Coherent Bose-Einstein condensation with fluctuating density

Abstract

Bose-Einstein condensation in the grand canonical ensemble admits a formulation in terms of a phase-density decomposition of the condensate mode operator $\hat{\ddot{I}}{ˆ}_0$. In the presence of macroscopic condensate number fluctuations this representation presents nontrivial implications. In particular, we show that, for the ideal gas, under the assumption of a well-defined phase and a fluctuating condensate density, the full hierarchy of correlation functions is determined by the statistics of the density. Within this framework, the modulus squared of the anomalous average $⟨\hat{\ddot{I}}{ˆ}_0⟩$ can provide only a fraction of the whole condensate density $\ddot{I}{}_0$ and for the grand canonical statistics of the ideal Bose gas one obtains the value $|⟨{\hat{\ddot{I}}ˆ}_0⟩{|}^2=(\ddot{I}€/4)\ddot{I}{}_0$. The remaining part is supplemented by the (macroscopic) fluctuations of $\hat{\ddot{I}}{ˆ}_0$, which become a distinctive feature of the BEC in this setting. This provides a transparent physical picture of a condensate of photons with a well-defined phase but large number fluctuations, as observed in dye-filled microcavity photon experiments. We also propose a way to access the square modulus of the anomalous average to test theoretical predictions.

9 pages

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