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Journal of Optics B Quantum and Semiclassical Optics

Time-of-flight measurement of the temperature of cold atoms for short trap-probe beam distances

Tomasz Brzozowski, Maria Maczynska, M. Zawada, Jerzy Zachorowski, Wojciech Gawlik

Published Jan 14, 2002• 83 citations
Publisher

Abstract

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.

DOI
10.1088/1464-4266/4/1/310

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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.
The basic model and the experimental measurement method of short-distance time-of-flight absorption spectra for determining the temperature of cold atoms are described. Based on the realization of temperature measurement of cold cesium atoms in a magneto-optical trap，the influences of measurement errors of the three experimental parameters，namely the falling distance h，the initial Gaussian radius σ0 of the cold cloud, and the Gaussian radius σp of probe beam, on the determination of temperature have been analyzed and compared.
We report the basic idea and experimental demonstration of measuring the temperature of cold cesium atomic cloud confined in a magneto-optical trap (MOT) by analyzing absorption spectrum observed in the short-distance time-of-flight (TOF) method. Compared with the conventional TOF scheme, we measure the temperature of cold atomic cloud in MOT by short-distance TOF method for our small vapor cell. If the cold atomic cloud is released, it will fall and expand due to gravity and its initial velocity distribution. Utilizing a cylindrical resonant probe beam positioned several millimeters beneath the MOT (in this paper, we analyzed the cases for 3mm, 5mm, and 8mm of center-to-center distance between the MOT region and the probe beam, respectively), we can record the short-distance TOF absorption spectrum with a photodiode when cold atoms go through the probe region. Analysis of the short-distance TOF absorption spectrum yields the effective temperature of the cold cloud in MOT.
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.
The error analyzing and comparing between theoretical and approximate simulated formula in measuring the temperature of cold atoms with short-distance time-of-flight(TOF) method are reported.The results shows that the approximate simulated formula aqrees well with the theoretical simulated formula when the ratio of the radius of probe to the cold atoms is less than 0.2.When the ratio of the radius of probe to the cold atoms approachs 0.5,the error between the approximate simulated formula with the theoretical simulated formula for TOF absorption signal is significant.
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.
The Gaussian radius and temperature of cold atomic cloud are important parameters in describing the state of cold atoms. The precise measuring of these two parameters is of great significance for studying the cold atoms. In this paper, we propose a new method named knife-edge to measure the Gaussian radius and temperature of the cold atomic cloud. A near-resonant and supersaturated laser beam, whose size is controlled by a knife-edge aperture, is used to push away the cold atoms in the free falling process of cold atomic cloud. By detecting the intensity of fluorescence signal, the numbers of residual atoms under different-sized near-resonant beams can be obtained. According to the characteristic of cold atoms′ distribution, we construct a theoretical model to derive the Gaussian radius of cold atomic cloud from the recorded residual atom number and near-resonant beam size. Since the Gaussian radius and temperature of cold atomic cloud are associated with each other, we can finally obtain the temperature of cold atomic cloud through the recorded residual atom number and beam size. By using this method, we successfully measure the Gaussian radii of cold atomic cloud at the heights of 10 mm and 160 mm below the center of 3D-MOT (three dimensional magneto-optical trap) to be (1.54 ± 0.05) mm and (3.29 ± 0.08) mm, respectively. The corresponding temperature of cold atomic cloud is calculated to be (7.50 ± 0.49) μK, which is well consistent with the experimental result obtained by using the time-of-flight method under the same condition. This experiment is conducted on the platform of Cesium atomic fountain clock of National Time Service Center, China.