The Berry Phase Of The Non-hermitian Rabi Model

At the end of the 20th century,quantum mechanics and information science produced a new science of quantum information.The interaction between light and matter is a basic problem in this discipline.Among them,the interaction model between a single-mode light field and a two-level atom is the simplest and has been the most widely studied.The Hermite property of operators has always been a universal consensus in quantum mechanics,because the eigenvalues of Hermite operators are real numbers,which have observable physical meanings.However,in the interaction process between the light field and the multi-level system,the energy attenuation caused by spontaneous radiation or ionization needs to be considered,so the attenuation term is introduced into the Hamiltonian,which leads to a non-Hermitian Hamiltonian.This paper uses the Fock state expansion method to explore the energy spectrum and Berry phase of the non-Hermitian Rabi model,and uses the results of numerical calculations to analyze the data.The paper structure is as follows:First,we briefly introduce the Rabi model,and use the Fock state eigenfunction expansion method to strictly solve the Rabi model,and get the corresponding eigen spectrum and Berry phase.Here,in order to facilitate the calculation,we have performed a rotation transformation on the Rabi model,which more intuitively reflects the parity symmetry of the system.Numerical simulation was carried out through MATLAB,and the image of the energy eigenvalue of the Rabi model and the variation of the Berry phase with the coupling strength was obtained.It was found that the adjacent excited state energy levels of the odd and even parity would cross,and the adjacent two energy levels of different parities The Berry meet will gradually converge.Afterwards,we extend the Rabi model to add a bias term to simulate the regulation of qubits by an external electric field.The energy spectrum and Berry phase of the model are theoretically deduced,and the numerical results are compared with the Rabi model to discuss the influence of the bias term.It is found that the existence of the bias term breaks the parity symmetry of the system and makes the parity no longer conserved,which has a greater impact on the energy spectrum and Berry phase of the system,especially the Rabi with or without bias term under resonance conditions.The Berry phase of the model is very different,which is instructive for the regulation of qubits.Finally,We studied the energy spectrum and Berry phase of the non-Hermitian Rabi model,and used the biorthogonal basis method to theoretically derive the energy spectrum and Berry phase of the model.Then we obtained the data through numerical simulation and found that the non-hermite Rabi model we constructed The eigenvalues obtained by the Hermitian Hamiltonian are all real numbers,which is very different from the complex solutions obtained by non-Hermitian operators.The energy spectrum obtained by simulation shows that as the dissipation coefficient increases,the energy spectrum curve of the odd-numbered energy level rises,and the energy spectrum curve of the even-numbered energy level decreases.When the dissipation factor is equal to 1,the energy spectrum of the adjacent excited state The resonance is exactly the same.The graph obtained by simulating the Berry phase found that the Berry phases of two adjacent energy levels will be the same when the coupling strength is greater.When the dissipation coefficient becomes larger and larger,the Berry phase curves of the adjacent two energy levels will increase.The closer the distance is,the gap narrows.