Quantum Phase Transition For Spin-Bose Model With Atom-Atom Interaction

Quantum electrodynamics mainly study the interaction between matter and electromagnetic.While cavity quantum electrodynamics,which describe the interaction between the atoms and quantized cavity field,have been in-depth researched in theoretical and experimental aspects.More typical research is about Jaynes-Cummings model and Dicke model.There are many studying about Dicke model's ground state properties according to the spin coherent state variational method,but this method becomes invalid in dealing with the ground state properties for Dicke model when the atom-atom interaction is contained.The atom-atom interaction strength is handled with the help of the iterative method,which is the main innovation point of this thesis.In this paper,we mainly study the ground state energy properties of ultra-cold atoms in optical cavity by means of the spin coherent state transformation and the ground state variational method.My main job is to study related phase transition of the ground state for the expanded Dicke model with atom-atom interaction.But must be noted that we only consider two body interaction potential.In terms of its method,we use the coherent state of light field to obtain the average of Hamiltonian.Then we use the unitary operator to act on the spin Hamiltonian in order to project it to self representation.Finally,Hamiltonian is parameterized and the expression of ground-state energy has been obtained.In normal phase region,we can easily derive the analytical expression of average ground-state energy,the scaled atomic population,the average photon-number with changes of the collective atom-field coupling strength.However,in superradiant phase,by iteration method the curves of related physical quantities,which are affected by the collective atom-field coupling strength,can be presented.Eventually,we discover quantum phase transition for the expanded Dicke model with atom-atom interaction is an first-order transition by means of ground-stateenergy variational method and the continuity of the derivative.The main content of this paper is divided into the following four aspects:The first chapter introduces the background knowledge of the interaction between the micro-cavity and atoms.The second chapter introduces the definition and physical properties of the spin coherent states.Moreover,the calculation of spin-bose model is presented by means of the spin coherent state variational method.The third chapter theoretically investigates the effect of the atom-atom interaction on Dicke sytem's quantum phase transition based on spin coherent state variation method.The stability of the ground state energy can be judged by using the derivative of the variational method.We can derive that the system undergoes the first-order phase transition by the continuity of the first derivative and second derivative.Eventually,the related curve graphics and phase diagram are drawn based on the iterative method.The fourth chapter gives the thesis' summary and outlook.