Quantum Phase Transition Of Density-dependent Two-photon Rabi Model

The quantum phase transition problem of finite systems is currently a hot research topic in the world.The two-photon Rabi model is an important finite quantum optical system.It is an interaction model between a two-level atom and a single-mode light field.It is an important subject in quantum optics.Different from the study of various quantum phenomena in the case of resonance,some recent scholars have shown that the Rabi model will have quantum phase transition under the limit of large detuning,which has become a research topic in this field.This research is for understanding finite systems.Phase change is important.This paper will study the quantum phase transition of the density-dependent two-photon Rabi model from the perspective of quantum fidelity and fidelity.The advantage of this research method is that it avoids the Landau theory and does not need to analyze the symmetry to study the quantum phase.change.In this paper,the fidelity of the density-dependent two-photon Rabi model is numerically calculated.The study shows that the fidelity of this model has finite scale scaling behavior near the quantum phase transition point,and the correlation length of the two-photon Rabi model with density correlation is obtained.Critical index and dynamic critical index.These results play an important role in understanding the universality of the quantum phase transition of the density-dependent two-photon Rabi model.Thanks to the density-dependent two-photon Rabi model,it is not complicated,and the universal critical behavior of the fidelity of quantum phase transition can be observed experimentally.The main research work of this paper is divided into two parts:In the first part,the maximum number of photons is used to make the Hilbert space of the truncated system,and the Hamiltonian of the density-dependent two-photon Rabi model is dimensionlessly processed,and the diagonalization matrix is numerically analyzed.Under the limit of large detuning,the fidelity condition of the system function under the driving parameters is analyzed and calculated,and the lowest point position of the ground state fidelity and the evolution characteristics of the image with parameters are analyzed.Discuss the re-scaled photon characteristics near the phase transition point and analyze the average ground state energy to determine the phase change type of the model.In the second part,we analyze the general scaling behavior of the fidelity rate and the scaling behavior of the generalized adiabatic sensitivity in the quantum two-photon Rabi model to study the quantum phase transition of this model,and obtain the variation with the driving parameters at different frequency ratios.The fidelity rate peak value and the generalized adiabatic sensitivity peak value are obtained by plotting the corresponding peak fitting straight line to obtain the corresponding parameters,and the adiabatic size of the fidelity of the model and the adiabatic size of the generalized adiabatic sensitivity are determined to determine the corresponding correlation length criticality.The index is used to determine the characteristics of universal sexual behavior.The universality of these two critical exponents is tested by the data shrinkage of fidelity and generalized adiabatic sensitivity.Finally,it is assumed how to observe the fidelity rate of quantum phase transition.behavior...