Characteristics Of The Zero-temperature In Spin-orbit Coupled 2-D Ultracold Fermi Gases

Spin-orbit coupling(SOC)is an important mechanism in quantum physics.As a realization of non-Abelian gauge fields in neutral cold atoms,SOC atomic gases have attracted a lot of attention in recent years.In the presence of SOC,various new and exotic superfluid phenomena may exist in ultra-cold atomic gases such as topological superfluid,Majorana fermions,FFLO state,etc.On the one hand,the introduction of SOC provides a chance to simulate the important quantum effect like topological insulators by utilizing the conveniently operable system of cold atoms.On the other hand,SOC atomic gases also provide a important platform to realize the topologically quantum calculation.In this paper,the mean field theory is used to study the zero temperature characteristics of two dimensional fermions gas under SOC.The article first briefly introduces some theoretical and experimental progress of ultracold Fermi gases and SOC quantum simulation.Secondly,we introduce the multi-body theory in a two-dimensional(2-D)ultracold Fermi gases.We use the method of mean field approximation derive the gap and atom number equations in the simply 2-D Fermi gases system.Then we use the mean-field theory to investigate zero temperature characteristic in2-D mass-balanced Fermi gases in the presence of a equal-Rashba-Dresselhaus(ERD)type of SOC.We derive the mean field gap and atom number equations and solve them numerically.We show that with an increasing ERD type SOC strength,the superfluid pairing gap is a constant without Zeeman fields.However,When the Zeeman fields is present,we find that the superfluid pairing gap can be enhanced with the increasing ERD type SOC strength.Then we use the mean-field theory to investigate zero temperature characteristic in a 2-D mass-imbalanced Fermi gases with ERD type of SOC and Zeeman field.The system exists three topologically distinct superfluid phases(US-0 phase,US-1 phase and US-2 phase).Through analysis the gap and atom number equations numerically and self-consistently,we find that superfluid order parameter can be suppressed more stronger by a Zeeman field as the mass difference increases.With increasing SOC,the weak atractive interaction region of the US-2 phase shrinks.When there is a finite SOC of the ERD type,0(27)? ?1,only in the weak atractive interaction region exists US-2 topologically superfluid phases;?(29)1,both weak and strong atractive interaction region exists US-2topologically superfluid phases.At last,we summarize the main contents of the article and make a prospect for the future research direction.