# Phase diagram of microcavity exciton-polariton condensates

## TL;DR

This paper investigates the phase transitions of exciton-polariton condensates in microcavities, revealing how different parameters influence the crossover between excitonic, polaritonic, and photonic states, and identifying conditions for Mott transitions.

## Contribution

The study introduces a self-consistent Hartree-Fock framework for exciton-polariton systems, providing detailed phase diagrams and insights into state crossovers and Mott transitions.

## Key findings

- Identified a crossover from excitonic to photonic condensates with increasing excitation density.
- Discovered the disappearance of excitonic condensates without detuning at high densities.
- Mapped phase transitions using photoluminescence signatures.

## Abstract

In this work, we study the exciton-polariton condensate phase transition in a microcavity matter-light system in which electron-hole Coulomb interaction and matter-light coupling effects are treated on an equal footing. In the framework of the unrestricted Hartree-Fock approximation applying the two-dimensional exciton-polariton model, we derive the self-consistent equations determining simultaneously the excitonic and the photonic condenstate order parameters. In the thermal equilibrium limit, we find a condensed state of the exciton-polariton systems and phase diagrams are then constructed. At a given low temperature, the condensate by its nature shows a crossover from an excitonic to a polaritonic and finally photonic condensed state as the excitation density increases at large detuning. Without the detuning, the excitonic condensed state disappears whereas the polaritonic or photonic phases dominate. The crossover is also found by lowering the Coulomb interaction at a finite matter-light coupling. Lowering the Coulomb interaction or increasing the temperature, the excitonic Mott transition occurs, at which the exciton-polariton condensates dissociate to free electron-hole/photon. Depending on temperature and excitation density, the phase transition of the exciton-polariton condensates is also addressed in signatures of photoluminescence mapping to the photonic momentum distribution.