Reduced Density Matrix And Quantum Correlation In Two-Qubit Quantum Rabi Model

The interaction between light and matter is an important avenue for human to understand nature,study,regulate and utilize the materials.From Planck’s black-body radiation to the birth of laser physics,the rise of quantum sensor,nuclear magnetic resonance,quantum information and other technologies,the interaction between light and matter plays a very important role.In recent years,it has been found that the super-strong coupling between light and matter can be realized in organic moleculars,superconductor quantum circuits,semiconductor polaron,optomechanical systems,etc.These discoveries provide experimental foundations for the research of quantum entanglement,nonlinear optics and quantum chemistry.In this thesis,we investigate the correlation between two qubits in a deep-strong coupling region caused by an optical cavity.Using the path integration method,we find the analytic expressions of the 4-by-4 reduced density matrix of the two qubits for each eigenenergy.The concurrence,quantum discord,steerable weight,and robustness of coherence are investigated for both the ground state at zero temperature and excited states at finite temperature.In chapter 1,we give a brief introduction to the simplest quantum Rabi model and related investigations.In chapter 2,we introduce the theoretical model of this thesis,i.e.,the two-qubit single-mode Rabi model,and the solutions of this model.Based on previous works,we derive the reduced density matrix between two qubits in the optical field analytically.After partial tracing of optical field quantum states,we find that,for each eigenenergy,the 4-by-4 reduced density matrix of the two qubits can be written in the analytical form of the confluent hypergeometric functions.In chapter 3,some kinds of measurements,i.e.,the concurrence,quantum discord,steerable weight,robustness of coherence,and von Neumann entropy,which are applied to describe the quantum entanglement and quantum correlations between the two qubits,are calculated for the ground state and excited states.It is found that in the deep-strong coupling region,von Neumann entropy increases with the increasing of coupling strength monotonically,however,all the other quantities experience the process of first increasing and then decreasing.An intermediate coupling between the qubits and the cavity field is required if one wants to establish maximal entanglement between the qubits.In chapter 4,we make a summation and prospect of our work.