Coherent-State Approach for Majorana Representation**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, and the Plan for Scientific and Technological Development of Jilin Province under Grant No. 20160520173JH

Abstract

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.