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arXiv 0807.3495cond-mat.othernlin.PS
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光晶格中超流费米子气体模型中的带隙孤子

Gap solitons in a model of a superfluid fermion gas in optical lattices

S. K. Adhikari, B. A. Malomed

摘要:

本文考虑了Bardeen-Cooper-Schrieffer(BCS)超流态费米气体的动力学模型,该模型被囚禁在一个一维或二维光晶格(OL)和一个沿横向作用的紧抛物势的组合中.该模型是基于一个方程的序参量(波函数),这是来自能量密度的弱耦合BCS超流体。该方程包括一个非线性的自排斥项的权力7/3,这占费米压力。将方程约化为一维或二维形式,在变分近似的指导下,通过数值模拟构造了稳定的一维和二维带隙孤子族。GS主要是被困在OL势的单个细胞中的紧凑物体。在线性极限,VA预测几乎精确的位置的窄布洛赫带分开的半无限和第一有限的差距,以及第一和第二有限的。构造了一维广义系统稳定的奇、偶束缚态族。我们还表明,GS可以拖动没有太多的失真由OL以中等速度($\sim $ 1毫米/秒,在物理单位)移动。预测的GS分别包含每个1D和2D设置的$\sim 10^{3}-10^{4}$和$\sim 10^{3}$原子。

英文摘要:

We consider a dynamical model for a Fermi gas in the Bardeen-Cooper-Schrieffer (BCS) superfluid state, trapped in a combination of a 1D or 2D optical lattice (OL) and a tight parabolic potential acting in the transverse direction(s). The model is based on an equation for the order parameter (wave function), which is derived from the energy density for the weakly coupled BCS superfluid. The equation includes a nonlinear self-repulsive term of power 7/3, which accounts for the Fermi pressure. Reducing the equation to the 1D or 2D form, we construct families of stable 1D and 2D gap solitons (GSs) by means of numerical simulations, which are guided by the variational approximation (VA). The GSs are, chiefly, compact objects trapped in a single cell of the OL potential. In the linear limit, the VA predicts almost exact positions of narrow Bloch bands that separate the semi-infinite and first finite gaps, as well as the first and second finite ones. Families of stable even and odd bound states of 1D GSs are constructed too. We also demonstrate that the GS can be dragged without much distortion by an OL moving at a moderate velocity ($\sim $ 1 mm/s, in physical units). The predicted GSs contain $\sim 10^{3}-10^{4}$ and $\sim 10^{3}$ atoms per 1D and 2D settings, respectively.

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