It is well known that the A-square term must be considered in both cavity and circuit quantum electrodynamics systems,because it arises in the derivation from the minimal coupling Hamiltonian at any finite coupling st...It is well known that the A-square term must be considered in both cavity and circuit quantum electrodynamics systems,because it arises in the derivation from the minimal coupling Hamiltonian at any finite coupling strength.In this paper,we study the quantum Rabi model with A-square terms using the Bogoliubov operator approach.After a unitary transformation,the A-square terms can be eliminated,resulting in a modified quantum Rabi model with renormalized parameters.A transcendental function responsible for the exact solution is then derived.The presence of the A-square terms is found to significantly alter the energy spectrum.The dynamics are also studied using the obtained exact wave function,which is sensitive to the strength of the A-square terms at strong coupling.We believe that these results could be observed in future light–matter interaction systems in the ultra-strong and deep strong coupling regimes.展开更多
We investigate the quantum phase transitions(QPTs)of the two-qubit quantum Rabi model with staggered qubit biases.In the limit of an infinite qubit-to-cavity frequency ratio,we analytically derive the mean-field Hamil...We investigate the quantum phase transitions(QPTs)of the two-qubit quantum Rabi model with staggered qubit biases.In the limit of an infinite qubit-to-cavity frequency ratio,we analytically derive the mean-field Hamiltonian and the order-parameter-dependent energy density functional,which yields the ground-state energy and order parameter.The rich superradiant phase transitions(SRPTs),including both second-and first-order QPTs and a tricritical point(TCP),are analytically derived.Specifically,we derive the analytical expressions for all phase transition points,including the nonperturbative point of the first-order SRPT.The analytical findings are further corroborated by numerical finite-size scaling analysis.It is found that both the critical correlation-length and order-parameter exponents at the TCP differ from those of the original second-order SRPTs,implying that the TCP belongs to a new universality class.This work provides a reliable theoretical framework for designing new,simple experimental platforms to explore the rich QPTs.展开更多
As one of the famous effects in the quantum Rabi model(QRM),Rabi oscillation may lead to the occurrence of quantum dynamical behaviors without classical dynamic counterparts,such as quantum collapse and revival effect...As one of the famous effects in the quantum Rabi model(QRM),Rabi oscillation may lead to the occurrence of quantum dynamical behaviors without classical dynamic counterparts,such as quantum collapse and revival effects.In this paper,we focus on studying the long-time quantum signatures of chaos in the large atom-light frequency ratios of the Rabi model.It is shown that the saturated values of the entanglement entropy for initial states located in chaotic sea are higher than that in the regular regions,and the Husimi Q function are more dispersed in phase space.Moreover,we observed that the long-time average entanglement entropy and spin variance correspond well with the semiclassical phase space.Our results imply that the correspondence principle is not invalidated by quantum collapse and revival effects in the large atom-light frequency ratios Rabi model.展开更多
We explore the possibility to generate new parity symmetry in the quantum Rabi model after a bias is introduced. In contrast to a mathematical treatment in a previous publication [J. Phys. A 46(2013) 265302], we consi...We explore the possibility to generate new parity symmetry in the quantum Rabi model after a bias is introduced. In contrast to a mathematical treatment in a previous publication [J. Phys. A 46(2013) 265302], we consider a physically realistic method by involving an additional spin into the quantum Rabi model to couple with the original spin by an Ising interaction, and then the parity symmetry is broken as well as the scaling behavior of the ground state by introducing a bias. The rule can be found that the parity symmetry is broken by introducing a bias and then restored by adding new degrees of freedom. Experimental feasibility of realizing the models under discussion is investigated.展开更多
An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation o...An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation or alternatively by assuming the form of the ground state wave function. The key of the method is to introduce a variational parameter λ,which can be determined by minimizing the energy functional. Using this method, we calculate the physical observables with high accuracy in comparison with the numerical exact ones. Our method evidently improves over the widely used general rotating-wave approximation（GRWA） in both qualitative and quantitative aspects.展开更多
