Superfluid to Normal Fluid Phase Transition in the Bose Gas Trapped in Two-Dimensional Optical Lattices at Finite Temperature

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• 作者：M. O. C. Pires ; E. J. V. de Passos
• 关键词：Superfluid phase transition ; Optical lattices ; Bose ; Hubbard model
• 刊名：Brazilian Journal of Physics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：47
• 期：1
• 页码：1-8
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics, general;
• 出版者：Springer US
• ISSN：1678-4448
• 卷排序：47

文摘

We develop the Hartree-Fock-Bogoliubov theory at finite temperature for Bose gas trapped in the two-dimensional optical lattice with the on-site energy low enough that the gas presents superfluid properties. We obtain the condensate density as function of the temperature neglecting the anomalous density in the thermodynamics equation. The condensate fraction provides two critical temperature. Below the temperature \(T_{C1}\), there is one condensate fraction. Above two condensate fractions merger up to the critical temperature \(T_{C2}\). At temperatures larger than \(T_{C2}\), the condensate fraction is null and, therefore, the gas is normal fluid. We resume by a finite-temperature phase diagram where three domains can be identified: the normal fluid, the superfluid with one stable condensate fraction and the superfluid with two condensate fractions being unstable one of them.