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 t...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.展开更多
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. T...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.展开更多
Noether’s theorem is one of the fundamental laws in physics,relating the symmetry of a physical system to its constant of motion and conservation law.On the other hand,there exist a variety of non-Hermitian parity-ti...Noether’s theorem is one of the fundamental laws in physics,relating the symmetry of a physical system to its constant of motion and conservation law.On the other hand,there exist a variety of non-Hermitian parity-time(PT)-symmetric systems,which exhibit novel quantum properties and have attracted increasing interest.In this work,we extend Noether’s theorem to a class of significant PT-symmetry systems for which the eigenvalues of the PT-symmetry Hamiltonian HPTchange from purely real numbers to purely imaginary numbers,and introduce a generalized expectation value of an operator based on biorthogonal quantum mechanics.We find that the generalized expectation value of a time-independent operator is a constant of motion when the operator presents a standard symmetry in the PT-symmetry unbroken regime,or a chiral symmetry in the PT-symmetry broken regime.In addition,we experimentally investigate the extended Noether’s theorem in PT-symmetry single-qubit and two-qubit systems using an optical setup.Our experiment demonstrates the existence of the constant of motion and reveals how this constant of motion can be used to judge whether the PT-symmetry of a system is broken.Furthermore,a novel phenomenon of masking quantum information is first observed in a PT-symmetry two-qubit system.This study not only contributes to full understanding of the relation between symmetry and conservation law in PT-symmetry physics,but also has potential applications in quantum information theory and quantum communication protocols.展开更多
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 ...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.展开更多
Controlling the balanced gain and loss in a PT-symmetric system is a rather challenging task. Utilizing Floquet theory, we explore the constructive role of periodic modulation in controlling the gain and loss of a PT-...Controlling the balanced gain and loss in a PT-symmetric system is a rather challenging task. Utilizing Floquet theory, we explore the constructive role of periodic modulation in controlling the gain and loss of a PT-symmetric optical coupler. It is found that the gain and loss of the system can be manipulated by applying a periodic modulation. Purther, such an original non-Hermitian system can even be modulated into an effective Hermitian system derived by the high-frequency Floquet method. Therefore, compared with other PT- symmetry control schemes, our protocol can modulate the unbroken PT-symmetric range to a wider parameter region. Our results provide a promising approach for controlling the gain and loss of a realistic system.展开更多
We investigate the quantum-memory-assisted entropic uncertainty relation(QMA-EUR)in a Heisenberg XYZ mixed-spin(1/2,1)model.Coupling strength,Dzyaloshinskii–Moriya(DM)interaction and inhomogeneous magnetic field,resp...We investigate the quantum-memory-assisted entropic uncertainty relation(QMA-EUR)in a Heisenberg XYZ mixed-spin(1/2,1)model.Coupling strength,Dzyaloshinskii–Moriya(DM)interaction and inhomogeneous magnetic field,respectively,contributing to QMA-EUR by a thermal entanglement in the hybrid-spin model are studied in detail.Furthermore,we compare the uncertainty of the bipartite hybrid model with those of qubit–qubit and qutrit–qutrit systems.Meanwhile,the effects of local PT-symmetric operation and weak measurement on the steering of entropic uncertainty are analyzed.We find that the local PT-symmetric operation can reduce the entropic uncertainty,and the entropic uncertainty can also be decreased by weak measurement reversal.展开更多
In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics,which yields that a state of the PT-symmetric quantum system at any time will remain approxim...In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics,which yields that a state of the PT-symmetric quantum system at any time will remain approximately in the m-th eigenstate up to a multiplicative phase factor whenever it is initially in the m-th eigenstate of the Hamiltonian. In addition, we estimate the approximation errors by the distance and the fidelity between the exact solution and the adiabatic approximate solution to the time evolution equation, respectively.展开更多
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 ...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.展开更多
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 alw...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.展开更多
基金partly funded by the Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2021MA091 and ZR2018MA044)Introduction and Cultivation Plan of Youth Innovation Talents for Universities of Shandong Province (Research and Innovation Team on Materials Modification and Optoelectronic Devices at extreme conditions)。
文摘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.
基金supported by the National Natural Science Foundation of China(Grant No.12088101,and U2330401).
