Coherent-State Approach for Majorana Representation  

作　　者：刘昊迪 傅立斌 王晓光 

机构地区：[1]Beijing Computational Science Research Center [2]Center for Quantum Sciences and School of Physics, Northeast Normal University [3]National Laboratory of Science and Technology on Computational Physics,Institute of Applied Physics and Computational Mathematics [4]Zhejiang Institute of Modern Physics,Department of Physics,Zhejiang University

出　　处：《Communications in Theoretical Physics》2017年第6期611-618,共8页理论物理通讯（英文版）

基　　金：Supported by the National Fundamental Research Program of China under Grant No.2013CBA01502;the National Natural Science Foundation of China under Grant Nos.11575027,11475146,and 11405008;the Fundamental Research Funds for the Central Universities under Grant No.2017FZA3005;the Plan for Scientific and Technological Development of Jilin Province under Grant No.20160520173JH

摘　　要：By representing a quantum state and its evolution with the Majorana stars on the Bloch sphere, the Majorana representation provides us an intuitive way to study a physical system with SU(2) symmetry. In this work,based on coherent states, we propose a method to establish the generalization of Majorana representation for a general symmetry. By choosing a generalized coherent state as a reference state, we give a more general Majorana representation for both finite and infinite systems and the corresponding star equations are given. Using this method, we study the squeezed vacuum states for three different symmetries, Heisenberg–Weyl, SU(2) and SU(1,1), and express the effect of squeezing parameter on the distribution of stars. Furthermore, we also study the dynamical evolution of stars for an initial coherent state driven by a nonlinear Hamiltonian, and find that at a special time point, the stars are distributed on two orthogonal large circles.By representing a quantum state and its evolution with the Majorana stars on the Bloch sphere, the Majorana representation provides us an intuitive way to study a physical system with SU（2） symmetry. In this work, based on coherent states, we propose a method to establish the generalization of Majorana representation for a general symmetry. By choosing a generalized coherent state as a reference state, we give a more general Majorana representation for both finite and infinite systems and the corresponding star equations are given. Using this method, we study the squeezed vacuum states for three different symmetries, Heisenberg Weyl, SU（2） and SU（I,1）, and express the effect of squeezing parameter on the distribution of stars. Furthermore, we also study the dynamical evolution of stars for an initial coherent state driven by a nonlinear Hamiltonian, and find that at a special time point, the stars are distributed on two orthogonal large circles.

关 键 词：majorana representation coherent state squeezed states SU(1 1) symmetry 

分 类 号：O41[理学—理论物理]