一维接触排斥相互作用单自旋翻转费米气体的基态和淬火动力学性质  

Properties of ground state and quench dynamics of one-dimensional contact repulsive single-spin flipped Fermi gases

作　　者：尹相国 于海如 郝亚江 张云波 Yin Xiang-Guo;Yu Hai-Ru;Hao Ya-Jiang;Zhang Yun-Bo(Collaborative Innovation Center of Extreme Optics,State Key Laboratory of Quantum Optics and Quantum Optics Devices,Institute of Theoretical Physics,Shanxi University,Taiyuan 030006,China;Institute of Theoretical Physics,Department of Physics,University of Science and Technology Beijing,Beijing 100083,China;Key Laboratory of Optical Field Manipulation of Zhejiang Province,Department of Physics,Zhejiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]山西大学理论物理研究所,量子光学与光量子器件国家重点实验室,极端光学协同创新中心,太原030006 [2]北京科技大学物理系,理论物理研究所,北京100083 [3]浙江理工大学物理系,浙江省光场调控重点实验室,杭州310018

出　　处：《物理学报》2024年第2期76-88,共13页Acta Physica Sinica

基　　金：山西省基础研究计划(批准号:202103021224033);国家自然科学基金(批准号:11704233,12074340);浙江理工大学科研启动基金(批准号:20062098-Y)资助的课题。

摘　　要：基于严格解方法,研究了一维排斥相互作用单自旋翻转费米气体的基态和淬火动力学性质.借助Bethe波函数,基态和不同本征态之间的单体关联函数和两体关联函数可以表示为简单函数之和,这一简洁形式可以极大地降低计算难度.系统初始状态为无相互作用的基态,当迅速把相互作用强度调节为有限大时,动量分布和关联函数出现周期性的振荡行为;当相互作用调节为比较弱时,振荡周期性好且振荡幅度小,系统可以用二能级模型近似;当相互作用调为非常强时,振荡周期性变差且振荡幅度大,但是依然存在主周期.此时整体偏离初态较远,但是在时间为mL^(2)/(2πh)时系统非常接近初态.Based on the exact solution method,the ground state and quench dynamics properties of one-dimensional single-spin flipped Fermi gas with repulsion interaction are studied.With the Bethe wave function,the singlebody correlation function and two-body correlation function of the ground state and those between different eigen-states can be reduced into a summation of simple functions,thereby greatly reducing the computational difficulty.For the system in the ground state,the single-body correlation functions and two-body correlation functions as well as momentum distributions for spin-up particles are investigated in real space with different interaction strengths.As the interaction strength increases,the number of nodes in the single-body correlation function remains unchanged,while the amplitude of oscillation decreases.Meanwhile,the number of peaks in the two-body correlation function increases by one due to interaction,indicating that the spin-down particle behaves as a spin-up particle.The momentum distribution becomes more smooth around Fermi surface with the interaction strength increasing.The interaction quench dynamics is investigated.The system is prepared in the ground state of ideal Fermi gas,and then the interaction strength is quenched to a finite positive value.The system evolves under time-dependent Schrödinger equation.The overlap between the initial state and eigenstate of post-quench interaction strength is expressed in the form of continued multiplication.The square of the modulus of this overlap,which represents the occupation probability,is calculated.We find that the occupation probabilities of the ground state and doubly degenerated excited state always have the first and the second largest value for an arbitrary interaction strength,respectively,which means that the difference in eigenenergy between these two states gives the primary period of oscillation.For relatively large particle number(N≥10),the primary period always does not change under different interaction strengths.It is found t

关 键 词：一维费米气体 动量分布 关联函数 淬火动力学 

分 类 号：O469[理学—凝聚态物理]