Non-Markovian Quantum Dynamics of Exciton-Polaritons

Abstract

Exciton-polaritons, hybrid light-matter quasiparticles formed when a material interacts with a confined electric field, have experimentally been shown to exhibit mesoscale coherent quantum propagation that remains robust at room temperature. However, an accurate and direct quantum dynamical simulation of this phenomenon that does not resort to semi-classical approximations is prohibitively expensive computationally, limiting the microscopic understanding of the rich dynamical interplay among phonons, photons, and electrons under collective light-matter coupling. To address this fundamental challenge, we develop a non-Markovian master equation approach which enables the fully quantum mechanical simulation of non-equilibrium exciton-polariton dynamics and captures phonon-induced decoherence and dissipation beyond the conventional Markovian limit. To carry out this task, a procedure is developed in which the wave vector space is coarse-grained and each diagonal element of the density matrix is evolved in parallel. To demonstrate the utility of this approach, we simulate exciton-polariton transport in TIPS-pentacene. We find that our approach reasonably captures the experimentally observed renormalization of the polariton group velocity, which originates from the phonon-induced non-Markovian Lamb shift. We further show that this renormalization cannot be reproduced within conventional Markovian theories.