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Physical Review A

Expansion of a Bose-Einstein condensate in a harmonic potential

Murray Holland, J. Cooper

Published Apr 1, 1996• 115 citations
Publisher

Abstract

We analyze the three-dimensional dynamic expansion of a weakly interacting Bose-Einstein condensate in a harmonic trap when the spring constants of the confining potential are instantaneously reduced. Our results are compared with experimental observation from a condensate of $^{87}\mathrm{Rb}$ atoms.

DOI
10.1103/physreva.53.r1954

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We analyze the three-dimensional dynamic expansion of a weakly interacting Bose-Einstein condensate in a harmonic trap when the spring constants of the confining potential are instantaneously reduced. Our results are compared with experimental observation from a condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms.
In this paper, we present a theoretical study of a Bose-Einstein condensate of interacting bosons in a quartic trap in one, two, and three dimensions. Using Thomas-Fermi approximation, suitably complemented by numerical solutions of the Gross-Pitaevskii equation, we study the ground sate condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate, and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic confinement.
We discuss Bose-Einstein condensation in harmonic traps where the confinement has undergone a splitting along one direction. We mostly consider three-dimensional potentials consisting of two cylindrical wells separated a distance 2a2a2a along the z axis. For ideal gases, the thermodynamics of the confined bosons has been investigated, performing exact numerical summations to describe the major details of the transition and comparing the results with the semiclassical density-of-states approximation. We find that for large particle number and increasing well separation, the condensation temperature evolves from the thermodynamic limit value Tc(0)(N){T}_{c}^{(0)}(N)Tc(0)​(N) to Tc(0)(N/2).{T}_{c}^{(0)}(N/2).Tc(0)​(N/2). The effects of adding a repulsive interaction between atoms has been examined resorting to the Gross-Pitaevskii-Popov procedure, and it is found that the shift of the condensation temperature exhibits different signs according to the separation between wells. In particular, for sufficiently large splitting, the trend opposes the well-known results for harmonic traps, since the critical temperature appears to increase with growing repulsion strength.
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With the integral representation of Bose functions, the Bose-Einstein condensation of non-interacting bosons in a three-dimensional harmonic trap was studied. The relation between the particle number and its phase transition temperature was clarified. Some next-order terms in the thermodynamic expansions were obtained. We plotted the chemical potential, the mean energy, and the specific heat and found most of these properties obtained by using the integral representation were almost identical with those of the series representation of Bose functions.
We discuss thermal and dynamical properties of Bose condensates confined by an external potential. First we analyze the Bose-Einstein transition temperature for an ideal Bose gas in a generic power-law potential and d-dimensional space. Then we investigate the effect of the shape of the trapping potential on the properties of a weakly-interacting Bose condensate. We show that using exotic trapping potentials the condensate can exhibit interesting coherent quantum phenomena, like superfluidity and tunneling. In particular, we consider toroidal and double-well potentials. The theoretical results are compared with recent experiments.