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arXiv:1011.3140 · Physical Review A

Phase transition to Bose-Einstein condensation for a bosonic gas confined in a combined trap

Baolong Lü, Xinzhou Tan, Bing Wang, Lijuan Cao, Hongwei Xiong

Published Nov 24, 2010• 3 citations
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Abstract

We present a study of phase transition to macroscopic superfluidity for an ultracold bosonic gas confined in a combined trap formed by a one-dimensional optical lattice and a harmonic potential, focusing on the critical temperature of this system and the interference patterns of the Bose gas released from the combined trap. Based on a semiclassical energy spectrum, we develop an analytic approximation for the critical temperature ${T}_{c}$, and compare the analytic results with that obtained by numerical computations. For finite temperatures below ${T}_{c}$, we calculate the interference patterns for both the normal gas and the superfluid gas. The total interference pattern shows a feature of ``peak on a peak.'' As a comparison, we also present the experimentally observed interference patterns of $^{87}\mathrm{Rb}$ atoms released from a one-dimensional optical lattice system in accord with our theoretical model. Our observations are consistent with the theoretical results.

DOI
10.1103/physreva.82.053629

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In response to a recent manuscript [cond-mat/0609685] on the analysis of interference patterns produced by ultracold atoms released from an optical lattice, we point out that in the presence of a Bose-Einstein condensate the interference pattern can be strongly modified by interaction effects and the presence of a harmonic trap superimposed on the lattice potential. Our results show that the visibility of the interference pattern is significant only if a sizeable condensate fraction is present in the trap.
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We study an ultracold Bose gas in an optical dipole trap consisting of one single focused laser beam. An analytical expression for the corresponding density of states beyond the usual harmonic approximation is obtained. We are thus able to discuss the existence of a critical temperature for Bose-Einstein condensation and find that the phase transition must be enabled by a cutoff near the threshold. Moreover, we study the dynamics of evaporative cooling and observe significant deviations from the findings for the well-established harmonic approximation. Furthermore, we investigate Bose-Einstein condensates in such a trap in Thomas-Fermi approximation and determine analytical expressions for chemical potential, internal energy, and Thomas-Fermi radii beyond the usual harmonic approximation.
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