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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Reliable algorithm for estimation of the temperature of cooled atoms

Elena Stoykova, Jean-Claude Keller

Published May 7, 1999• 0 citations
Publisher

Abstract

A reliable algorithm for temperature estimation of cooled atoms is proposed and investigated by 2D-Monte-Carlo simulation for the ensemble of 133Cs atoms provided time-of-flight (TOF) and spatial distributions of falling atoms are found in two planes below the atomic cloud using fluorescence or transmission measurements. We assume that the atoms, being normally distributed in space, are left to fall freely at a certain moment and we suppose that collisions between them do not cause substantial distortion of the ideal TOF-distribution.

DOI
10.1117/12.347616

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The time-of-flight (TOF) method is one of the most common ways to measure the temperature of cold atoms. In the cold atomic fountain setup, the geometry of the probe beam will introduce the measurement errors to the spatial distribution of cold atomic cloud, which will lead to the measurement errors on atomic temperature. Using deconvolution, we recover the atomic cloud profile from the TOF signal. Then, we use the recovered signals other than the TOF signals to obtain a more accurate atomic temperature. This will be important in estimating the effects of cold atom collision shift and the shift due to transverse cavity phase distribution on an atomic fountain clock.
We report a novel method for temperature measurement in a cesium fountain clock and experimental investigation about its dependence respect to diverse operational parameters. The temperature of the Cs atomic cloud is inferred from the width of the velocity distribution, which is obtained from two measurements in different regions of the spatial distribution of the atomic cloud using the time of flight (TOF) method. We use a simple process to determine the velocity distribution by calculating the square speed point by point from these two TOF signals. This new method is demonstrated to characterize the temperature of the Cs atoms on the CENAM Cs fountain clock. The minimum temperature reached in the CENAM Cs fountain clock is 612(193) nK.
We analyse the time-of-flight method of measuring the temperature of cold trapped atoms in the specific case of short distances of the probe beam from the trap centre and finite atomic cloud size. We theoretically examine the influence of the probe beam shape and its distance from the initial position of the cloud on the temperature evaluation. These results are then verified with a three-dimensional Monte Carlo simulation and applied to our experimental data to show that the proposed procedure allows accurate and reliable determination of the temperature.
We report an alternative algorithm to the deconvolution method for obtaining Gaussian velocity distribution for temperature measurements in Cs fountain clocks. We estimate the velocity distribution of the cloud of cold atoms from time-of-flight signals, at different times, by calculating the square speed point by point (PBP). Then, the temperature of the Cs atomic cloud is inferred from the width (e-1/2) of the velocity distribution. We have done an exhaustive comparison of the PBP algorithm with the deconvolution method using both theoretical and experimental data for Gaussian velocity distributions. Finally, when comparing the process to obtain the velocity distribution in both the PBP algorithm and the deconvolution method, it is found that our approach is easier to implement and automate.
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Based on the real sense of the time-of-flight , we demonstrate an alternative method of measuring the temperature of cold atoms in magneto-optical traps (MOTs) using a high-finesse optical microcavity, which acts as a pointlike single-atom counter. A cloud of atoms trapped in magneto-optical traps is positioned about 5 mm above the cavity, and the atoms fall freely down through the cavity. The temperature of the cold atoms in the MOT is determined by counting the exact arrival times of the single atoms. A theoretical model based on a ballistic expansion of a cloud of trapped atoms falling in the earth’s gravitational field is used to fit the probability distribution of atom arrivals, and the fittings agree very well with the experimental results. This method could be used for systems with little room, where an extra probe beam is hard to involve, or with fewer atoms initially.