arXiv 0909.09202009-09-04cond-mat.quant-gas

圆阵中玻色-爱因斯坦凝聚体的稳定性

Stability of Bose-Einstein condensates in a circular array

E. T. D. Matsushita, E. J. V. de Passos

备注：: 11 pages,2 figures, 5 tables

摘要：

在Bose-哈伯德模型和Bogoliubov理论的框架下，研究了超冷玻色原子在圆形阵列中的超流相性质。我们推导并求解了该模型的Gross-Pitaevskii方程，发现原子凝聚在定义明确的准动量态。对有效二次巨正则哈密顿量中的耦合结构的详细分析表明，只有成对的不同的和相同的准动量是耦合的。解相应的Bogoliubov-de Gennes方程，我们看到每对不同的准动量在激发能谱中产生双峰，并且在凝聚体中零能模和占据态的准动量是相同的。通过研究元激发在控制参数空间中的行为，确定了凝聚体的动力学和能量稳定性。我们的研究表明，超流冷凝只存在于第一布里渊区的中心区域，而在最后一个季度没有，因为它们是能量不稳定的，独立的控制参数。

英文摘要：

The properties of the superfluid phase of ultra cold bosonic atoms loaded in a circular array are investigated in the framework of the Bose-Hubbard model and the Bogoliubov theory. We derive and solve the Gross-Pitaevskii equation of the model to find that the atoms condense in states of well-defined quasimomentum. A detailed analysis of the coupling structure in the effective quadratic grand-canonical Hamiltonian shows that only pairs of distinct and identical quasimomenta are coupled. Solving the corresponding Bogoliubov-de Gennes equations we see that each pair of distinct quasimomenta gives raise to doublets in the excitation energy spectrum and that the quasimomenta of the zero-energy mode and of the occupied state in the condensates are identical. The dynamical and energetic stabilities of the condensates are determined by studying the behavior of the elementary excitations in the control parameters space. Our investigation establishes that superflow condensates exists only in the central region of the first Brillouin zone whereas there is none in the last quarters since they are energetically unstable, independently of the control parameters.

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