Solution And Evolution Of The Two-qubit Quantum Rabi Model

The Rabi model describes the interaction between light and matter,which was introduced 70 years ago,it is one of the simplest and most universal models in modern physics.However,in quite a long period of time,people usually use J-C model,which can be achieved from Rabi model after taking the rotating-wave approximation(RWA),to describes the interaction between a two-level system and a quantized harmonic oscillator in the field of quantum optics,because the Hamiltonian is often an infinite dimension Non-Diagonal matrix in Hilbert space.Recently,the interest on the quantum Rabi model has been relighted due to the realization of ultrastrong qubit-photon coupling in circuit QED experiments,where the rotating-wave approximation breaks down,and the systems dynamics must be governed by the Rabi model.The work in this dissertation is based on the generalizations and extensions of the Rabi model,and includes following theoretical investigations and results.1.With transformed rotating-wave approximation(TRWA),the analytical solutions for two qubits Rabi model are achieved in resonant condition.If the frequencies of two qubit?1,?1 and photon field ? satisfy resonant relation,the two-qubit Rabi model can be mapped into the solvable formation in qubit-photons Fock states space.The energy spectrum could be checked experimentally,furthermore,two-qubit quantum Rabi model could be examined.2.we have studied the two-qubit quantum Rabi model in reservoir.Here,two-qubit system consist of two qubits and photon field,if the system interact with environments,the Boson field of reservoir,coupling between qubits and reservoir,and coupling between reservoir field and photon field should be considered additionally.In single Lorentzian model,with the pseudomode approach,the Hamiltonian describing the interaction between two qubits and the reservoir and the optical field is a complicated matrix in complete Fock states space.Then,the algebraic structure of Hamiltonian is analyzed in the photon number space,a closed quasi-exact eigenstates space is found,and the quasiexact solution can be clearly found from the algebraic structure of Hamiltonian.3.In non-Markov environment,we propose to use a superconducting transmission line resonator(TLR)to connect two qubits.Then we use the pseudomode method to solve the master equation and get the evolutions of the quantum coherence and entanglement of the quantum systems and investigate the evolutional characters of the entangled system initially structured in pure states4.We propose a scheme to enhance trapping of entanglement of two qubits,in a thermal reservoir,by weak measurement and quantum measurement reversal.While after the system undergoing the evolution process,a suitable post-measurement(weak measurement or quantum measurement reversal)on these two qubits are performed.This work is dedicated to the study of the spectrum and eigenstates of the two-qubit Rabi model describing the interaction between atoms or superconducting qubit with quantized field.These solutions are very important for getting the information about the structure and symmetries of the model.We can guide the subsequent experiment and provide the basis of theory.We study the evolution of the qubit-qubit entanglement and propose a scheme to enhance trapping of entanglement of two qubits.