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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.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 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

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 fields.It is well-known that quantum measurement can destroy or disturb quantum systems.However,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+ion.It is already shown that the measurement at high frequencies would break the pt symmetry.Notably,even for an inadequately fast measurement frequency,if the measurement strength is sufficiently strong,the pt symmetry breaking can occur.The 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

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 equations.The 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 presented.The 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

Solvability of a class of pt-symmetric non-Hermitian Hamiltonians：Bethe ansatz method

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Chinese Physics B 2017年第6期26卷 14-21页

作者： M Baradaran H Panahi Department of Physics University of Guilan Rasht 41635-1914Iran

We use the Bethe ansatz method to investigate the Schrdinger equation for a class of pt-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obtained in terms of the roots of a set of algebraic equations. Also, it is shown that the problems possess sl（2） hidden symmetry and then the exact solutions of the problems are obtained by employing the representation theory of sl（2） Lie algebra. It is found that the results of the two methods are the same.

关键词： pt-symmetry Bethe ansatz method Lie algebraic approach quasi-exactly solvable

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 nanometer.The 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

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 cavity.In 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 system.Resorting 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 temperature.Furthermore,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

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 respectively.The gain and loss on the lattice site are modeled by the delta potential with positive and negative imaginary values.The 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 system.Furthermore,we find that the resonance states can be formed in the pt-symmetric delta potential,which is similar to the case of real delta potential.The 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

Multi-peak solitons in pt-symmetric Bessel optical lattices with defects

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Frontiers of physics 2016年第5期11卷 127-136页

作者： Hongcheng Wang College of Electronic Engineering Dongguan University of Technology Dongguan 523808 China CREOL The College of Optics and Photonics University of Central Florida Orlando FL 32816-2700 USA

This paper presents a theoretical analysis of the existence and stability of multi-peak solitons in parity-time-symmetric Bessel optical lattices with defects in nonlinear media. The results demonstrate that there always exists a critical propagation constant μc for the existence of multi-peak solitons regardless of whether the nonlinearity is self-focusing or self-defocusing. In self-focusing media, multi-peak solitons exist when the propagation constant μ 〉 μc. In the self-defocusing case, solitons exist only when μ 〈 μc. Only low-power solitons can propagate stably when random noise perturbations are present. Positive defects help stabilize the propagation of multi-peak solitons when the nonlinearity is self-focusing. When the nonlinearity is self-defocusing, however, multi-peak solitons in negative defects have wider stable regions than those in positive defects.

关键词： lattice solitons multi-peak solitons pt-symmetry defect solitons

Quantum Mechanics of Complex Octic Potential in One Dimension

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Journal of Quantum Information Science 2013年第1期3卷 42-49页

作者： Ram Mehar Singh Department of Physics Chaudhary Devi Lal UniversitySirsaIndia

For gaining further insight into the nature of the eigenspectra of a complex octic potential [say], we investigate the quasi exact solutions of the Schr?dinger equation in an extended complex phase space characterized by . The analyticity property of the eigenfunction alone is found sufficient to throw light on the nature of eigenvalues and eigenfunction of a system. Explicit expressions of eigenvalues and eigenfunctions for the ground state as well as for the first excited state of a complex octic potential and its variant are worked out. It is found that imaginary part of the eigenvalue turns out to be zero for real coupling parameters, whereas it becomes non-zero for complex coupling parameters. However, the pt-symmetric version of a non-hermitian Hamiltonian possesses the real eigenvalue even if coupling parameters in the potential are complex.

关键词： Schrodinger Equation Complex Potential pt-symmetry Ansatz