非平衡超冷费米量子气体非对称哈伯德模型的基态性质
Ground State Properties of an Asymmetric Hubbard Model for Unbalanced Ultracold Fermionic Quantum Gases
摘要：
为了描述谐振阱中光晶格上的非平衡超冷费米量子气体，研究了具有类塞曼磁场的吸引（$U<0$）非对称（$t_\uparrow\neq t_\downarrow$）哈伯德模型.考虑到模型的空间非均匀性，本文主要研究Hartree-Fock水平上的解。Hartree-Fock哈密顿量是对角化的，特别强调超流相。对于自旋无关跳跃的特殊情况下，我们解析地确定所得到的自洽方程的解的数量和弱耦合下可能的基态的性质。非平衡费米混合物的数值结果内的局部密度近似。特别是，我们发现了一个迷人的壳结构，涉及正常和超流相。对于一般的自旋相关跳跃情况，我们计算了基态的态密度和可能的超流相。特别是，我们发现了一个新的磁化超流相。
英文摘要：
In order to describe unbalanced ultracold fermionic quantum gases on optical lattices in a harmonic trap, we investigate an attractive ($U<0$) asymmetric ($t_\uparrow\neq t_\downarrow$) Hubbard model with a Zeeman-like magnetic field. In view of the model's spatial inhomogeneity, we focus in this paper on the solution at Hartree-Fock level. The Hartree-Fock Hamiltonian is diagonalized with particular emphasis on superfluid phases. For the special case of spin-independent hopping we analytically determine the number of solutions of the resulting self-consistency equations and the nature of the possible ground states at weak coupling. Numerical results for unbalanced Fermi-mixtures are presented within the local density approximation. In particular, we find a fascinating shell structure, involving normal and superfluid phases. For the general case of spin-dependent hopping we calculate the density of states and the possible superfluid phases in the ground state. In particular, we find a new magnetized superfluid phase.
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