Investigation On The Engtanglement Of Two Qubits Ultra-stongly Coupling To A Quantum Oscillator

Quantum entanglement is the most indispensable concepttion in quantum information. How to prepare and maintain the entanglement is the most important problem in quantum information. The optical systems based on Rabi model can be used to prepare and maintain entanglement,it has broad application prospects. When the coupling between the qubits and the oscillator is in the ultra-strong region and their detune is large, the analytical expressions of the eigenvalues and the eigenfunctions are obtained by using adiabatic approximation and generalized rotating-wave approximation. The dynamical behavior of the system, including Fock state and coherent state initial status for the quantum harmonic oscillator,has also been discussed. The collapse and revival phenomena has garnered particular attention. Utilizing adiabatic approximation method,the reservation of one initially entangled state of two qubits by the quantum oscillator is accomplished through the careful choice of the four parameters, the average number of the coherent state of the oscillator, the ultra-strong coupling strength, the ratio of two frequencies of qubit and oscillator, and the inter-interaction coupling of the two qubits.Maintaining the entanglement of the two qubits with very high fidelity will be helpful for the quantum information process.Our thesis contains four parts:1. The interaction between the qubits is added in Rabi model. It is investigated by using the adiabatic approximation method. The effect of the entanglement on the interaction parameter is also investigated.2. Using adiabatic approximation, a two arbitrary qubits Rabi model has been studied in ultra-strong coupling. The influence of inconsistent coupling strength on collapse and revival phenomena is studied.3. The inversion-symmetry breaking and non-linear interaction Rabi model has been studied by the method of adiabatic approximation, in ultra-strong coupling. We show that the inversion-symmetry breaking and non-linear interaction changes the time and height o f collapse and revival.4. Utilizing generalized rotating-wave approximation method, Rabi model is investigated. The generalized approximation works for all values of the coupling strength and for a wide range of detuning values.