Simulating Anisotropic Quantum Rabi Model Via Frequency Modulation

Anisotropic quantum Rabi model is a generalization of quantum Rabi model,which allows its rotating and counter-rotating terms to have two different coupling constants.It provides us with a fundamental model to understand various physical features concerning quantum optics,solid-state physics,and mesoscopic physics.In this paper,we propose an experimental feasible scheme to implement anisotropic quantum Rabi model in a circuit quantum electrodynamics system via periodic frequency modulation.An effective Hamiltonian describing the tunable anisotropic quantum Rabi model can be derived from a qubit-resonator coupling system modulated by two periodic driving fields.All effective parameters of the simulated system can be adjusted by tuning the initial phases,the frequencies and the amplitudes of the driving fields.We show that the periodic driving is able to drive a coupled system in dispersive regime to ultrastrong coupling regime,and even deep-strong coupling regime.The derived effective Hamiltonian allows us to obtain pure rotating term and counter-rotating term,then the ratio of coupling constants of RT and CRT can be controlled in a wide range of parameter space,which makes us to study the transitions from JC regime to anti-JC regime.After we obtain the anti-JC model,we remain interaction terms to obtain degenerate anisotropic quantum Rabi model by modulating parameters.Numerical simulation of the fidelity shows that such effective Hamiltonian is valid in ultra strong coupling regime,and stronger coupling regime.Moreover,our scheme can be generalized to the multi-qubit case.Considering N qubits coupled to a resonator,we can obtain the simulated anisotropic quantum Dicke model with the same treatment.We also give some applications of the simulated system to the schr?dinger cat states and quantum gate generalization.We consider how to generate superposition of coherent states for a single-qubit case to obtain the even and odd schr?dinger cat states.Then,by numerical simulation,the entanglement of two-qubit is studied,and the two-qubit quantum gate is equivalent to CNOT gate.The presented proposal will pave a way to further study the stronger anisotropic Rabi model whose coupling strength is far away from ultrastrong coupling and deep-strong coupling regimes in quantum optics.