The Study On The Antiferromagnetism Of Onsager Vortices In Exciton-polariton Bose-einstein Condensates

As a driven-dissipative quantum fluid system,the exciton-polariton Bose-Einstein condensates(BEC)in a quantum well of semiconductor microcavity has become an effective tool for studying non-equilibrium physical systems in recent years.The exciton-polariton formed by the strong coupling of microcavity photon and quantum well(QW)exciton has excellent characteristics such as superfluidity,room temperature formation,integration and easy manipulation.For the superfluidity of systems,many researchers have explored the topological states in two-dimensional quantum turbulence in polariton systems.The quantized vortex and vortex array with topological phase transition have become the best candidates for constructing photonic networks and quantum optical devices because of their unique stability and optical controllability.This article first introduces the structure of microcavity semiconductors and the formation principle of exciton-polariton BEC in quantum wells,reviews the development path of polariton BEC systems,and summarizes the technologies and applications that have been implemented.We introduced the two-dimensional turbulence and quantized vortices in the exciton-polariton BEC,as well as the classical phenomenon of two-dimensional turbulence evolution,the Onsager vortex cluster.This paper presents a specific method for simulating the evolution of exciton-polariton BEC using the Gross-Pitaevskii(GP)equation and the solving skills of the GP equation.Subsequently,by designing a nonresonant microcavity pumping scheme,we have formed two novel vortex arrays in a two-dimensional long potential well based on the exciton-polariton BEC: a stable antiferromagnetic vortex array and an Onsager vortices cluster antiferromagnetic array.By adjusting the pumping scheme and deriving the GP equation,we found that the formation of vortex arrays is a negative temperature phenomenon caused by the reverse energy cascade of quantum turbulence in a two-dimensional limited space.For these new topological quantum states,we analyzed their energy level structure and provided the reason for the spontaneous occurrence of ordered vortex arrays from the perspective of turbulence decay.After that,we explored the vortex dynamics of a vortex array in a two-dimensional long potential well,and calculated the force on a vortex unit.The results obtained were in good agreement with the velocity and trajectory changes of the vortex,explaining the reason why the vortex moved in a stable elliptical trajectory.We also analyzed the velocity field in the vortex array and explained the relationship between the velocity effective potential and the particle number distribution.Finally,we give the parameter range of vortex array formation,and provide two schemes for adding control beams to regulate the vortex array,fully demonstrating the controllability of the BEC system.In this work,two types of antiferromagnetic vortex arrays have been discovered in two-dimensional long potential wells that have never been seen before.We have explored the formation methods and principles of vortex arrays,as well as the dynamic behavior in vortex arrays,and provided the formation range of vortex arrays under various system parameters and the regulatory effect of pump schemes on the array.This work is a supplement and exploration to the vortex properties and nonlinear turbulence evolution in two-dimensional exciton-polaritons BEC.The new pumping scheme provides a directional guidance for future experiments on exciton-polaritons BEC,and provides theoretical support for the development of semiconductor microcavities in the field of all optical control and optical devices.