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Investigation of the effect of quantum measurement on parity-time symmetry

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Science China(Physics,Mechanics & Astronomy) 2022年第6期65卷 36-43页

作者： Wei-Chen Wang Yi Xie Man-Chao Zhang Jie Zhang Chun-Wang Wu Ting Chen Bao-Quan Ou Wei Wu Ping-Xing Chen Department of Physics College of Liberal Arts and SciencesNational University of Defense TechnologyChangsha 410073China Interdisciplinary Center for Quantum Information National University of Defense TechnologyChangsha 410073China

symmetry,including the parity-time(pt)-symmetry,is a striking topic,widely discussed and employed in many *** is well-known that quantum measurement can destroy or disturb quantum ***,can and how does quantum measurement destroy the symmetry of the measured system?To answer the pertinent question,we establish the correlation between the quan-tum measurement and Floquet pt-symmetry and investigate for the first time how the measurement frequency and measurement strength affect the pt-symmetry of the measured system using the 40Ca+*** is already shown that the measurement at high frequencies would break the pt ***,even for an inadequately fast measurement frequency,if the measurement strength is sufficiently strong,the pt symmetry breaking can *** current work can enhance our knowledge of quantum measurement and symmetry and may inspire further research on the effect of quantum measurement on symmetry.

关键词： quantum measurement pt-symmetry ion trap

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Ground state cooling of magnomechanical resonator in pt-symmetric cavity magnomechanical system at room temperature

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Frontiers of physics 2020年第5期15卷 145-154页

作者： Zhi-xin Yang Liang Wang Yu-Mu Liu Dong-Yang Wang Cheng-Hua Bai Shou Zhang Hong-Fu Wang Department of Physics College of ScienceYanbian UniversityYanji 133002China Center for Quantum Sciences and School of Physics Northeast Normal UniversitChangchun 130024China School of Physics Harbin Institute of TechnologyHarbin 150001China

We propose to realize the ground state cooling of magnomechanical resonator in a parity-time(pt).symmetric cavity magnomechanical system composed of a loss ferromagnetic sphere and a gain microwave *** the scheme,the magnomechanical resonator can be cooled close to its ground state via the magnomechanical interaction,and it is found that the cooling effect in pt-symmetric system is much higher than that in non-pt-symmetric *** to the magnetic force noise spectrum,we investigate the final mean phonon number with experimentally feasible parameters and find surprisingly that the ground state cooling of magnomechanical resonator can be directly achieved at room ***,we also illustrate that the ground state cooling can be flexibly controlled via the external magnetic field.

关键词： ground state cooling magnomechanical resonator pt-symmetry

Sub-Nanometer Displacement Sensor Based on Coupling of Balanced Loss and Gain Cavities

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Photonic Sensors 2019年第3期9卷 259-267页

作者： Yuntuan FANG Xiaoxue LI School of Computer Science and Telecommunication Engineering Jiangsu University Zhenjiang 212013 China

Sub-nanometer displacement measurement is still a challenge in the current sensor field. In this study, a new type of displacement sensor is designed which is based on the coupling effect of two balanced gain and loss resonators. The optical properties of the sensor have been studied through the coupled mode theory and scatter matrix. The pole effect in the coupling system can be used to measure the subanometer displacement. The resolution of the sensor can reach 0.001 nm over a dynamic range of 20 nm. The sensor has the highest sensitivity within the range of one *** environmental disturbance and structure parameter perturbation have been demonstrated to make trivial effect on the sensor performance.

关键词： Displacement sensor pt-symmetry pole

Exceptional points and quantum dynamics in a non-Hermitian two-qubit system

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Chinese Physics B 2024年第6期33卷 212-218页

作者：张益玺张振涛杨震山魏晓志梁宝龙 School of Physics Science and Information Technology Shandong Key Laboratory of Optical Communication Science and TechnologyLiaocheng UniversityLiaocheng 252059China

We study the exceptional-point(EP) structure and the associated quantum dynamics in a system consisting of a non-Hermitian qubit and a Hermitian qubit. We find that the system possesses two sets of EPs, which divide the systemparameter space into pt-symmetry unbroken, partially broken and fully broken regimes, each with distinct quantumdynamics characteristics. Particularly, in the partially broken regime, while the pt-symmetry is generally broken in the whole four-dimensional Hilbert space, it is preserved in a two-dimensional subspace such that the quantum dynamics in the subspace are similar to those in the pt-symmetry unbroken regime. In addition, we reveal that the competition between the inter-qubit coupling and the intra-qubit driving gives rise to a complex pattern in the EP variation with system parameters.

关键词： non-Hermitian system exceptional point pt-symmetry

Cpt-Frames for Non-Hermitian Hamiltonians

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Communications in Theoretical Physics 2013年第9期60卷 328-334页

作者：曹怀信郭志华陈峥立 College of Mathematics and Information Science Shaanxi Normal University

Based on the pt-symmetric quantum theory, the concepts of pt-frame, pt-symmetric operator and Cpt-frame on a Hilbert space K and for an operator on K are proposed. It is proved that the spectrum and point spectrum of a pt-symmetric linear operator are both symmetric with respect to the real axis and the eigenvalues of an unbroken pt-symmetric operator are real. For a linear operator H on Cd, it is proved that H has unbroken pt- symmetry if and only if it has d different eigenvalues and the corresponding eigenstates are eigenstates of pt. Given a Cpt-frame on K, a new positive inner product on K is induced and called Cpt-inner product. Te relationship between the Cpt-adjoint and the Dirac adjoint of a densely defined linear operator is derived, and it is proved that an operator which has a bounded Cpt-frame is Cpt-Hermitian if and only if it is T-symmetric, in that case, it is similar to a Hermitian operator. The existence of an operator C consisting of a Cpt-frame is discussed, These concepts and results will serve a mathematical discussion about pt-symmetric quantum mechanics.

