Spin Coherent-state Transformation And Analytical Solutions Of Ground-state For Spin-Bose Models

Cavity quantum electrodynamics (Cavity QED) is a subject that mainly studies material interaction with the electromagnetic field in a certain region. One of the most basic model is a two-level atom interacting with a single field model, the so-called Jaynes-Cummings (J-C) model. In this thesis, through the study of the spin and boson coupling system, we propose the first pervasive variational method to give the ground state analytical solution to spin and boson coupling model. This is a new kind of variational method, in which the effective pseudo-spin Hamiltonian resulting from the expectation value in the boson-field coherent state is diagonalized by the spin-coherent-state transformation, then getting a Minimum value by Partial derivative to the energy functional, finally the analytical solution of ground state energy we could get. It is a very effective method that do not need any other approximation besides using the boson coherent state as the trial wave function. The main topics list in the following three aspects:The first chapter briefly introduces the developing process of cavity quantum electrodynamics, the dynamics of interaction between the atom and the cavity.The second chapter briefly introduces the definition and properties of Spin coherent state.The third chapter briefly introduces the Spin-Bose model, then it is the main to give the analytical ground state energy of J-C model with and without the rotating wave approximation, at the same time, we compare and discuss the result with the numerical diagonalization’s. Finally we found it are perfect agreement with the results of numerical diagonalization in the weak and strong coupling region between the light field and atoms.In the fourth chapter, we extend a atom to arbitrary atom number and calculate the ground energy of Dicke Hamiltonians with and without the rotating wave approximation. And compare the results with the numerical diagonalization’s respectively. And we found that the results obtained by our method are lower than the numerical diagonalization one’s, and the results of exact diagonalization will more and more close to the spin coherent state transform’s results with increasing the atoms. However, the variation-method based on the Holstein-Primakoff transformation is only valid in principle for the thermodynamic limit with the atom-number tending to infinity.In the fifth chapter, we summarize the contents of the entire paper and state the value of the spin coherent states transform to solve Ground-state energy of Spin-Bose model, and look forward to more research about it.