Mean-field and cumulant approaches to modelling organic polariton physics

TL;DR

This thesis develops mean-field and cumulant methods to model the complex many-body dynamics of organic polaritons, enabling efficient simulations and detailed analysis of their transport and interaction phenomena.

Contribution

It introduces combined mean-field and matrix product operator techniques, along with cumulant expansions, to accurately simulate and analyze organic polariton systems with many-body interactions.

Findings

Efficient simulation of organic laser dynamics.

Observation of reversible dark exciton conversion.

Analysis of organic polariton transport phenomena.

Abstract

In this thesis we develop methods for many-body open quantum systems and apply them to systems of organic polaritons. The methods employ a mean-field approach to reduce the dimensionality of large-scale problems. Initially assuming the absence of correlations in the many-body state, this approach is built upon in two ways. First, we show how the mean-field approximation can be combined with matrix product operator methods to efficiently simulate the non-Markovian dynamics of a many-body system with strong coupling to multiple environments. We apply this method to calculate the threshold and photoluminescence for a realistic model of an organic laser. Second, we extend the mean-field description by systematically including higher-order correlations via cumulant expansions of the Heisenberg equations of motion. We investigate the validity and convergence properties of these expansions, both with respect to expansion order and system size, for many-body systems with many-to-one network structures. We then show how the cumulant expansions may be used to calculate spatially resolved dynamics of organic polaritons. This enables a study of organic polariton transport in which we observe reversible conversion to dark exciton states and sub-group-velocity propagation. The methods established in this work offer versatile tools for analysing large, many-body open quantum systems and investigating finite-size effects. Their application reveals the intricate dynamics of organic polaritons resulting from the interplay of strong light-matter coupling and vibrational effects.