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Journal of the Optical Society of America B

Measurements of temperature and spring constant in a magneto-optical trap

Christopher D. Wallace, T. Dinneen, K. Y. N. Tan, Anantharaman Kumarakrishnan, P. L. Gould, Juha Javanainen

Published May 1, 1994• 93 citations
Publisher

Abstract

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.

DOI
10.1364/josab.11.000703

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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.
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.
We have measured the spring constant, friction parameter, and temperature of the motion of caesium atoms in a magneto-optical trap. The results are very different from those predicted by models based on the scattering force, which have been used up to now. We show that the behaviour can be understood in terms of the sub-Doppler cooling mechanisms which have been observed in molasses, involving atomic motion through a polarization gradient. These mechanisms can operate in a trap because the atoms congregate in a region of low magnetic field. The lowest temperature measured was (30 ± 15) μK.
Alkaline-earth-metal atoms present an ideal platform for exploring magneto-optic trap (MOT) dynamics, enabling unique and definitive tests of laser cooling and trapping mechanisms. We have measured the trapping beam intensity, detuning, magnetic-field gradient, trap density, and lifetime dependence of the spring constant $\ensuremath{\kappa}$ and damping coefficient $\ensuremath{\alpha}$ for a ${}^{1}{S}_{0}{\ensuremath{-}}^{1}{P}_{1}$ 88Sr{}^{88}\mathrm{Sr}88Sr MOT by fitting the oscillatory response of the atom cloud to a step-function force. We find that the observed behavior of $\ensuremath{\kappa}$ and $\ensuremath{\alpha}$ provide a unified and consistent picture of trap dynamics that agrees with Doppler cooling theory at the level of 1010%.10 Additionally, we demonstrate that the trapped atom temperature can be determined directly from measured value of $\ensuremath{\kappa}$ and the trap size, in excellent agreement with free-expansion temperature measurements. However, the experimentally determined temperature is much higher than Doppler cooling theory, implying significant additional heating mechanisms.
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.