周期驱动的二能级系统中的准宇称-时间对称动力学  

Quasi-parity-time symmetric dynamics in periodically driven two-level non-Hermitian system

作　　者：胡洲 曾招云[2] 唐佳 罗小兵 Hu Zhou;Zeng Zhao-Yun;Tang Jia;Luo Xiao-Bing(Department of Physics,Zhejiang Sci-Tech University,Hangzhou 310018,China;School of Mathematics and Physics,Jinggangshan University,Ji’an 343009,China)

机构地区：[1]浙江理工大学物理系,杭州310018 [2]井冈山大学数理学院,吉安343009

出　　处：《物理学报》2022年第7期175-186,共12页Acta Physica Sinica

基　　金：浙江省自然科学基金(批准号:LY21A050002);国家自然科学基金(批准号:11975110,12164022);江西省教育厅科技项目(批准号:GJJ211026);浙江理工大学科研启动基金(批准号:20062318-Y)资助的课题。

摘　　要：本文研究了一个周期驱动的非宇称-时间对称二能级量子系统的非厄米动力学.通过经典相空间分析方法,解出了该非厄米系统的Floquet态和准能谱,并解析构造了由该非厄米哈密顿量支配下的量子态的非幺正时间演化算符,给出了不同参数区域的量子态演化.本文数值和分析证明,该非宇称-时间对称二能级Floquet系统,类似于宇称-时间对称系统,存在一个准能谱从实数谱到复数谱的相变.本文还揭示了在量子态的动态演化中存在一种准宇称-时间对称动力学,即,该系统的粒子布居概率演化完全满足时间空间对称(宇称-时间对称),但是由于相位演化违反了宇称-时间对称性的要求,因此包含相位信息的量子态演化不满足时间空间对称(宇称-时间对称).这些结果加深了对非厄米物理的理解,拓展和推广了传统的宇称-时间对称概念.In recent years,there have been intensive studies of non-Hermitian physics and parity-time(PT)symmetry due to their fundamental importance in theory and outstanding applications.A distinctive character in PTsymmetric system is phase transition(spontaneous PT-symmetry breaking),i.e.an all-real energy spectrum changes into an all-complex one when the non-Hermitian parameter exceeds a certain threshold.However,the conditions for PT-symmetric system with real energy spectrum to occur are rather restrictive.The generalization of PT-symmetric potenials to wider classes of non-PT-symmetric complex potentials with all-real energy spectra is a currently important endeavor.A simple PT-symmetric two-level Floquet quantum system is now being actively explored,because it holds potential for the realization of non-unitary single-qubit quantum gate.However,studies of the evolution dynamics of non-PT-symmetric two-level non-Hermitian Floquet quantum system are still relatively rare.In this paper,we investigate the non-Hermitian physics of a periodically driven non-PT-symmetric twolevel quantum system.By phase-space analysis,we find that there exist so-called pseudo fixed points in phase space representing the Floquet solutions with fixed population difference and a time-dependent relative phase between the two levels.According to these pseudo fixed points,we analytically construct a non-unitary evolution operator and then explore the dynamic behaviors of the non-PT-symmetric two-level quantum system in different parameter regions.We confirm both analytically and numerically that the two-level non-Hermitian Floquet quantum system,although it is non-par it y-time-symmetric,still features a phase transition with the quasienergy spectrum changing from all-real to all-complex energy spectrum,just like the PT symmetric system.Furthermore,we reveal that a novel phenomenon called quasi-PT symmetric dynamics occurs in the time evolution process.The quasi-PT symmetric dynamics is so named in our paper,in the sense that the timeevolution o

关 键 词：宇称-时间对称 周期驱动二能级系统 非厄米物理 动力学演化 

分 类 号：O413.1[理学—理论物理]