The open quantum system can be described by either a Lindblad master equation or a non-Hermitian Hamiltonian(NHH).However,these two descriptions usually have different exceptional points(EPs),associated with the degen...The open quantum system can be described by either a Lindblad master equation or a non-Hermitian Hamiltonian(NHH).However,these two descriptions usually have different exceptional points(EPs),associated with the degeneracies in the open quantum system.Here,considering a dissipative quantum Rabi model,we study the spectral features of EPs in these two descriptions and explore their connections.We find that,although the EPs in these two descriptions are usually different,the EPs of NHH will be consistent with the EPs of master equation in the weak coupling regime.Further,we find that the quantum Fisher information(QFI),which measures the statistical distance between quantum states,can be used as a signature for the appearance of EPs.Our study may give a theoretical guidance for exploring the properties of EPs in open quantum systems.展开更多
The hidden Z2 symmetry of the asymmetric quantum Rabi model(AQRM)has recently been revealed via a systematic construction of the underlying symmetry operator.Based on the AQRM result,we propose an ansatz for the gener...The hidden Z2 symmetry of the asymmetric quantum Rabi model(AQRM)has recently been revealed via a systematic construction of the underlying symmetry operator.Based on the AQRM result,we propose an ansatz for the general form of the symmetry operators for AQRM-related models.Applying this ansatz we obtain the symmetry operator for three models:the anisotropic AQRM,the asymmetric Rabi–Stark model(ARSM),and the anisotropic ARSM.展开更多
An analytical method is developed to study the two-mode quantum Rabi model.For certain specific parameter conditions,especially for the resonant conditions,we obtain an infinite number of the exact solutions of the ei...An analytical method is developed to study the two-mode quantum Rabi model.For certain specific parameter conditions,especially for the resonant conditions,we obtain an infinite number of the exact solutions of the eigenfunctions and associated energies.It is shown that there exist new types of the exact energies which do not correspond to the level-crossings.Our analytical method may find applications in some related models.展开更多
We apply the second-order Born-Oppenheimer （BO） approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating w...We apply the second-order Born-Oppenheimer （BO） approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approxi- mation. By comparing with the numerical results, we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode.展开更多
We investigate the two-mode quantum Rabi model(QRM)describing the interaction between a two-level atom and a two-mode cavity field.The quantum phase transitions are found when the ratioηof transition frequency of ato...We investigate the two-mode quantum Rabi model(QRM)describing the interaction between a two-level atom and a two-mode cavity field.The quantum phase transitions are found when the ratioηof transition frequency of atom to frequency of cavity field approaches infinity.We apply the Schrieffer–Wolff(SW)transformation to derive the low-energy effective Hamiltonian of the two-mode QRM,thus yielding the critical point and rich phase diagram of quantum phase transitions.The phase diagram consists of four regions:a normal phase,an electric superradiant phase,a magnetic superradiant phase and an electromagnetic superradiant phase.The quantum phase transition between the normal phase and the electric(magnetic)superradiant phase is of second order and associates with the breaking of the discrete Z_(2) symmetry.On the other hand,the phase transition between the electric superradiant phase and the magnetic superradiant phase is of first order and relates to the breaking of the continuous U(1)symmetry.Several important physical quantities,for example the excitation energy and average photon number in the four phases,are derived.We find that the excitation spectra exhibit the Nambu–Goldstone mode.We calculate analytically the higher-order correction and finite-frequency exponents of relevant quantities.To confirm the validity of the low-energy effective Hamiltonians analytically derived by us,the finite-frequency scaling relation of the averaged photon numbers is calculated by numerically diagonalizing the two-mode quantum Rabi Hamiltonian.展开更多
A general approach is proposed to the quantum Rabi model and its several variants within the extended coherent states.The solutions to all these models including the anisotropy and the nonlinear Stark coupling are the...A general approach is proposed to the quantum Rabi model and its several variants within the extended coherent states.The solutions to all these models including the anisotropy and the nonlinear Stark coupling are then obtained in an unified way.The essential characteristics such as the possible first-order phase transition can be detected analytically.This approach can be easily applied to the recent experiments with various tunable parameters without much additional effort,so it should be very helpful to the analysis of the experimental data.展开更多
