Quasi-equilibrium polariton condensates in the non-linear regime and beyond

TL;DR

This paper develops a microscopic mean-field BCS theory to analyze many-body polariton condensates in a semiconductor microcavity, covering equilibrium and non-equilibrium regimes, and explores their interactions, universal behaviors, and potential for BCS pairing.

Contribution

It introduces a comprehensive BCS-based model for polariton condensates that accounts for non-linear interactions, universal properties, and non-equilibrium effects, extending beyond previous equilibrium-focused studies.

Findings

Exact single-particle polariton properties at low density

Analytic expressions for the equation of state with contact interactions

Identification of conditions favoring BCS regime with overlapping pairs

Abstract

We investigate the many-body behavior of polaritons formed from electron-hole pairs strongly coupled to photons in a two-dimensional semiconductor microcavity. We use a microscopic mean-field BCS theory that describes polariton condensation in quasi-equilibrium across the full range of excitation densities. In the limit of vanishing density, we show that our theory recovers the exact single-particle properties of polaritons, while at low densities it captures non-linear polariton-polariton interactions within the Born approximation. For the case of highly screened contact interactions between charge carriers, we obtain analytic expressions for the equation of state of the many-body system. This allows us to show that there is a photon resonance at a chemical potential higher than the photon cavity energy, where the electron-hole pair correlations in the polariton condensate become universal and independent of the details of the carrier interactions. Comparing the effect of different ranged interactions between charge carriers, we find that the Rytova-Keldysh potential (relevant to transition metal dichalcogenides) offers the best prospect of reaching the BCS regime, where pairs strongly overlap and the minimum pairing gap occurs at finite momentum. Finally, going beyond thermal equilibrium, we argue that there are generically two polariton branches in the driven-dissipative system and we discuss the possibility of a density-driven exceptional point within our model.