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.12264040,12204311,11804228,11865013,and U21A20436)the Jiangxi Natural Science Foundation(Grant Nos.20212BAB211018,20192ACBL20051)+8 种基金the Project of Jiangxi Province Higher Educational Science and Technology Program(Grant Nos.GJJ190891,and GJJ211735)the Key-Area Research and Development Program of Guangdong Province(Grant No.2018B03-0326001)supported in part by the Nippon Telegraph and Telephone(NTT)Corporation Researchthe Japan Science and Technology(JST)Agency[via the Quantum Leap Flagship Program(Q-LEAP)Moonshot R&D Grant Number JPMJMS2061]the Japan Society for the Promotion of Science(JSPS)[via the Grants-in-Aid for Scientific Research(KAKENHI)Grant No.JP20H00134]the Army Research Office(ARO)(Grant No.W911NF-18-1-0358)the Asian Office of Aerospace Research and Development(AOARD)(Grant No.FA2386-20-1-4069)the Foundational Questions Institute Fund(FQXi)(Grant No.FQXi-IAF19-06)。
文摘Noether’s theorem is one of the fundamental laws in physics,relating the symmetry of a physical system to its constant of motion and conservation law.On the other hand,there exist a variety of non-Hermitian parity-time(PT)-symmetric systems,which exhibit novel quantum properties and have attracted increasing interest.In this work,we extend Noether’s theorem to a class of significant PT-symmetry systems for which the eigenvalues of the PT-symmetry Hamiltonian HPTchange from purely real numbers to purely imaginary numbers,and introduce a generalized expectation value of an operator based on biorthogonal quantum mechanics.We find that the generalized expectation value of a time-independent operator is a constant of motion when the operator presents a standard symmetry in the PT-symmetry unbroken regime,or a chiral symmetry in the PT-symmetry broken regime.In addition,we experimentally investigate the extended Noether’s theorem in PT-symmetry single-qubit and two-qubit systems using an optical setup.Our experiment demonstrates the existence of the constant of motion and reveals how this constant of motion can be used to judge whether the PT-symmetry of a system is broken.Furthermore,a novel phenomenon of masking quantum information is first observed in a PT-symmetry two-qubit system.This study not only contributes to full understanding of the relation between symmetry and conservation law in PT-symmetry physics,but also has potential applications in quantum information theory and quantum communication protocols.
基金supported in part by the‘Qing Lan Project’of Jiangsu Province(2020)the‘333 Project’of Jiangsu Province(No.BRA2020246)+1 种基金the National Natural Science Foundation of China(12271488,11975145,and 11972291)the Ministry of Science and Technology of China(G2021016032L).
文摘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.
基金Acknowledgements We acknowledge helpful discussion with Chaohong Lee. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11465008, 11574405, and 11426223）, the Hunan Provincial Natural Science Foundation （Grant Nos. 2015JJ2114, 2015JJ4020, and 14JJ3114）, and the Scientific Research Fund of Hunan Provincial Education Department （Grant No. 14A118）.
文摘Controlling the balanced gain and loss in a PT-symmetric system is a rather challenging task. Utilizing Floquet theory, we explore the constructive role of periodic modulation in controlling the gain and loss of a PT-symmetric optical coupler. It is found that the gain and loss of the system can be manipulated by applying a periodic modulation. Purther, such an original non-Hermitian system can even be modulated into an effective Hermitian system derived by the high-frequency Floquet method. Therefore, compared with other PT- symmetry control schemes, our protocol can modulate the unbroken PT-symmetric range to a wider parameter region. Our results provide a promising approach for controlling the gain and loss of a realistic system.
基金supported by the National Natural Science Foundation of China under Grant Nos.91950112 and 11174081the National Key Research and Development Program of China under Grant No.2016YFB0501601。
文摘We investigate the quantum-memory-assisted entropic uncertainty relation(QMA-EUR)in a Heisenberg XYZ mixed-spin(1/2,1)model.Coupling strength,Dzyaloshinskii–Moriya(DM)interaction and inhomogeneous magnetic field,respectively,contributing to QMA-EUR by a thermal entanglement in the hybrid-spin model are studied in detail.Furthermore,we compare the uncertainty of the bipartite hybrid model with those of qubit–qubit and qutrit–qutrit systems.Meanwhile,the effects of local PT-symmetric operation and weak measurement on the steering of entropic uncertainty are analyzed.We find that the local PT-symmetric operation can reduce the entropic uncertainty,and the entropic uncertainty can also be decreased by weak measurement reversal.
基金supported by the National Natural Science Foundation of China(Grant Nos.11171197 and 11371012)the Science Research Foundation of Education Department of Shaanxi Provincial Government(Grant No.11JK0513)+2 种基金the Fundamental Research Funds for the Central Universities(Grant No.GK201402005 and GK201301007)the Postdoctoral Science Foundation of China(Grant No.2014M552405)the Natural Science Research Program of Shaanxi Province(Grant No.2014JQ1010)
文摘In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics,which yields that a state of the PT-symmetric quantum system at any time will remain approximately in the m-th eigenstate up to a multiplicative phase factor whenever it is initially in the m-th eigenstate of the Hamiltonian. In addition, we estimate the approximation errors by the distance and the fidelity between the exact solution and the adiabatic approximate solution to the time evolution equation, respectively.
基金Supported by the National Natural Science Foundation of China under Grant No.11171197
文摘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.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 61308019） and the Foundation for Distinguished Young Talents in Higher Education of Guangdong （Grant No. Yq2013157）. H. Wang also acknowledges the financial support from China Scholarship Council.
文摘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.
