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arXiv:cond-mat/0210593 · Physical Review A

Anomalous fluctuations of two-dimensional Bose-Einstein condensates

Hongwei Xiong, Shujuan Liu, Guoxiang Huang

Published May 28, 2003• 13 citations
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Abstract

We investigate the particle-number fluctuations due to the collective excitations created in a two-dimensional (2D) and a quasi-2D Bose-Einstein condensates (BECs) at low temperature. We find that the fluctuations display an anomalous behavior, i.e., for the 2D BEC they are proportional to ${N}^{2},$ where N is the total number of particles. For the quasi-2D BEC, the particle-number fluctuations are proportional not only to ${N}^{2}$ but also to the square root of the trapping frequency in the strongly confined direction.

DOI
10.1103/physreva.67.055601

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We investigate the particle-number fluctuations due to the collective excitations created in a two-dimensional (2D) and a quasi-2D Bose-Einstein condensates (BECs) at low temperature. We find that the fluctuations display an anomalous behavior, i.e., for the 2D BEC they are proportional to N2,{N}^{2},N2, where N is the total number of particles. For the quasi-2D BEC, the particle-number fluctuations are proportional not only to N2{N}^{2}N2 but also to the square root of the trapping frequency in the strongly confined direction.
The particle-number fluctuations originated from collective excitations are investigated for a three-dimensional, repulsively interacting Bose-Einstein condensate (BEC) confined in a harmonic trap. The contribution due to the quantum depletion of the condensate is calculated and the explicit expression of the coefficient in the formulas denoting the particle-number fluctuations is given. The results show that the particle-number fluctuations of the condensate follow the law $〈\ensuremath{\delta}{N}_{0}^{2}〉\ensuremath{\sim}{N}^{22/15}$ and the fluctuations vanish when temperature approaches the BEC critical temperature.
Fluctuations are fundamental in physics and important for understanding and characterizing phase transitions. In this spirit, the phase transition to the Bose-Einstein condensate (BEC) is of specific importance. Whereas fluctuations of the condensate particle number in atomic BECs have been studied in continuous systems, experimental and theoretical studies for lattice systems were so far missing. Here, we explore the condensate particle number fluctuations in an optical lattice BEC across the phase transition in a combined experimental and theoretical study. We present both experimental data using ultracold ^{87}Rb atoms and numerical simulations based on a hybrid approach combining the Bogoliubov quasiparticle framework with a master equation analysis for modeling the system. We find strongly anomalous fluctuations, where the variance of the condensate number δN_{BEC}^{2} scales with the total atom number as N^{1+γ} with an exponent around γ_{theo}=0.74(10) and γ_{exp}=0.62(9), which we attribute to the 2D/3D crossover geometry. Our Letter highlights the importance of the trap geometry on the character of fluctuations and on fundamental quantum mechanical properties.
We discuss Bose-Einstein condensation (BEC) in quasi-2D trapped gases and find that well below the transition temperature T(c) the equilibrium state is a true condensate, whereas at intermediate temperatures T<T(c) one has a quasicondensate (condensate with fluctuating phase). The mean-field interaction in a quasi-2D gas is sensitive to the frequency omega(0) of the (tight) confinement in the "frozen" direction, and one can switch the sign of the interaction by changing omega(0). Variation of omega(0) can also reduce the rates of inelastic processes. This offers promising prospects for tunable BEC in trapped quasi-2D gases.
The occurrence of phase fluctuations due to thermal excitations in Bose-Einstein condensates (BECs) is studied for a variety of temperatures and trap geometries. We observe the statistical nature of the appearance of phase fluctuations and characterize the dependence of their average value on temperature, number of particles, and the trapping potential. We find pronounced phase fluctuations for condensates in very elongated traps in a broad temperature range. The results are of great importance for the realization of BEC in quasi-1D geometries, for matter wave interferometry with BECs, as well as for coherence properties of guided atom laser beams.