Study Of The Nonclassical States In The Light-matter Interaction Systems

There are rich and complex physical phenomena in the interaction system between light and matter.The quantum Rabi model is most basic model to describe the interaction system between light and matter.Its ground state includes some nonclassical states,such as squeezed state,cat state,and entangled state,these states are of great significance to the development of modern quantum technologies such as quantum precision measurement,quantum computing,and quantum information processing.In recent years,with the advancement of quantum simulation experimental platforms,people have been able to simulate the interaction between light and matter in these systems and have gained greater flexibility in adjusting experimental parameters.This has sparked interest in studying the interaction between light and matter under various parameter regimes,greatly promoting exploration in this field.In particular,as a few-body system undergoing a quantum phase transition,the superradiant phase transition behavior of the ground state of the quantum Rabi model has recently been experimentally simulated.This thesis begins by focusing on the nonclassical state in the quantum Rabi model,the parameters describing the properties of the nonclassical states are extracted through the polaron picture,and these properties are corresponding to the processes before and after the superradiation phase transition.By analyzing the difference of these properties,the range of coupling strength is classified,and the parity chain changes with the increase of coupling strength are revealed.For the ground state of the quantum Rabi model,the polaron picture is not only suitable for the full parameter interval but also can obtain the analytical expression of the Winger function that characterizes the nonclassical states.We further improve the polaron picture to study the change of the nonclassical state during the process of the superradiant phase transition.In the regime of the superradiant phase transition of the quantum Rabi model,as the coupling strength increases,we find that the ground state undergoes a process from the vacuum state to the squeezed vacuum state in the normal phase,and from the squeezed cat state to the cat state without squeezing in the superradiant phase.We also calculate the entanglement entropy of the system and find that the system is described by separable states before the critical point and entangled states after the critical point.By analyzing the photon occupancy in the ground-state Fock space of the quantum Rabi model,we obtained the physical picture of squeeze accumulation to squeeze release during the superradiant phase transition.In addition,we also discover a pair of novel semi-cat states,which is caused by a necessary antipolariton with a very small but non-zero weight.By analyzing the changes in the properties of the nonclassical states,we reveal the change of the parity chain of the quantum Rabi model during the process of the superradiant phase transition.In the quantum Rabi-Stark model,a nonlinear dispersion interaction term is introduced to the quantum Rabi model,which exhibits two types of quantum phase transitions,including a first-order quantum phase transition,and superradiant phase transitions in two different limits.Before the critical point of the first-order quantum phase transition,the ground state belongs to the even parity space,and the main component of nonclassical states it contains is the even cat state.After the critical point of the first-order quantum phase transition,the ground state belongs to the odd parity space,and the main component of nonclassical states it contains is the odd cat state.For the superradiant phase transitions,in the frequency ratio limit,the critical behavior is the same as that of the quantum Rabi model and the Dicke model,and the Stark term only changes the critical coupling strength;but in the Stark term limit,the critical behavior is different from that of the former,we find that the system is described by separable states before the critical point and entangled states after the critical point.By analyzing the changes in the properties of the nonclassical states,we unveil the intriguing modifications in the parity chain of the quantum Rabi-Stark model during the superradiant phase transition in the Stark term limit.The study of nonclassical states in light-matter interaction systems can help people understand the physical image of superradiant phase transitions,and it can also inspire people to prepare these nonclassical states in light-matter interaction systems.