Polaron Picture And Its Application In Light-matter Interaction Models

In recent years,with the rapid development of super conducting quantum circuit experiment technology,one has realized the strong coupling between light and matter in experiment which the strength of coupling and the frequency of photon or resonance frequency of atom are in the same order of magnitude.The intensity is far beyond the limit of traditional QED,and the experiment of Niemczyk's research group have pointed out that the J-C model doesn't apply for the cases when the light-matter coupling reached to an ultra-strong regime,and the interaction between single-mode light field and a two-lever atom system should be described by the quantum Rabi model.Therefore,it is of great significance to further study the full quantum Rabi model and its extended model.In this thesis,the two qubit Rabi model and its related models are calculated by using polaron pictures and variational method,and some novel physical phenomena are found when light and matter interact with each other.It can be divided into the following parts:First of all,we introduce the theoretical and experimental history of the interaction between light and atoms,and draw out the existing theoretical research results of the quantum Rabi model.Then the existing research methods and results of quantum Rabi model and two-bit quantum Rabi model are reviewed.In the third chapter we mainly introduce the applicable conditions of the existing methods which solved the two-qubit quantum Rabi model,and then introduce how to solve the two-qubit quantum Rabi model by applying the polaron picture.The calculation results show that our method can obtain the ground-state energy with high accuracy in all regimes of the coupling strengths g,while there is no constraint to the ration of tunneling frequency ? and field frequency ?,which is not simultaneously possible using previous methods.Besides,we also discover a new phenomenon which is not present in the one-qubit Rabi model: with the increase of coupling strength g,there is a transition of the ground state of the system from a multipolaron state to a bipolaron state.However,the tunneling frequency? counteracts this process.Specifically,when tunneling frequency ? = 0,the system always stays in the bipolaron state.In chapter 4,we apply polaron picture to solve the quantum Rabi-Stark model,and obtain the ground state energy and some other simpler physical observables of the model.Then the spectrum collapse behavior of the model at ? = ±? is introduced,and we find that the polaron picture can give a good explanation for this behavior.Finally,we also introduced the spectroscopy collapse behavior of two-photon quanrum Rabi model,and the reasons for the spectrum collapse of the two models are compared,it is found that the fundamental reason is that the nonlinear term flattens the potential wells of the two models at the energy spectrum collapse point,so the atoms do not need to consume energy when tunneling between the two potential wells,and therefore all the spectrum collapse at the same point.In Chapter 5,we introduce the Von Neumann entropy in the quantum Rabi-Stark model,and we find that this model will have second-order phase transition similar to that in the Rabi model,and the coupling strength between the light field and the atoms has an inhibition effect on the increase of von Neumann entropy in the ground state of the system.However,when the energy spectrum collapse behavior occurs in this model,it will suddenly be 0.This provides the opportunity for us to study the relationship between entanglement and phase transition.Finally,we summarize the work of this paper and give a outlook of our future work.