F=1自旋相干态在外场中的量子演化  

Quantum Dynamics of Spin-1 Coherent State in External Fields

作　　者：师春娟 张杰 SHI Chunjuan;ZHANG Jie(College of Physics and Optoelectronics,Taiyuan Universilry of Technology,Taiyuan 030024,China)

机构地区：[1]太原理工大学物理与光电工程学院,山西太原030024

出　　处：《山西大学学报（自然科学版）》2020年第3期517-525,共9页Journal of Shanxi University(Natural Science Edition)

基　　金：山西量子光学和量子光学器件国家重点科学实验室开放项目(KF201808)。

摘　　要：文章研究自旋F=1系统中自旋相干态的演化。系统中3×3的单粒子密度矩阵可分为单极矩(monopole),偶极矩(dipole)和四极矩(quadrupole)等三类。和2×2的赝自旋1/2系统中的泡利矩阵不同,系统中任意一个自旋角动量(dipole)矩阵的平方不再是一个单位矩阵,而是对应的不同的四极矩,这使得自旋F=1系统的物理问题更加丰富。通过SU(3)李代数群将系统的角动量和四极矩张量进行分类,并计算了它们之间的对易关系。并给出了F=1系统中自旋相干态表达式并和自旋1/2系统做了比较。由于四极矩张量和角动量之间的不对易性,使得基于角动量代数来计算相干态的演化已经失效。因此从基本的对易关系[a_m,a~?_m]出发,在粒子数表象中计算量子态的演化和外磁场的影响。文章给出3种可以解析描述的演化规律。基于此研究了二阶关联的演化,后者是自旋压缩特性的基本构成单元。同时我们将所有的代数结果和严格对角化数值方法进行了比较。The evolution of coherent spin state(CSS)in the spin-1 system is studied,where single-particle density matrix can be classified into three kinds,including monopole,dipole,and quadrupole.Different from pseudospin-1/2 system,the square of any angular momentum matrix is not equal to the identity matrix in the present system,but corresponds to quadrupole moments,which leads to richer physics in the spin-1 system.The angular momentum and quadrupole tensors are classified by the SU(3)Lie algebra and the commutation relations between them are calculated,moreover,the formulas of CSS in the spin-1 system is given and compared with the one in the pseudospin-1/2 system.Due to the non-commutativity between the angular momentum and quadrupole tensors,calculations based on angular momentum algebra become invalid in the angular momentum representation.Thus,the evolution of quantum states and the influence of external magnetic fields are calculated in particle number representation,where the fundamental commutativity-relation of[a_m,a~?_m]is considered.We gives three analytical results to understand the evolution rules.Simultaneously,the quadratic correlations are also calculated,which are the basic units for the studying of the quantum entanglements and spin squeezing dynamics.Finally,all the algebra results are conformed using the full exact diagonalization methods.

关 键 词：自旋相干态 二阶塞曼效应 自旋压缩 

分 类 号：O469[理学—凝聚态物理]