Rabi Phase Transition In Cross Cavity And The Fitting Of Band Structure Of MoSSe

We have studied a crossover cavity which two optical resonators interact with a two-level atom at the same time.There is a gain on one of the optical resonators,while there is a dissipation on the another one.For simplicity,we assume that the gain and dissipation exactly meet parity and time inversion symmetry(PT symmetry).The interaction between the two-level atom and the light field can cause the Rabi phase transition of the single atom,and the Hamiltonian of the intersected cavity has spontaneous PT symmetry breaking under the condition of PT symmetry.These two mechanisms exist in the system at the same time,and they will compete with each other and influence each other,resulting in a richer phase diagram in the cavity.Our research focuses on the phase change mechanism of such a rich phase diagram and the phase change behavior of the transformation between different phases.We use the master equation to describe the entire quantum system.Thus,we can obtain the standard Heisenberg-Langevin equation by ignoring the quantum coherence term.On this basis,when the system is in the PT asymmetric state,the gain of the input optical vibration cavity cannot overcome the dissipation of the environment,so that the system will remain in a steady state.By solving the steady-state equations,we can obtain the critical point gc of the Rabi phase transition of the system.On the other hand,when the system is in the PT symmetric state,it can be expected that since the input energy can overcome the dissipated energy,there exists a set of solutions that oscillate at a certain characteristic frequency.For this oscillatory solution,there will also be a critical point gc.In order to retrieve the information of the quantum fluctuation of the optical field in the optical cavity,we used the unitary transformations in g<gc and g>gc to obtain the equivalent master equation of the optical cavity.And we obtained the remaining information of the phase diagram by solving the master equation,thus we can obtain a complete phase diagram.Another of our work is to give the inter-layer coupling of the electron bands in the different stacked forms of the double layer of MoSSe,which allowing the theory to be compared precisely with the digital simulation.Firstly,we used the band model to fit the monolayer of MoSSe,so that the parameters needed in the model could be obtained by comparing with the Measured data.On this basis,we consider the model of two-layer superposition,so that we only need to determine one parameter of inter-layer coupling in the end,which greatly simplifies the estimation of the entire model parameter.Since the upper and lower layers of the double layer of MoSSe that correspond to the sulfur and selenium atomic layers respectively,there are 4 stacking modes for the double layer of MoSSe.The inter-layer coupling intensity obtained by theoretical model and numerical fitting for the four stacking methods is basically consistent.Considering that the inter layer coupling results from the overlap of the inter layer electron wave function,this is in line with the expected result.