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arXiv:0808.1501 · Physical Review A

Genuine phase diffusion of a Bose-Einstein condensate in the microcanonical ensemble: A classical field study

Alice Sinatra, Yvan Castin

Published Nov 10, 2008• 20 citations
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Abstract

Within the classical field model, we find that the phase of a uniform Bose-Einstein condensate at nonzero temperature undergoes a true diffusive motion in the microcanonical ensemble, the variance of the condensate phase change between time zero and time $t$ growing linearly in $t$. The phase diffusion coefficient obeys a simple scaling law in the double thermodynamic and Bogoliubov limit. We construct an approximate calculation of the diffusion coefficient, in fair agreement with the numerical results over the considered temperature range, and we extend this approximate calculation to the quantum field.

DOI
10.1103/physreva.78.053615

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Within the classical field model, we find that the phase of a uniform Bose-Einstein condensate at nonzero temperature undergoes a true diffusive motion in the microcanonical ensemble, the variance of the condensate phase change between time zero and time ttt growing linearly in ttt. The phase diffusion coefficient obeys a simple scaling law in the double thermodynamic and Bogoliubov limit. We construct an approximate calculation of the diffusion coefficient, in fair agreement with the numerical results over the considered temperature range, and we extend this approximate calculation to the quantum field.
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We study the ground state occupation number and its fluctuations for the Bose-Einstein condensate of trapped atoms using the microcanonical ensemble. The analytic formulas are obtained with the help of the saddle point method. We show that microcanonical fluctuations below the critical temperature tend to zero and scale with the number of particles as 1/N1/\sqrt{N}1/N​.