We theoretically investigate the exact solutions for generalized parity–time(PT)-reversal-symmetric Rabi models driven by external fields with monochromatic periodic, linear, and parabolic forms, respectively. The co...We theoretically investigate the exact solutions for generalized parity–time(PT)-reversal-symmetric Rabi models driven by external fields with monochromatic periodic, linear, and parabolic forms, respectively. The corresponding exact solutions are presented in terms of the confluent Heun equations without any approximation. In principle, the analytic solutions derived here are valid in the whole parameter space. Such a kind of study may offer potential coherent control schemes of the PT-symmetric two-level systems.展开更多
In this paper,we propose a scheme to achieve a multiphonon-resonance quantum Rabi model and adiabatic passage in a strong-coupling cavity optomechanical system.In the scheme,when the driving bichromatic laser beam is ...In this paper,we propose a scheme to achieve a multiphonon-resonance quantum Rabi model and adiabatic passage in a strong-coupling cavity optomechanical system.In the scheme,when the driving bichromatic laser beam is adjusted to the off-resonant j-order red-and blue-sideband,the interaction between the cavity and mechanical oscillator leads to a j-phonon resonance quantum Rabi model.Moreover,we show that there exists a resonant multi-phonon coupling via intermediate states connected by counter-rotating processes when the frequency of the simulated bosonic mode is near a fraction of the transition frequency of the simulated two-level system.As a typical example,we theoretically analyze the two-phonon resonance quantum Rabi model,and derive an effective Hamiltonian of the six-phonon coupling.Finally,we present a method of six-phonon generation based on adiabatic passage across the resonance.Numerical simulations confirm the validity of the proposed scheme.Theoretically,the proposed scheme can be extended to the realization of 3j-phonon state.展开更多
Quantum systems that undergo quantum phase transitions exhibit divergent susceptibility and can be exploited as probes to estimate physical parameters.We generalize the dynamic framework for criticality-enhanced quant...Quantum systems that undergo quantum phase transitions exhibit divergent susceptibility and can be exploited as probes to estimate physical parameters.We generalize the dynamic framework for criticality-enhanced quantum sensing by the quantum Rabi model(QRM)to its anisotropic counterpart and derive the correspondingly analytical expressions for the quantum Fisher information(QFI).We find that the contributions of the rotating-wave and counterrotating-wave interaction terms are symmetric at the limit of the infinite ratio of qubit frequency to field frequency,with the QFI reaching a maximum for the isotropic QRM.At finite frequency scaling,we analytically derive the inverted variance of higher-order correction and find that it is more affected by the rotating-wave coupling than by the counterrotating-wave coupling.展开更多
Among viruses, Rhabdovirus, more commonly known as rabies, is largely monitored throughout landscapes because of its known risks and deadliness. While vaccination and education efforts have been enforced and apparentl...Among viruses, Rhabdovirus, more commonly known as rabies, is largely monitored throughout landscapes because of its known risks and deadliness. While vaccination and education efforts have been enforced and apparently successful in the past decades, many questions still exist in some regions about the virus’s spread and potential. In the United States, the state of Tennessee’s Department of Health has documented rabies reports from the 1940s-2010s, but not as many spatial analyses have been performed to further map and assess rabid animals in this variable landscape. Our study proposed to create distribution and density models to give an idea of the types of locations rabid animals have consistently been found. A predictive model was also created using software that simulated landscape fragmentation and habitat connectivity, to provide further insight for potential disease spread. Our results display that Tennessee’s central region, which is a more homogenous landscape, tended to host a lot of rabid animals and maintained a rather consistent distribution throughout the years. The predictive model was simulated on a less homogenous landscape and displayed that spread potential can be affected by natural barriers. Each of these spatial results could be of service in future disease monitoring, hopefully for the benefit of wildlife and people alike.展开更多
基金supported by the National Science Foundation of China under Grant Nos.12305009(XYC)and 11834005(QHC)the China Postdoctoral Science Foundation under Grant No.2022M720387(XYC).
