Detecting an exciton crystal by statistical means

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.Comment: 5 pages, 5 figure

Exciton Condensates and Superconductors-Technical Differences and Physical Similarities

“…We will first discuss the two possibilities to measure the phase transition by modern spectroscopic techniques. In this case one focusses on physically separated bilayers and extremely short laser pulses and experimental of τ < 0.1 ns so that the movement of the excitons can be neglected [19]. In this case, the electrons of the underlying system can be effectively regarded as a two-level system (the first level corresponding to typical electrons and the second level corresponding to excitons) [19] in accordance with previous studies of Rydberg atoms [4]…”

“…We therefore observe a cubic dependence on the inter-exciton distance r. This inter-exciton exchange leads to the fact that excitons may form Wigner crystals [18] [19] as electrons or Rydberg atoms do [3].…”

“…If the excitons can be observed on a timescale small enough in order to assume that they are fixed in space we should expect the formation of an emergent long-range order of Wigner-crystal type [18] [19].…”

“…The number of excitons drops by increasing interaction but the variance first increases with increasing interaction whereas for the interaction being larger than a critical value it sharply drops. This change can be associated to the formation of crystalline order [19].…”