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IEEE Transactions on Instrumentation and Measurement

Alternative Algorithm for Temperature Measurements of Cold Atoms in Cs Fountain Clocks

Maria G. Espinosa-Olivares, Eduardo de Carlos-Lopez, José Mauricio López-Romero, Sergio López-López

Published Jan 28, 2015• 2 citations
Publisher

Abstract

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.

DOI
10.1109/tim.2015.2390956

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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.
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.
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 introduce a new approach to determine if a cloud of cold atoms has or not a unique, well-defined temperature. In the first case, the temperature can be determined using the width of the velocity distribution. However, the temperature in a cloud of cold atoms may not be well-defined if the velocity distribution does not turn out to be Gaussian. In this case, the width of the velocity distribution cannot be associated to a unique temperature, and additional considerations exposed here should be followed to measure the temperatures of two groups of atoms forming the whole cloud. Also an uncertainty evaluation is presented.
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.
We consider the ballistic expansion of a cloud of trapped atoms falling under the influence of gravity. Using a simple coordinate transformation, we derive an analytical expression for the time-of-flight signal. The properties of the signal can be used to infer the initial temperature of the cloud. We first assume a point size cloud with an isotropic velocity distribution to explain the physical basis of the calculation. The treatment is then generalized to include a finite-size cloud with an anisotropic velocity distribution, and an exact result for the signal is derived. The properties of the signal are discussed, and an intuitive picture is presented to explain how initial conditions determine the features of the signal.
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.