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Physical Review Letters

Emergence of Interaction Effects in Bose-Einstein Condensation

Murray Holland, D. S. Jin, M. L. Chiofalo, J. Cooper

Published May 19, 1997• 85 citations
Publisher

Abstract

We present a quantitative evaluation of the predictions of mean-field theory for describing a Bose-Einstein condensate in a magnetic trap by comparing directly with experimental observations. We study the release energy from ballistic expansion and the cloud density profile as a function of mean-field effects. Significant departure of the cloud shape from both the noninteracting limit and the strongly repulsive limit is observed for our parameters, consistent with theoretical prediction.

DOI
10.1103/physrevlett.78.3801

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We present a quantitative evaluation of the predictions of mean-field theory for describing a Bose-Einstein condensate in a magnetic trap by comparing directly with experimental observations. We study the release energy from ballistic expansion and the cloud density profile as a function of mean-field effects. Significant departure of the cloud shape from both the noninteracting limit and the strongly repulsive limit is observed for our parameters, consistent with theoretical prediction.
The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground-state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.
Experiments on Bose-Einstein condensates at finite temperature typically extract the system parameters, such as temperature, atom number, and condensed fraction from time-of-flight images taken after a free expansion time. This paper systematically examines the effect of repulsive interactions between the condensed and thermal atoms in partially condensed clouds on the expansion profile of the thermal cloud. An analytical expression for the expansion can be obtained only if the interactions between the Bose-Einstein condensate and thermal atoms are neglected, resulting in a Bose-enhanced distribution for the thermal component. Here, the deformation of the cloud due to interactions and the effects on estimated parameters are investigated by simulating the expansion using a ballistic approximation. By fitting the simulated expansion profiles with a Bose-enhanced distribution, the errors of using such a fit are estimated, and the results are explained phenomenologically. The simulation was also used as a fitting function for experimental data, showing better agreement of the extracted condensed fraction with the semi-ideal model than results from a Bose-enhanced fit.
We present measurements of finite-temperature atom clouds cooled below the transition temperature for Bose-Einstein condensation. We study the dynamics of the interface region between the Bose condensed and noncondensed components of the atom clouds, where the time-dependent density profile is highly sensitive to interactions between the two components. We observe directly the effects of repulsion from the condensate on the dynamics of noncondensed atoms. The measurements are compared to calculations based on Hartree-Fock-Bogoliubov mean-field theory. We infer a value for the spatial second-order correlation function for noncondensed atoms of g 0,NC (2) ( r = 0) = 1.8 ± 0.3.
We investigate the possibilities of distinguishing the mean-field and fluctuation effects on the critical temperature of a trapped Bose gas with repulsive interatomic interactions. Since in a direct measurement of the critical temperature as a function of the number of trapped atoms these effects are small compared to the ideal gas results, we propose to observe Bose-Einstein condensation by adiabatically ramping down the trapping frequency. Moreover, analyzing this adiabatic cooling scheme, we show that fluctuation effects can lead to the formation of a Bose-Einstein condensate at frequencies which are much larger than those predicted by the mean-field theory.
We investigate the properties of a coherent array containing about 200 Bose-Einstein condensates produced in a far detuned 1D optical lattice. The density profile of the gas, imaged after releasing the trap, provides information about the coherence of the ground-state wave function. The measured atomic distribution is characterized by interference peaks. The time evolution of the peaks, their relative population, as well as the radial size of the expanding cloud are in good agreement with the predictions of theory. The 2D nature of the trapped condensates and the conditions required to observe the effects of coherence are also discussed.