Nonlinear Excitation Of Steady-State Quantum Systems With Power-Law And Coupled Interaction

In recent years,the successful observation of solitons in Bose-Einstein condensate and the beneficial exploration of the evolution characteristics of exciton polaritons have made the nonlinear excitation of steady-state quantum systems have important research value in many fields such as quantum computing,quantum transmission and quantum navigation.Based on the nonlinear Schr(?)dinger equation model and the Gross-Pitaevskii equation model,this thesis mainly studies the dynamics of kink solitons,a typical nonlinear phenomenon in BoseEinstein condensation,and the evolution dynamics of exciton polariton condensation system.The kink soliton dynamics behavior is studied for quantum systems with power-law nonlinear interactions.Based on the F-expansion method,the kink soliton solutions of NLSE with power-law nonlinear term,third-order dispersion term,linear attenuation term and selfsteepening term in one-dimensional and two-dimensional cases are derived by setting appropriate parameters,and their characteristics are demonstrated graphically.At the same time,the accuracy and stability of the results are verified by using the G′/ G method and increasing the perturbation.It is proved that there is a stable kink soliton solution in the powerlaw nonlinear quantum system,which not only has the key soliton characteristics shown in the classical nonlinear Schrodinger equation,but also has the typical power-law characteristics.The above results are helpful for the observation of kink solitons in steadystate quantum systems such as liquid crystals and nonlinear optical fibers.The evolution dynamics of the vortex superposition state of the exciton polariton BoseEinstein condensation system under vortex manipulation is studied.By establishing the driving-dissipation Gross-Pitaevskii equation model and using the improved variational method to set the system angle evolution wave function,the evolution formula of the system is derived.Meanwhile,the evolution characteristics of the rotating system and the nonrotating system are analyzed,and the influence of different angular velocities and centrifugal potentials on the evolution law of the system is explored.The periodic oscillation mode is determined,and the mode matching between numerical simulation and analytical derivation is shown,which proves the applicability of the theoretical derivation results.This research work has important guiding significance for the development of related gyroscope equipment.Based on the previous research on the exciton polariton condensate system,the exciton polariton Bose-Einstein condensate dynamics under the interaction of exciton and photon coupling is studied.Based on the coupled Gross-Pitaevskii equation model and the improved variational method,the wave function of the system is proposed,and the analytical solution of the system under the disturbance and rotation in the polar angle direction is derived.At the same time,the evolution mode of the system under different rotational angular velocity and coupling interaction strength is analyzed,and the evolution process of the system in metastable oscillation and monotone decay state is illustrated.It is found that the results of analytical derivation and numerical simulation have good matching under the same parameter settings,which has potential significance for the study of nonlinear excitation and quantum navigation of coupled quantum systems.