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Chinese Journal of Physics

Time Evolution of Freely Expanded Bose-Einstein Condensates Containing Small Numbers of Atoms

De-Sheng Hong, K. H. Huang, Tsin-Fu Jiang, D. J. Han

Published Apr 1, 2007• 0 citations

Abstract

We investigate the time evolution of freely expanded Bose-Einstein condensates by measuring their aspect ratios at different times after their release from a magnetic trap. In these measurements the condensates contain no more than 9000 87Rb atoms. By varying the trapping frequency and atom number, we measure the condensate aspect ratios at different expansion times in free space. We compare our measurements with those calculated from the Thomas-Fermi model and a direct numerical solution. Under our trapping condition, the data of the time dependent aspect ratios of the freely expanded condensates reasonably agrees with the numerical calculations, but shows a clear deviation from the predictions of the Thomas-Fermi model when the atom number in the condensates is small.

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We investigate the time evolution of freely expanded Bose-Einstein condensates by measuring their aspect ratios at different times after their release from a magnetic trap. In these measurements the condensates contain no more than 9000 87Rb atoms. By varying the trapping frequency and atom number, we measure the condensate aspect ratios at different expansion times in free space. We compare our measurements with those calculated from the Thomas-Fermi model and a direct numerical solution. Under our trapping condition, the data of the time dependent aspect ratios of the freely expanded condensates reasonably agrees with the numerical calculations, but shows a clear deviation from the predictions of the Thomas-Fermi model when the atom number in the condensates is small.

We present an analytical approximation for nonlinear dynamics of trapped Bose-Einstein condensates. The approximation is a substantial improvement over the Thomas-Fermi approximation and is shown to be applicable for systems with a rather small number of atoms N. The calculated aspect ratios after ballistic expansion are found to be in good agreement with those observed in recent experiments. The approximation is useful in providing a simple and easy quantitative computational tool for the analysis of experimental data.

In this work, we analyze the free expansion of Bose-Einstein condensates containing multicharged vortices. The atomic cloud is initially confined in a three-dimensional asymmetric harmonic trap. We apply both approximate variational solutions and numerical simulations of the Gross-Pitaevskii equation. The data obtained provide a way to establish the presence as well as the multiplicity of vortices based only on the properties of the expanded cloud which can be obtained via time-of-flight measurements. In addition, several features such as the evolution of the vortex core size and the asymptotic velocity during free expansion were studied considering the atomic cloud as being released from different harmonic trap configurations.

Free expansion of an untrapped Bose–Einstein condensate with repulsive inter-atomic interaction is studied. By use of the Zakharov's theory, time-evolution of the spatial extent of the condensate is investigated analytically. For the case that the condensate is initially confined in a harmonic trap, the characteristic time scale of the free expansion is shown to remain in the order of the inverse of the trap frequencies, regardless of the strength of the interaction. This explains consistently the time scale for the damping of the aspect ratio in the JILA and MIT experiments.