Elementary Excitations And Nonlinear Tunneling Process Of The Spinor Exciton-Polaritons

Along with the improvement of the semiconductor technology and the quality of the laser,the exciton-polaritons,a kind of quasiparticle formed by the strong coupling of excitons and photons,have become a new experimental method to realize Bose-Einstein condensates.The polaritons are different from the normal Bose-Einstein condensates,which have the finite lifetime and they can be produced in the nonequilibrium systems driven by the dissipation and driving of the semiconductor microcavity.The photon part of the polariton will leak out from the microcavity continuously and the scientists can get all the information of the polaritons by observing the leaked photons.The Hamiltonian of the polariton is non-Hermitian,so it is an excellent experimental platform to realize the non-Hermitian topology,non-equilibrium Hall effect,non-equilibrium Landau tunneling,and so on.In this thesis,we mainly study the influence of the spin degree of the freedom of the polaritons and provide two theoretical models.One model is considering the different polarization forms of photons,and when they are coupled with excitons,they can be regarded as a quasiparticle with pseudospin of 1/2.In the equilibrium system,the two-component condensate has a phase transition from spin-nonpolarized phase to spin-polarized phase,and the dissipation of polaritons will affect this kind of phase transition on the ground state and the excited state.The other model is putting the polaritons condensate into a double-well so that the condensate in different potential wells can be regarded as two independent components with the interactions.Based on the current experimental conditions and the above hypotheses,the singular quantum behaviors of the polaritons with the freedom of the spin and gives the physical explanation are studied in this thesis.The specific research topics are as follows:1.The steady-state and the linear elementary excitation of the spinor polaritonsBy the mean-field method,the ground state of spinor polaritons will change from spin-nonpolarized phase to spin-polarized phase as the increase of the interaction between different component polaritons.Then,the excitation spectra of polaritons in different phases and their polarization modes by using Bogoliubov transformation are given in this thesis.To observe the negative energy part of the Bogoliubov spectrum,the photoluminescence spectrum of spinor polaritons,which provides the theoretical support for the experimental observation is calculated.2.Dynamics of the dark-bright solitons in spinor polaritonsThe dark-bright solitons in nonlinear excitations are much more stable and have the anti-noise ability.They are a significant method to transfer information.By the Hamiltonian variational method,the motion equations of the dark-bright solitons'center of mass of the polaritons are derived numerically and analytically.Then we test the anti-noise ability and the transverse instability of dark bright solitons and find that dark-bright solitons can propagate in the dissipative system with enough long time scale to be observed by current experiments.3.Nonlinear Landau-Zener tunneling in the polariton condensatesBy using a two-mode approximation,the effective Landau-Zener model of the polaritons in the periodic potential well is obtained in this thesis.In addition,the influence of the reservoir and the relative phase of the condensate in the two potential wells on the polariton's tunneling process are studied in this thesis.Furthermore,the corresponding relationship between the effective model and the energy band in the phase space is also illustrated.