also changes the temperature. Therefore the trap density and temperature cannot be controlled separately. The cloud compression is studied as a method of increasing atomic density above what is possible in steady state trap without noticeable influence on the cloud temperature. Cloud compression is also found when the cloud is translated by changing the magnetic field zero-point although in a less predictable fashion than the compression.