Detecting an exciton crystal by statistical means

TL;DR

This paper uses statistical analysis of exciton ensembles modeled by a disordered quantum Ising system to identify phase transitions between liquid and crystal states, providing a new method for detecting exciton crystals.

Contribution

It introduces a numerical simulation approach combining probability distribution functions and correlation functions to detect exciton crystal phases.

Findings

Clear evidence of liquid and crystal phases in exciton ensembles.

Distribution function P(M) effectively monitors phase transition.

Correlation functions corroborate the phase identification.

Abstract

We investigate an ensemble of excitons in a coupled quantum well excited via an applied laser field. Using an effective disordered quantum Ising model, we perform a numerical simulation of the experimental procedure and calculate the probability distribution function $P(M)$ to create $M$ excitons as well as their correlation function. It shows clear evidence of the existence of two phases corresponding to a liquid and a crystal phase. We demonstrate that not only the correlation function but also the distribution $P(M)$ is very well suited to monitor this transition.