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.

本研究提出了一种新型的、优化的数值方法，用以模拟半导体微腔中的激子-极化激子超流体。激子-极化激子是由与激子强耦合的光子形成的带自旋的准粒子。它们具有独特的性质，不仅从基础研究的视角来看引人入胜，而且在众多潜在应用中也极具价值。然而，由于描述其演化的非线性微分方程的结构复杂，其数值建模具有挑战性。在本论文中，我们提议采用改进的四阶Runge-Kutta方法来求解这些方程，并进一步优化以实现高效的计算。这些算法以C++程序的形式实现，适用于并行环境，并利用向量指令。这些程序构成了EPCGP套件，该套件已被用于激子-极化激子的理论研究。