关键词： Cpt-frame pt-frame pt-symmetry operator

An analytical solution for quantum scattering through a pt-symmetric delta potential

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Frontiers of physics 2021年第4期16卷 213-220页

作者： Ying-Tao Zhang Shan Jiang Qingming Li Qing-Feng Sun College of Physics Hebei Normal UniversityShijiazhuang 050024China International Center for Quantum Materials School of PhysicsPeking UniversityBeijing 100871China Collaborative Innovation Center of Quantum Matter Beijing 100871China CAS Center for Excellence in Topological Quantum Computation University of Chinese Academy of SciencesBeijing 100190China

We employ the Lippmann–Schwinger formalism to derive the analytical solutions of the transmission and reflection coefficients through a one-dimensional open quantum system,in which particle loss or gain on one lattice site located at x=0,or particle loss and gain on the lattice sites located at x=±L 2 are considered *** gain and loss on the lattice site are modeled by the delta potential with positive and negative imaginary *** analytical solution reveals the underlying physics that the sum of the transmission and reflection coefficients through an open quantum system(even a pt-symmetric open system)may not be 1,i.e.,qualitatively explains that the number of particles is not conserved in an open quantum ***,we find that the resonance states can be formed in the pt-symmetric delta potential,which is similar to the case of real delta *** results of our analysis can be treated as the starting point of studying quantum transport problems through a non-Hermitian system using Green’s function method,and more general cases for high-dimensional systems may be deduced by the same procedure.

关键词： transmission non-Hermitian pt-symmetry Green function

Integrable nonlocal pt-symmetric generalized so(3,R)-mKdV equations

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Communications in Theoretical Physics 2023年第12期75卷 19-24页

作者： Shou-Ting Chen Wen-Xiu Ma School of Mathematics and Statistics Xuzhou University of TechnologyXuzhou 221008JiangsuChina Department of Mathematics Zhejiang Normal UniversityJinhua 321004ZhejiangChina Department of Mathematics King Abdulaziz UniversityJeddah 21589Saudi Arabia Department of Mathematics and Statistics University of South FloridaTampaFL 33620-5700United States of America School of Mathematical and Statistical Sciences North-West UniversityMafikeng CampusPrivate Bag X2046Mmabatho 2735South Africa

Based on a soliton hierarchy associated with so(3,R),we construct two integrable nonlocal pt-symmetric generalized mKdV *** key step is to formulate two nonlocal reverse-spacetime similarity transformations for the involved spectral matrix,and therefore,integrable nonlocal complex and real reverse-spacetime generalized so(3,R)-mKdV equations of fifth-order are *** resulting reduced nonlocal integrable equations inherit infinitely many commuting symmetries and conservation laws.

关键词： integrable equation lax pair nonlocal reduction pt-symmetry zero curvature equation

Solution of Schrdinger Equation for Two-Dimensional Complex Quartic Potentials

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Communications in Theoretical Physics 2009年第3期51卷 397-406页

作者： Ram Mehar Singh Fakir Chand S.C.Mishra Department of Physics Ch. Devi Lal University Department of Physics Kurukshetra University

We investigate the quasi-exact solutions of the Schrodinger wave equation for two-dimensional non-hermitian complex Hamiltonian systems within the frame work of an extended complex phase space characterized by x = x1 ＋ ip3, y = x2 ＋ ip4, px= p1＋ ix3, py= p2 ＋ ix4. Explicit expressions of the energy eigenvalues and the eigenfunctions for ground and first excited states for a complex quartic potential are obtained. Eigenvalue spectra of some variants of the complex quartic potential, including pt-symmetrie one, are also worked out.

关键词： Schrodinger equation complex Hamiltonian eigenvalues eigenfunctions pt-symmetry

Dynamics of 2×2 matrix non-Hermitian quantum systems on Bloch sphere

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Communications in Theoretical Physics 2024年第4期76卷 66-71页

作者： Libin Fu Graduate School of China Academy of Engineering Physics Beijing 100193China

By casting evolution to the Bloch sphere, the dynamics of 2 × 2 matrix non-Hermitian systems are investigated in detail. This investigation reveals that there are four kinds of dynamical modes for such systems. The different modes are classified by different kinds of fixed points, namely,the elliptic point, spiral point, critical node, and degenerate point. The Hermitian systems and the unbroken pt non-Hermitian cases belong to the category with elliptic points. The degenerate point just corresponds to the systems with exceptional point(EP). The topological properties of the fixed point are also discussed. It is interesting that the topological charge for the degenerate point is two, while the others are one.

关键词： non-Hermitian quantum system two-level system dynamics on the Bloch sphere pt-symmetry fixed points