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arXiv:cond-mat/0605507 · Advances in atomic, molecular, and optical physics

Fluctuations in Ideal and Interacting Bose–Einstein Condensates: From the Laser Phase Transition Analogy to Squeezed States and Bogoliubov Quasiparticles

Vitaly V. Kocharovsky, Vl. V. Kocharovsky, Martin Holthaus, C. H. Raymond Ooi, Anatoly A. Svidzinsky, Wolfgang Ketterle, Marlan O. Scully

Published Jan 1, 2006• 89 citations
arXivHTMLPDF
DOI
10.1016/s1049-250x(06)53010-1

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Influence of the interaction between atoms on the squeezing properties of atomic lasers

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The influence of the interaction between atoms in Bose-Einstein condensate (BEC) on the squeezing properties of atomic lasers is studied under Bogoliubov approximation. The results show that the fluctuations of two quadrature components of the atomic laser can be squeezed and the interaction between atoms in BEC is disadvantageous to the squeeze of atomic lasers.

Acta Physica Sinica•Jan 1, 2004•4 citations
We consider equilibrium canonical-ensemble fluctuations of the Bose-Einstein condensate (BEC) in a trap using the particle-number conserving operator formalism of Girardeau and Arnowitt [Phys. Rev. 113, 755 (1959)] and the concept of the canonical-ensemble quasiparticles. We find explicit expressions for the characteristic function and all cumulants of the ground-state occupation statistics both for the dilute weakly interacting and ideal Bose gases. We present analytical formulas for the moments of the ground-state occupation fluctuations in the weakly interacting and ideal Bose gases in a box (``homogeneous gas'') as well as in the ideal Bose gas in an arbitrary power-law trap, in particular, in an arbitrary harmonic trap. We calculate the effect of Bogoliubov coupling between quasiparticles on suppression of the ground-state occupation fluctuations at moderate temperatures and their enhancement at very low temperatures. We clarify a crossover between ideal-gas and weakly interacting gas statistics, which is governed by a pair-correlation, squeezing mechanism. The important conclusion is that in most cases the ground-state occupation fluctuations are anomalously large and are not Gaussian even in the thermodynamic limit.
We present a new method of calculating the distribution function and fluctuations for a Bose-Einstein condensate (BEC) of N interacting atoms. The present formulation combines our previous master equation and canonical ensemble quasiparticle techniques. It is applicable both for ideal and interacting Bogoliubov BEC and yields remarkable accuracy at all temperatures. For the interacting gas of 200 bosons in a box we plot the temperature dependence of the first four central moments of the condensate particle number and compare the results with the ideal gas. For the interacting mesoscopic BEC, as with the ideal gas, we find a smooth transition for the condensate particle number as we pass through the critical temperature.