文摘It is well known that the A-square term must be considered in both cavity and circuit quantum electrodynamics systems,because it arises in the derivation from the minimal coupling Hamiltonian at any finite coupling strength.In this paper,we study the quantum Rabi model with A-square terms using the Bogoliubov operator approach.After a unitary transformation,the A-square terms can be eliminated,resulting in a modified quantum Rabi model with renormalized parameters.A transcendental function responsible for the exact solution is then derived.The presence of the A-square terms is found to significantly alter the energy spectrum.The dynamics are also studied using the obtained exact wave function,which is sensitive to the strength of the A-square terms at strong coupling.We believe that these results could be observed in future light–matter interaction systems in the ultra-strong and deep strong coupling regimes.
基金supported by the National Science Foundation of China under Grants No.12105001the Natural Science Foundation of Anhui Province under Grant No.2108085QA24supported by the National Key R&D Program of China under Grants No.2024YFA1408900。
文摘We investigate the quantum phase transitions(QPTs)of the two-qubit quantum Rabi model with staggered qubit biases.In the limit of an infinite qubit-to-cavity frequency ratio,we analytically derive the mean-field Hamiltonian and the order-parameter-dependent energy density functional,which yields the ground-state energy and order parameter.The rich superradiant phase transitions(SRPTs),including both second-and first-order QPTs and a tricritical point(TCP),are analytically derived.Specifically,we derive the analytical expressions for all phase transition points,including the nonperturbative point of the first-order SRPT.The analytical findings are further corroborated by numerical finite-size scaling analysis.It is found that both the critical correlation-length and order-parameter exponents at the TCP differ from those of the original second-order SRPTs,implying that the TCP belongs to a new universality class.This work provides a reliable theoretical framework for designing new,simple experimental platforms to explore the rich QPTs.
基金supported by the National Natural Science Foundation of China under Grant Nos.12275078,11875026,12035005 and 2020YFC2201400Science Foundation of Hengyang Normal University of China under Contract No.2020QD24sponsored by the innovative research group of Hunan Province under Grant No.2024JJ1006。
文摘As one of the famous effects in the quantum Rabi model(QRM),Rabi oscillation may lead to the occurrence of quantum dynamical behaviors without classical dynamic counterparts,such as quantum collapse and revival effects.In this paper,we focus on studying the long-time quantum signatures of chaos in the large atom-light frequency ratios of the Rabi model.It is shown that the saturated values of the entanglement entropy for initial states located in chaotic sea are higher than that in the regular regions,and the Husimi Q function are more dispersed in phase space.Moreover,we observed that the long-time average entanglement entropy and spin variance correspond well with the semiclassical phase space.Our results imply that the correspondence principle is not invalidated by quantum collapse and revival effects in the large atom-light frequency ratios Rabi model.
基金Supported by the National Natural Science Foundation of China under Grant Nos.61475045 and 11347142the Natural Science Foundation of Hunan Province,China under Grant No.2015JJ3092
文摘We explore the possibility to generate new parity symmetry in the quantum Rabi model after a bias is introduced. In contrast to a mathematical treatment in a previous publication [J. Phys. A 46(2013) 265302], we consider a physically realistic method by involving an additional spin into the quantum Rabi model to couple with the original spin by an Ising interaction, and then the parity symmetry is broken as well as the scaling behavior of the ground state by introducing a bias. The rule can be found that the parity symmetry is broken by introducing a bias and then restored by adding new degrees of freedom. Experimental feasibility of realizing the models under discussion is investigated.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674139,11604009,and 11704025)the Program for Changjiang Scholars and Innovative Research Team in University,China(Grant No.IRT-16R35)+1 种基金the Fundamental Research Funds for the Central Universities,Chinathe financial support of the Future and Emerging Technologies(FET)programme within the Seventh Framework Programme for Research of the European Commission,under FET-Open Grant No.618083(CNTQC)
文摘An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation or alternatively by assuming the form of the ground state wave function. The key of the method is to introduce a variational parameter λ,which can be determined by minimizing the energy functional. Using this method, we calculate the physical observables with high accuracy in comparison with the numerical exact ones. Our method evidently improves over the widely used general rotating-wave approximation（GRWA） in both qualitative and quantitative aspects.
