费米气体中的紧束缚能隙孤子
Tightly bound gap solitons in a Fermi gas
摘要：
在简并费米气体（DFG）的平均场流体动力学模型的框架下，利用数值方法和变分近似（VA）研究了周期性光晶格势（OL势）中简并费米气体（或由自旋上下的费米子之间的弱相互作用产生的BCS超流体）中基本能隙孤子（FGS）的形成.一个有效的一维（1D）的配置被认为是，假设强横向限制，在平行，一个适当的1D模型的DFG（相当于已知的五次方程的Tonks-Girardeau气体在OL）被认为是太。在OL诱导光谱的前两个带隙中发现的FGS（除非它们非常接近间隙的边缘）具有紧密结合的形状，基本上被限制在OL的单个单元中。在第二个带隙中，我们也发现了反对称的紧束缚次基孤子（SFS），其中点为零。SFS也被限制在OL的单个细胞中，但是，与FGS不同，它们是不稳定的。在$^6$ Li原子的DFG中，利用现有的实验技术可以产生由$\sim 10^4 - 10^5$原子组成的孤子.
英文摘要：
Within the framework of the mean-field-hydrodynamic model of a degenerate Fermi gas (DFG), we study, by means of numerical methods and variational approximation (VA), the formation of fundamental gap solitons (FGSs) in a DFG (or in a BCS superfluid generated by weak interaction between spin-up and spin-down fermions), which is trapped in a periodic optical-lattice (OL) potential. An effectively one-dimensional (1D) configuration is considered, assuming strong transverse confinement; in parallel, a proper 1D model of the DFG (which amounts to the known quintic equation for the Tonks-Girardeau gas in the OL) is considered too. The FGSs found in the first two bandgaps of the OL-induced spectrum (unless they are very close to edges of the gaps) feature a tightly-bound shape, being essentially confined to a single cell of the OL. In the second bandgap, we also find antisymmetric tightly-bound subfundamental solitons (SFSs), with zero at the midpoint. The SFSs are also confined to a single cell of the OL, but, unlike the FGSs, they are unstable. The predicted solitons, consisting of $\sim 10^4 - 10^5$ atoms, can be created by available experimental techniques in the DFG of $^6$Li atoms.
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