Simulation Of Mixed Quantum Rabi Model And Its Applications On Generation Of Squeezed Cat State

Quantum Rabi model,which is a simplest model describing light-matter interaction,plays an important role in various physical systems such as quantum optics,solid-state systems,molecular systems and so on.In recent years,the quantum Rabi model has been widely studied,and some approximations,generalizations and applications of the model are discussed.The mixed quantum Rabi model is a generalization of quantum Rabi model,which contains both linear coupled single photon and nonlinear coupled two-photon terms.The mixed quantum Rabi model is widely used in many quantum physical systems,such as circuit QED system and trapped ion system.In this paper,we propose an experimental feasible scheme to implement anisotropic mixed quantum Rabi model in the coupled system of qubits and harmonic oscillators via periodic driving modulation.All effective parameters of the simulated system can be adjusted by tuning the frequencies,the amplitudes and the initial phase of the driving fields.We find that the single photon term and two-photon term can be turned on or turned off respectively under suitable parameters,that is to say,we can obtain the standard quantum Rabi model and two-photon quantum Rabi model by tuning the effective parameters.In fact,we can also tune the parameters of the rotating terms and counter-rotating terms in the standard quantum Rabi model and two-photon quantum Rabi model,so as to deduce the single photon J-C model,the two-photon J-C model,the mixed J-C model and the corresponding anti J-C model.We analyze the parameter range of the Hamiltonian of the mixed quantum Rabi model.Numerical simulation of the fidelity shows that the model can achieve high fidelity in a large parameter range,which verifies the availability of the Hamiltonian of the model.we also discuss the application of the effective Hamiltonian of the mixed quantum Rabi model in the preparation of squeezed cat state.The time evolution operator is solved by using Lie algebra method,and the corresponding evolution state is obtained by applying the time evolution operator to the initial state.Under different parameters and special evolution operator conditions,we can obtain the Schr¨odinger cat state and the squeezed cat state.Squeezed cat state has more advantages in the direction of quantum information,especially in the direction of precise measurement.The presented proposal can also be extended to the coupling system of N qubits and resonators which will bring new inspiration for the further study of the mixed quantum Rabi model and the interaction between light and matter under different conditions.