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Acta Sinica Quantum Optica

The Error Analyzing and Comparing between Theoretical and Approximate Simulated Formula in Measuring The Temperature of Cold Atoms with Short-distance Time-of-flight Method

Hai Wang

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

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.

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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 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.
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 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 experimental setup for cooling and trapping~(87)Rb atoms in magneto-optical trap(MOT) and the process of them are briefly introduced in this paper.The number of cold atoms is measured by detecting the fluorescence emitted from~(87)Rb atoms.The laser probe beam is set at the positions which are 4mm,7mm,10mm below the atoms cloud,the short-distance time-of-flight(TOF) Absorption signals are obtained during the falling of atoms.The average temperature of cold atoms is obtained by numerical simulating.The results show that the number of cold atoms is about 10~(9),the density is about 10~(11)/cm~3 and the cooling temperature of atomic cloud is about 200 μK,such cold atoms can be used as good EIT medium.
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.