Controllability of Quantum Systems with SU(1,1)Dynamical Symmetry  

作　　者：WU Jianwu WU Rebing ZHANG Jing LI Chunwen 

机构地区：[1]Beijing Aerospace Automatic Control Institute,Beijing 100854,China [2]Department of Automation,Tsinghua University,Beijing 100084,China [3]Center for Quantum Information Science and Technology,BNRist,Beijing 100084,China

出　　处：《Journal of Systems Science & Complexity》2021年第3期827-842,共16页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.61803357,61833010,61773232,61622306 and 11674194;the National Key R&D Program of China under Grant Nos.2018YFA0306703 and 2017YFA0304304;the Tsinghua University Initiative Scientific Research Program;the Tsinghua National Laboratory for Information Science and Technology Cross-discipline Foundation。

摘　　要：This paper presents sufficient and necessary conditions for the propagator controllability of a class of infinite-dimensional quantum systems with SU(1,1)dynamical symmetry through the isomorphic mapping to the non-unitary representation of SU(1,1).The authors prove that the elliptic condition of the total Hamiltonian is both necessary and sufficient for the controllability and strong controllability.The obtained results can be also extended to control systems with SO(2,1)dynamical symmetry.

关 键 词：Control of quantum mechanical systems CONTROLLABILITY nonlinear geometric control SU(1 1)symmetry systems on noncompact Lie groups 

分 类 号：O413.1[理学—理论物理]