Fluctuation statistics of mesoscopic Bose-Einstein condensates: Reconciling the master equation with the partition function to reexamine the Uhlenbeck-Einstein dilemma
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627 (United States) and Institute for Quantum Studies and Department of Physics, Texas A and M University, College Station, Texas 77843-4242 (United States)
The atom fluctuation statistics of an ideal, mesoscopic, Bose-Einstein condensate are investigated from several different perspectives. By generalizing the grand canonical analysis (applied to the canonical ensemble problem), we obtain a self-consistent equation for the mean condensate particle number that coincides with the microscopic result calculated from the laser master equation approach. For the case of a harmonic trap, we obtain an analytic expression for the condensate particle number that is very accurate at all temperatures, when compared with numerical canonical ensemble results. Applying a similar generalized grand canonical treatment to the variance, we obtain an accurate result only below the critical temperature. Analytic results are found for all higher moments of the fluctuation distribution by employing the stochastic path integral formalism, with excellent accuracy. We further discuss a hybrid treatment, which combines the master equation and stochastic path integral analysis with results obtained based on the canonical ensemble quasiparticle formalism [Kocharovsky et al., Phys. Rev. A 61, 053606 (2000)], producing essentially perfect agreement with numerical simulation at all temperatures.
- OSTI ID:
- 20857694
- Journal Information:
- Physical Review. A, Vol. 74, Issue 3; Other Information: DOI: 10.1103/PhysRevA.74.032506; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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