The Quantum Properties Of Two Arbitrary Quibits Without Rotating Wave Approximation

The researches of the interaction between particles and light field have always played an important role in quantum optics and condensed matter physics,the entanglement between particles during the process of interaction can reflect the nonlocal correlation of quantum systems.The extended coherent states(ECS)has been applied in the thesis to explore the entanglement properties of two arbitrary qubits without rotating wave approximation,and the entangled evolution between the two qubits in Rabi model with arbitrary qubits is researched by numerical calculations combined to the analytical solution in the vacuum light field and coherent state light field.Firstly,we use the ECS to strictly solve the Rabi model of two arbitrary qubits without rotating wave approximation,and establish the zero-order approximation to solve the Rabi model,so obtain the approximate analytical solution of the intrinsic energy spectrum and the corresponding eigenwave,according to the approximate analytical solution of the intrinsic energy spectrum,we analyze the reason why the decoupling lines in the energy spectrum of the strict solution persist,we also determine four initial states of the the qubits by eigenwave function,which are two Bell states whose entanglement is maximal and two zero-entangled states.Secondly,we set vacuum state as the initial state of the light field.In the case of weak coupling,when the differences between transition frequency of the light field and the two identical qubits are equal,the entanglement evolutions are almost identical.When the transition frequency of two non-identical qubits are symmetrically detuned relative to the frequency of light field,the period of entanglement has an inverse relationship with the detuning;when setting the bell triplet state as the initial state of two qubits,the larger the detuning is,the easier the entanglement can remains in a larger state;for the bell singlet state,slight detuning of the qubits’ frequency will break the stable state of maximum entanglement,however when the detuning increases to a certain value,there will also be stable fluctuation around the maximum value during the evolution.When entanglement of initial states is zero-entangled states,for upper energy state whose entanglement is separated as the initial state of two qubits,the two qubits are separated for most time of the evolution,and transient weak entanglement appearperiodically,while the initial state of two qubits is the lower energy state,entanglement evolution is exactly opposite to the condition of the upper energy state,which means most time of the entanglement evolution is in a weaker state,separated entanglement only appears instantly and periodically,the entanglement approach to zero with increasing of the detuning in both conditions.In the resonance condition and when the coupling strength between the light field and one quibit is different from another,we find the principal peaks and secondary peaks appear alternately in the entanglement evolution of two qubits,the entanglement evolves periodically in the whole process.Finally,in the system of interaction between two qubits and coherent state as the light fields,when the bell triplet state is the initial state of two qubits,the larger the differences between transition frequency of the light field and the two identical qubits is,the easier the entanglement can remain in the larger state,for the bell singlet state,the differences between transition frequency of the light field and the qubits would make no effection to the stable state of maximum entanglement;When the transition frequency of two non-identical qubits are symmetrically detuned relative to the frequency of light field,larger detuning promote more obvious periodicity of the entanglement evolution,and the period is proportional to the detuning.When setting separated entanglement of qubits as the initial state,the larger detuning is,the longer it will take for the two qubits to start to entangle.