The Ground Characteristics For Two-Component Spin-Orbit Coupled Bose-Einstein Condensate Under Rotation

In this paper,we inestigate the ground-states of spin-orbit coulping BEC by analytical approximate and numerical calculation.We constrain BEC in a extrnal trap.By adjusting rotating and spin-orbit coupling,we observe the ground-state density distribution and spin textures.The effect of rotating and soun-orbit coupling on BEC are studied,find new vortex structure and spin textures.These results enrich the ground state phase of BEC.First,we get energy function under rotation and spin-orbit coulping by schrodinger function,we obtain though variational method.We provide two calculation method which can solve the GP equation effectively via programing.Second,we study the ground states properties of the spin BEC in a pure harmonic potential trap.Under the rotation and spin-orbit coupling,new structures appear in the ground states of BEC,such as striped structures,spin domain wall,and so on.We first analyze the system from the analysis and find that the density distribution of the condensates are not only effect by the interaction between atoms and rotation angle frequency,but also by the spin-orbit coupling.Afterwards,we use computer to simulate the ground state of the system through numerical calculation.The results of numerical calculation are same as the analytical approximate.When the interaction strength between the atoms of a component is smaller than the interaction of atoms in each component,the strength of the spin-orbit coupling and the rotation speed increase.According to the ground state density distribution,the system can be divided into two different categories: the ground state density distribution of one type of system is two discs;the other type of system is two rings.We also use the Thomas Fermi approximation to obtain the analytical approximation conditions for converting two discs into two rings.When the rotation angle frequency is a certain value,only adjusted thespin-orbit coupling strength,and we find the spin domain wall.If we increase the coupling strength,the number of domain walls will increase.When the intercomponent interation is larger than the intracomponent interation and the strength of the spin orbit is a constant,we obtain the ground state of the system by a numerical calculation method.Analysing results of numerical simulation,it can be concluded that when the frequency of rotation angle is small,the two-component condensate forms two spin drops under strong repulsion.Increasing the rotation angle frequency gradually,under the effect of rotation,vortex will appear in the ground state of the system.As the vorticity increases,the system is gradually distributed as two rings.However,it is worth noting that when the angular frequency of rotation exceeds the constraint frequency of the harmonic trap,the system will be discretized under the influence of strong centrifugal force.In addition,the stripe structure will appear with the increase of the strength of the spin orbit when the rotational angular frequency is zero.In a word,the introduction of spin orbit coupling enriches the ground state structure of the system,and produces more novel structure of the ground state.Those will have a particularly important impact on experimental studies.Finally,we investigate ground state of the Bose-Einstein condensate in a harmonic plus gaussian trap.We find that the range of the rotation frequency parameters are extensive because of the addition of gaussian potential.Namely,the system will be able to resist the effect of centrifugal force and take shape of two rings when the rotation frequency exceeds the constraint frequency of the harmonic potential.Change the interactions and the strength of spin orbit concurrently,we find the transform from phase mixing to phase separated is not only decided by the competition between the intra-and intercomponent interaction strengths,but also decided the strength of spin orbit.Increase the strength of spin orbit,the phase separated will become phase mixing,and also can generate the spin domain wall.This makes the study of cold atoms more complex and meaningful.