The Nonlinear Property Study Of Parity-Time Symmetry Model Satisfied By The Polariton Condensates

In recent years,the polariton condensates system formed by two-dimensional quantum well excitons and microcavity photons has become a hot issue due to its characteristics of short lifetime,light effective mass,strong interaction,high condensation temperature,coexistence of gain and dissipation,and strong controllability.It becomes not only a suitable replacement for the ultracold atomic gas Bose-Einstein condensate(BEC),but also an ideal platform for designing the next generation of practical quantum devices and optical information processing devices.On the other hand,non-Hermite systems with Parity-Time(PT)symmetry have real eigenspectrum at critical points,which extend quantum theory to complex domains.To design the gain and dissipation with PT symmetry in the exciton polariton system is not only a new equilibrium mechanism,but also provides a new model for studying the nonlinear characteristics of polariton BEC.As far as we know,this equilibrium mechanism and the stable polariton BEC condensates under the PT symmetric external potential have not been reported.The main work of this paper includes:1.The stable soliton is found by introducing a composite nonresonant pumping,and it is found that the inhomogeneous part of the pumping can be used to control the profile of the soliton.A composite nonresonant pumping composed of constants and Bessel functions is introduced,the homogeneous part is used to balance the constant loss,and the inhomogeneous spatial modulation part is used to compensate the gain or loss caused by the denominator of the nonlinear saturation gain term.Bright and dark solitons in one-dimensional systems,and bright solitons and vortices in two-dimensional systems are found using the preconditioned Newton conjugate gradient method.These solitons can be stabilized by designing homogeneous and inhomogeneous pumping.It is found that the intensity of the total gain loss is a necessary condition of soliton stabilization.2.Due to the non-equilibrium characteristics of the polariton BEC system,it is very difficult to construct a PT symmetry model satisfied by the system.On the basis of the balance between gain and loss by the composite pumping,we introduce a PT symmetrical external potential to design the PT symmetrical model satisfied by the polariton BEC.3.In the case of weak nonlinearity,the phase transition point of the one-dimensional PT symmetrical system is obtained,and the characteristics of the linear spectrum are displayed.In the case of normal nonlinearity,the zero-background bright solitons and various types of dark solitons are found in a one-dimensional system.The effect of the PT-symmetric external potential on the stability of the soliton is discussed,and it is found that the effective balance between gain and loss by the composite pumping is a necessary condition for the stability of the soliton.By analyzing the profile and stability of the soliton,the competition relationship between the PT symmetric external potential and the inhomogeneous pumping is clarified,the parameter regions for exciting various solitons are shown,and the stable interval of these solitons is defined by evolution and linear stability analysis.Finally,we achieve the goal of manipulating the symmetry-breaking soliton by controlling the imaginary part of the PT symmetry external potential,and reveal the potential application value of the system in all-optical switching.In addition,we also find various types of solitons and vortices in the two-dimensional PT-symmetric system,and discussed the effects of the PT-symmetric external potential and inhomogeneous pumping on the stability of the soliton.The study of nonlinear properties of PT symmetric polariton BEC systems not only fills the gap in this direction,but also provides theoretical support for experimental research in this field,and explores its potential applications in quantum devices and optical information processing.