基金Project supported by the Key-Area Research and Development Program of GuangDong Province,China (Grant No. 2019B030330001)the National Natural Science Foundation of China (Grant Nos. 12025509, 11874434, and 11704420)+1 种基金the Science and Technology Program of Guangzhou (China)(Grant No. 201904020024)partially supported by the Guangzhou Science and Technology Projects (Grant No. 202002030459)
文摘The open quantum system can be described by either a Lindblad master equation or a non-Hermitian Hamiltonian(NHH).However,these two descriptions usually have different exceptional points(EPs),associated with the degeneracies in the open quantum system.Here,considering a dissipative quantum Rabi model,we study the spectral features of EPs in these two descriptions and explore their connections.We find that,although the EPs in these two descriptions are usually different,the EPs of NHH will be consistent with the EPs of master equation in the weak coupling regime.Further,we find that the quantum Fisher information(QFI),which measures the statistical distance between quantum states,can be used as a signature for the appearance of EPs.Our study may give a theoretical guidance for exploring the properties of EPs in open quantum systems.
基金the Australian Research Council(Grant Nos.DP170104934 and DP1801010)。
文摘The hidden Z2 symmetry of the asymmetric quantum Rabi model(AQRM)has recently been revealed via a systematic construction of the underlying symmetry operator.Based on the AQRM result,we propose an ansatz for the general form of the symmetry operators for AQRM-related models.Applying this ansatz we obtain the symmetry operator for three models:the anisotropic AQRM,the asymmetric Rabi–Stark model(ARSM),and the anisotropic ARSM.
基金Supported by the National Natural Science Foundation of China under Grant No.11965011。
文摘An analytical method is developed to study the two-mode quantum Rabi model.For certain specific parameter conditions,especially for the resonant conditions,we obtain an infinite number of the exact solutions of the eigenfunctions and associated energies.It is shown that there exist new types of the exact energies which do not correspond to the level-crossings.Our analytical method may find applications in some related models.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10975181 and 11175247)the National Basic Research Program of China(Grant No.2012CB922104)
文摘We apply the second-order Born-Oppenheimer （BO） approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approxi- mation. By comparing with the numerical results, we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode.
基金supported by the National Natural Science Foundation of China(Grant No.12135003)。
文摘We investigate the two-mode quantum Rabi model(QRM)describing the interaction between a two-level atom and a two-mode cavity field.The quantum phase transitions are found when the ratioηof transition frequency of atom to frequency of cavity field approaches infinity.We apply the Schrieffer–Wolff(SW)transformation to derive the low-energy effective Hamiltonian of the two-mode QRM,thus yielding the critical point and rich phase diagram of quantum phase transitions.The phase diagram consists of four regions:a normal phase,an electric superradiant phase,a magnetic superradiant phase and an electromagnetic superradiant phase.The quantum phase transition between the normal phase and the electric(magnetic)superradiant phase is of second order and associates with the breaking of the discrete Z_(2) symmetry.On the other hand,the phase transition between the electric superradiant phase and the magnetic superradiant phase is of first order and relates to the breaking of the continuous U(1)symmetry.Several important physical quantities,for example the excitation energy and average photon number in the four phases,are derived.We find that the excitation spectra exhibit the Nambu–Goldstone mode.We calculate analytically the higher-order correction and finite-frequency exponents of relevant quantities.To confirm the validity of the low-energy effective Hamiltonians analytically derived by us,the finite-frequency scaling relation of the averaged photon numbers is calculated by numerically diagonalizing the two-mode quantum Rabi Hamiltonian.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11834005 and 11674285).
文摘A general approach is proposed to the quantum Rabi model and its several variants within the extended coherent states.The solutions to all these models including the anisotropy and the nonlinear Stark coupling are then obtained in an unified way.The essential characteristics such as the possible first-order phase transition can be detected analytically.This approach can be easily applied to the recent experiments with various tunable parameters without much additional effort,so it should be very helpful to the analysis of the experimental data.
