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arXiv 1407.4252cond-mat.quant-gas
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平顶偶极凝聚体的一般理论

A general theory of flattened dipolar condensates

D. Baillie, P. B. Blakie

摘要:

我们发展了一个由沿一个方向的谐波约束产生的扁平偶极玻色-爱因斯坦凝聚体(BEC)的理论。短程接触相互作用和长程偶极-偶极相互作用(DDI)的作用被认为是,和偶极子被允许沿任意方向极化。我们讨论的对称性的冷凝物和部分的激发光谱确定的稳定性,并引入两个有效的相互作用参数,使我们能够提供一个一般性的描述的冷凝物的属性,rotons,和稳定性。我们对角化的完整理论,以获得基准结果的凝聚和准粒子激发,并表征系统的精确平均场稳定性。我们为描述凝聚体和准粒子的许多近似方案提供了统一的公式,包括标准准二维(准2D)近似、两种变分拟法和托马斯-费米(TF)近似。这些计划中的一些已被广泛使用的文献中,尽管没有得到证实的确切理论。我们提供这种验证,并建立各种理论表现良好的制度。

英文摘要:

We develop theory for a flattened dipolar Bose-Einstein condensate (BEC) produced by harmonic confinement along one direction. The role of both short-ranged contact interactions and long-ranged dipole-dipole interactions (DDIs) is considered, and the dipoles are allowed to be polarised along an arbitrary direction. We discuss the symmetry properties of the condensate and the part of the excitation spectrum determining stability, and introduce two effective interaction parameters that allow us to provide a general description of the condensate properties, rotons, and stability. We diagonalize the full theory to obtain benchmark results for the condensate and quasiparticle excitations, and characterize the exact mean field stability of the system. We provide a unified formulation for a number of approximate schemes to describe the condensate and quasiparticles, including the standard quasi-two-dimensional (quasi-2D) approximation, two kinds of variational ansatz, and a Thomas-Fermi (TF) approximation. Some of these schemes have been widely used in the literature despite not being substantiated against the exact theory. We provide this validation and establish the regimes where the various theories perform well.

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