Disorder Effects on Exciton–Polariton Condensates

Abstract

SummaryThe impact of a random disorder potential on the dynamical properties of Bose Einstein condensates is a very wide research field. In microcavities, these studies are even more crucial than in the condensates of cold atoms, since random disorder is naturally present in the semiconductor structures. In this chapter, we consider a stable condensate, defined by a chemical potential, propagating in a random disorder potential, like a liquid flowing through a capillary. We analyze the interplay between the kinetic energy, the localization energy, and the interaction between particles in 1D and 2D polariton condensates. The finite life time of polaritons is taken into account as well. In the first part, we remind the results of [G. Malpuech et al. Phys. Rev. Lett. 98, 206402 (2007).] where we considered the case of a static condensate. In that case, the condensate forms either a glassy insulating phase at low polariton density (strong localization), or a superfluid phase above the percolation threshold. We also show the calculation of the first order spatial coherence of the condensate versus the condensate density. In the second part, we consider the case of a propagating non-interacting condensate which is always localized because of Anderson localization. The localization length is calculated in the Born approximation. The impact of the finite polariton life time is taken into account as well. In the last section we consider the case of a propagating interacting condensate where the three regimes of strong localization, Anderson localization, and superfluid behavior are accessible. The localization length is calculated versus the system parameters. The localization length is strongly modified with respect to the non-interacting case. It is infinite in the superfluid regime whereas it is strongly reduced if the fluid flows with a supersonic velocity (Cerenkov regime). I IntroductionIn a normal fluid, the viscosity arises because of the elastic scattering of the particles which compose it. This includes both the scattering on the external potential, for example, the walls of the capillary, and the scattering of the particles on each other, if their velocities are different. In contrast to that, for a condensate of weakly interacting bosons (a Bose-Einstein condensate -BEC), which will be the main object studied in this chapter, single independent particles are replaced by collective sonic-like excitations [1,2]. As a result, such condensate propagating with a velocity smaller than the speed of sound cannot dissipate its kinetic energy by scattering on a disorder potential or on the non-condensed particles. This collective behavior results in a vanishing mechanical viscosity, called superfluidity.However, sometimes the potential fluctuations can be large enough to destroy the superfluid behavior of a Bose condensate by provoking its complete localization. The question of the interplay between kinetic energy, localization energy, and the interaction between particles has been widely studied in solid state physic...

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