Numerical modeling of exciton-polariton Bose--Einstein condensate in a microcavity

A novel, optimized numerical method of modeling of an exciton–polariton superfluid in a semiconductor microcavity was proposed. Exciton–polaritons are spin-carrying quasiparticles formed from photons strongly coupled to excitons. They possess unique properties, interesting from the point of view of fundamental research as well as numerous potential applications. However, their numerical modeling is challenging due to the structure of nonlinear differential equations describing their evolution. In this paper, we propose to solve the equations with a modified Runge–Kutta method of 4th order, further optimized for efficient computations. The algorithms were implemented in form of C++ programs fitted for parallel environments and utilizing vector instructions. The programs form the EPCGP suite which has been used for theoretical investigation of exciton–polaritons.本研究提出了一种用于半导体微腔中激子极化激元（exciton–polariton）超流建模的新型优化数值方法。激子极化激元是由光子与激子强耦合形成的携带自旋的准粒子，其具备独特的物理性质，无论在基础研究领域还是诸多潜在应用场景中均具有重要研究价值。然而，由于描述其演化过程的非线性微分方程的结构特性，对其进行数值建模颇具挑战。本文提出采用改进的四阶龙格-库塔（Runge-Kutta）方法求解该类方程，并针对高效计算需求做了进一步优化。该算法以C++程序的形式实现，适配并行计算环境并支持向量指令集。上述程序构成了EPCGP套件，该套件已被用于激子极化激元的理论研究。