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
We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obt...We use the Bethe ansatz method to investigate the Schrdinger 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.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
This special issue is dedicated to the emerging field of non-Hermitian photonics of complex media, with emphasis on PT-symmetric optical structures. In particular, the papers highlight the variety of applications bein...This special issue is dedicated to the emerging field of non-Hermitian photonics of complex media, with emphasis on PT-symmetric optical structures. In particular, the papers highlight the variety of applications being considered and the ways in which non-Hermitian optics can improve their performance.展开更多
Submission Open:15 March 2017 Submission Deadline:15 April 2017 The idea of parity-time(PT)symmetry,first introduced in quantum mechanics,was recently realized in the context of photonics in the form of balanced gain-...Submission Open:15 March 2017 Submission Deadline:15 April 2017 The idea of parity-time(PT)symmetry,first introduced in quantum mechanics,was recently realized in the context of photonics in the form of balanced gain-loss structures with special symmetries.In recent years。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
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
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
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
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 ...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.展开更多
With a view to getting further insight into the solutions of one-dimensional analogous Schr?dinger equation for a non-hermitian (complex) Hamiltonian system, we investigate the quasi-exact PT- symmetric solutions for ...With a view to getting further insight into the solutions of one-dimensional analogous Schr?dinger equation for a non-hermitian (complex) Hamiltonian system, we investigate the quasi-exact PT- symmetric solutions for an octic potential and its variant using extended complex phase space approach characterized by x=x1+ip2, p=p1+ix2, where (x1, p1) and (x2, p2) are real and considered as canonical pairs. Besides the complexity of the phase space, complexity of potential parameters is also considered. The analyticity property of the eigenfunction alone is found sufficient to throw light on the nature of eigenvalue and eigenfunction of a system. The imaginary part of energy eigenvalue of a non-hermitian Hamiltonian exist for complex potential parameters and reduces to zero for real parameters. However, in the present work, it is found that imaginary component of the energy eigenvalue vanishes even when potential parameters are complex, provided that PT-symmetric condition is satisfied. Thus PT- symmetric version of a non-hermitian Hamiltonian possesses the real eigenvalue.展开更多
A new example of PT-symmetric quasi-exactly solvable (QES) 22×-matrix Hamiltonian which is associated to a trigonometric Razhavi potential is con-sidered. Like the QES analytic method considered in the Ref. [1] [...A new example of PT-symmetric quasi-exactly solvable (QES) 22×-matrix Hamiltonian which is associated to a trigonometric Razhavi potential is con-sidered. Like the QES analytic method considered in the Ref. [1] [2], we es-tablish three necessary and sufficient algebraic conditions for this Hamilto-nian to have a finite-dimensional invariant vector space whose generic ele-ment is polynomial. This non hermitian matrix Hamiltonian is called qua-si-exactly solvable [3].展开更多
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...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.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
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
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 lattic...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.展开更多
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 schem...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.展开更多
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...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.展开更多
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 doe...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.展开更多
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.
文摘We use the Bethe ansatz method to investigate the Schrdinger 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.
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.
文摘This special issue is dedicated to the emerging field of non-Hermitian photonics of complex media, with emphasis on PT-symmetric optical structures. In particular, the papers highlight the variety of applications being considered and the ways in which non-Hermitian optics can improve their performance.
文摘Submission Open:15 March 2017 Submission Deadline:15 April 2017 The idea of parity-time(PT)symmetry,first introduced in quantum mechanics,was recently realized in the context of photonics in the form of balanced gain-loss structures with special symmetries.In recent years。
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 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 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.
文摘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.
文摘With a view to getting further insight into the solutions of one-dimensional analogous Schr?dinger equation for a non-hermitian (complex) Hamiltonian system, we investigate the quasi-exact PT- symmetric solutions for an octic potential and its variant using extended complex phase space approach characterized by x=x1+ip2, p=p1+ix2, where (x1, p1) and (x2, p2) are real and considered as canonical pairs. Besides the complexity of the phase space, complexity of potential parameters is also considered. The analyticity property of the eigenfunction alone is found sufficient to throw light on the nature of eigenvalue and eigenfunction of a system. The imaginary part of energy eigenvalue of a non-hermitian Hamiltonian exist for complex potential parameters and reduces to zero for real parameters. However, in the present work, it is found that imaginary component of the energy eigenvalue vanishes even when potential parameters are complex, provided that PT-symmetric condition is satisfied. Thus PT- symmetric version of a non-hermitian Hamiltonian possesses the real eigenvalue.
文摘A new example of PT-symmetric quasi-exactly solvable (QES) 22×-matrix Hamiltonian which is associated to a trigonometric Razhavi potential is con-sidered. Like the QES analytic method considered in the Ref. [1] [2], we es-tablish three necessary and sufficient algebraic conditions for this Hamilto-nian to have a finite-dimensional invariant vector space whose generic ele-ment is polynomial. This non hermitian matrix Hamiltonian is called qua-si-exactly solvable [3].
文摘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.
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.
基金the National Natural Science Foundation of China(Grant Nos.12074097 and 11921005)the Natural Science Foundation of Hebei Province(Grant No.A2020205013)+2 种基金the National Key R&D Program of China(Grant No.2017YFA0303301)the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.DB28000000)Beijing Municipal Science&Technology Commission(Grant No.Z191100007219013).
文摘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.
基金the National Natural Science Foundation of China under Grant No.61822114.
文摘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.
文摘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.
基金This work was supported by the National Basic Research Program of China(Grant No.2016YFA0301903)the National Natural Science Foundation of China(Grant Nos.12074433,12004430,12174447,12174448,and 11904402).
文摘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.
