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arXiv 0801.2952cond-mat.stat-mech
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旋转囚禁的玻色-爱因斯坦凝聚体

Rotating trapped Bose-Einstein condensates

Alexander L. Fetter

摘要:

在回顾了盒子和谐振阱中的理想玻色-爱因斯坦气体之后,我讨论了相互作用对玻色-爱因斯坦凝聚体(BEC)形成的影响,以及小振幅扰动的动力学(Bogoliubov方程)。当凝聚体以角速度Ω旋转时,一个或多个涡旋成核,并产生许多可观察到的结果。随着更快的旋转,涡旋形成密集的三角形阵列,这些涡旋的集体行为具有额外的实验意义。对于径向陷阱频率ω_perp附近的欧米茄,最低朗道级近似变得适用,提供了一个简单的图片,这种快速旋转的凝聚。最终,当ω接近ω_perp时,旋转的稀气体预计会经历从超流体到各种高度相关(非超流体)状态的量子相变,类似于强垂直磁场中电子的分数量子霍尔效应。

英文摘要:

After reviewing the ideal Bose-Einstein gas in a box and in a harmonic trap, I discuss the effect of interactions on the formation of a Bose-Einstein condensate (BEC), along with the dynamics of small-amplitude perturbations (the Bogoliubov equations). When the condensate rotates with angular velocity Omega, one or several vortices nucleate, with many observable consequences. With more rapid rotation, the vortices form a dense triangular array, and the collective behavior of these vortices has additional experimental implications. For Omega near the radial trap frequency omega_perp, the lowest-Landau-level approximation becomes applicable, providing a simple picture of such rapidly rotating condensates. Eventually, as Omega approaches omega_perp, the rotating dilute gas is expected to undergo a quantum phase transition from a superfluid to various highly correlated (nonsuperfluid) states analogous to those familiar from the fractional quantum Hall effect for electrons in a strong perpendicular magnetic field.

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