Path integral approach to bosonisation and nonlinearities in exciton-polariton systems

TL;DR

This paper develops a path integral formalism to analyze exciton-polariton nonlinearities, incorporating finite temperature effects, exciton state mixing, and dark exciton contributions, providing a clearer understanding of the underlying physics.

Contribution

It introduces a comprehensive theoretical framework for exciton nonlinearities in strong coupling regimes, clarifying the limitations of traditional interaction constants.

Findings

The formalism accounts for temperature, state mixing, and dark excitons.

It shows exciton interaction constants are material-specific, not tunable parameters.

The approach reconciles contradictory reports on scattering rates and nonlinearities.

Abstract

Large exciton-polariton optical nonlinearities present a key mechanism for photonics-based communication, ultimately in the quantum regime. Enhanced nonlinear response from various materials hosting excitons and allowing for their strong coupling with light is therefore the topic of intense studies, both in theoretical and experimental domains. Reports on the scattering rates arising due to various system's nonlinearities, such as the exciton-exciton Coulomb interaction and the Pauli blocking that leads to the saturation of the exciton oscillator strength, however, are contradictory. In this work, we develop a formalism allowing to track the exciton nonlinearities appearing in the regime of strong coupling with photons, that includes finite temperatures, mixing of the exciton excited states, and the dark exciton contributions to saturation self-consistently. The equilibrium path integration approach employed here to address the polariton composite nature, leads to a transparent hierarchy of various contributions to nonlinearity. At the same time, by taking the simplest limit of zero temperature and so-called "rigid" excitons, through our framework we retrieve the expressions derived in conventional approaches for exciton interaction constants. In particular, our theory allows to clearly show that such interaction constants cannot be used as fitting parameters tunable in a wide range of values, as they are strictly defined by the material properties, and that other explanations are due for large optical nonlinearities recently reported.