Coherent-State Approach for Majorana Representation
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 Major...
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| Published in | Communications in theoretical physics Vol. 67; no. 6; pp. 611 - 618 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
01.06.2017
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| Online Access | Get full text |
| ISSN | 0253-6102 |
| DOI | 10.1088/0253-6102/67/6/611 |
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| Summary: | 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. |
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| Bibliography: | majorana representation, coherent state, squeezed states, SU（1,1） symmetry 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. 11-2592/O3 Hao-Di Liu 1＇2 ,Li-Bin Fu ,a and Xiao-Guang Wang （ 1Beijing Computational Science Research Center, Beijing 100084, China 2Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China 3National Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computa- tional Mathematics, Beijing 100088, China 4Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou 310027, China） |
| ISSN: | 0253-6102 |
| DOI: | 10.1088/0253-6102/67/6/611 |