基金Project supported in part by the National Natural Science Foundation of China(Grant No.11874251)the Scientific Research Starting Foundation of Shaanxi Normal University,Chinathe Scientific Research Plan Funded by the Education Department of Shaanxi Province,China(Grant No.17JK0786)
文摘We theoretically investigate the exact solutions for generalized parity–time(PT)-reversal-symmetric Rabi models driven by external fields with monochromatic periodic, linear, and parabolic forms, respectively. The corresponding exact solutions are presented in terms of the confluent Heun equations without any approximation. In principle, the analytic solutions derived here are valid in the whole parameter space. Such a kind of study may offer potential coherent control schemes of the PT-symmetric two-level systems.
基金This work was supported by the National Natural Science Foundation of China under Grant Nos.11874114,11674060,11705030,and 12074070the Natural Science Foundation of Fujian Province under Grant No.2020J01471.
文摘In this paper,we propose a scheme to achieve a multiphonon-resonance quantum Rabi model and adiabatic passage in a strong-coupling cavity optomechanical system.In the scheme,when the driving bichromatic laser beam is adjusted to the off-resonant j-order red-and blue-sideband,the interaction between the cavity and mechanical oscillator leads to a j-phonon resonance quantum Rabi model.Moreover,we show that there exists a resonant multi-phonon coupling via intermediate states connected by counter-rotating processes when the frequency of the simulated bosonic mode is near a fraction of the transition frequency of the simulated two-level system.As a typical example,we theoretically analyze the two-phonon resonance quantum Rabi model,and derive an effective Hamiltonian of the six-phonon coupling.Finally,we present a method of six-phonon generation based on adiabatic passage across the resonance.Numerical simulations confirm the validity of the proposed scheme.Theoretically,the proposed scheme can be extended to the realization of 3j-phonon state.
基金supported by the National Natural Science Foundation of China(Grant Nos.12274080,11874114,and 11875108)the National Youth Science Foundation of China(Grant No.12204105)+1 种基金the Educational Research Project for Young and Middle-aged Teachers of Fujian Province(Grant No.JAT210041)the Natural Science Foundation of Fujian Province(Grant Nos.2021J01574,and 2022J05116).
文摘Quantum systems that undergo quantum phase transitions exhibit divergent susceptibility and can be exploited as probes to estimate physical parameters.We generalize the dynamic framework for criticality-enhanced quantum sensing by the quantum Rabi model(QRM)to its anisotropic counterpart and derive the correspondingly analytical expressions for the quantum Fisher information(QFI).We find that the contributions of the rotating-wave and counterrotating-wave interaction terms are symmetric at the limit of the infinite ratio of qubit frequency to field frequency,with the QFI reaching a maximum for the isotropic QRM.At finite frequency scaling,we analytically derive the inverted variance of higher-order correction and find that it is more affected by the rotating-wave coupling than by the counterrotating-wave coupling.
文摘Among viruses, Rhabdovirus, more commonly known as rabies, is largely monitored throughout landscapes because of its known risks and deadliness. While vaccination and education efforts have been enforced and apparently successful in the past decades, many questions still exist in some regions about the virus’s spread and potential. In the United States, the state of Tennessee’s Department of Health has documented rabies reports from the 1940s-2010s, but not as many spatial analyses have been performed to further map and assess rabid animals in this variable landscape. Our study proposed to create distribution and density models to give an idea of the types of locations rabid animals have consistently been found. A predictive model was also created using software that simulated landscape fragmentation and habitat connectivity, to provide further insight for potential disease spread. Our results display that Tennessee’s central region, which is a more homogenous landscape, tended to host a lot of rabid animals and maintained a rather consistent distribution throughout the years. The predictive model was simulated on a less homogenous landscape and displayed that spread potential can be affected by natural barriers. Each of these spatial results could be of service in future disease monitoring, hopefully for the benefit of wildlife and people alike.
