中文摘要：

应用泛函路径积分方法研究了自旋轨道耦合作用下的两组分费米气体在零温时的配对不平衡。通过鞍点处的热力学势得到能隙序参量方程与粒子数方程,求解自洽方程可以得到系统的一系列相变图,即热力学势、能隙参数、束缚能等一些物理量随着自旋轨道耦合系数之间的变化关系,得到了系统热力学势在不同的束缚能作用下的变化特征,粒子数的凝聚分数随耦合系数的变化。通过比较超流体的热力学势和相分离态来得到相图,分析了自旋轨道耦合对粒子数极化下的配对不平衡产生的影响。

英文摘要：

We study the ground state properties of a two-component ultracold superfluid Fermi gas with Rashba spin-orbit coupling at zero temperature in two-dimensional. The gap-order parameter and number densities are found analytically throught the thermodynamic potential at saddle point by using the function- al and integral method. We obtain the phase diagram by solve the self-consistent equations. Under the in- fluence of spin orbit couping,and we construct the phase diagram by comparing the thermodynamic poten- tial of superfluid and phase-separated states. The balance of pairing will be broken due to the unequal chemical potentials in the two-component ultracold Fermi gas in two-dimensional with spin orbit coupling.