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Journal of Experimental and Theoretical Physics Letters

Bose–Einstei condensation of dipolar excitons in a ring trap

Alexander V. Chaplik

Published Dec 1, 2016• 1 citation
Publisher

Abstract

The temperature of Bose–Einstein condensation and the fraction of particles in a condensate for a system of spatially indirect dipole excitons in an electrostatic ring trap have been found. If only levels of the radial motion close to the bottom of the potential well of the trap are populated considerably, the oscillatory model of the single-particle spectrum is applicable. In this case, even the strong exciton–exciton interaction can be taken into account.

DOI
10.1134/s0021364016230065

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The temperature of Bose–Einstein condensation and the fraction of particles in a condensate for a system of spatially indirect dipole excitons in an electrostatic ring trap have been found. If only levels of the radial motion close to the bottom of the potential well of the trap are populated considerably, the oscillatory model of the single-particle spectrum is applicable. In this case, even the strong exciton–exciton interaction can be taken into account.
The phase diagram of Bose-Einstein condensates of dipolar excitons accumulated in lateral electrostatic traps is determined. Spatially periodic luminescence structures of the exciton Bose condensate and their critical dependence on pump level and temperature are observed. Coherence in the dipolar exciton Bose-Einstein condensates is studied by direct measurement of the 1-st and 2-nd order correlators with variations in pump level and temperature. These results are indicative of large-scale coherence of the exciton Bose condensate.
The experiments on Bose-Einstein condensation (BEC) of dipolar (spatially-indirect) excitons in the lateral traps in GaAs/AlGaAs Schottky-diode heterostructures with double and single quantum wells are presented. The condensed part of dipolar excitons under detection in the far zone is placed in k -space in the range which is almost two orders of magnitude less than thermal exciton wave vector. BEC occurs spontaneously in a reservoir of thermalized excitons. Luminescence images of Bose-condensate of dipolar excitons exhibit along perimeter of circular trap axially symmetrical spatial structures of equidistant bright spots which strongly depend on excitation power and temperature. By means of two-beam interference experiments with the use of cw and pulsed photoexcitation it was found that the state of dipolar exciton Bose-condensate is spatially coherent and the whole patterned luminescence configuration in real space is described by a common wave function.
The system under consideration is a multicomponent gas of interacting paraexcitons and orthoexcitons confined in a three-dimensional potential trap. We calculate the spatially resolved optical emission spectrum due to interband transitions involving weak direct and phonon-mediated exciton-photon interactions. For each component, the occurrence of a Bose-Einstein condensate changes the spectrum in a characteristic way so that it directly reflects the constant chemical potential of the excitons and the renormalization of the quasiparticle excitation spectrum. Moreover, the interaction between the components leads, in dependence on temperature and particle number, to modifications of the spectra indicating phase separation of the subsystems. Typical examples of density profiles and luminescence spectra of ground-state paraexcitons and orthoexcitons in Cu2O{\text{Cu}}_{2}\text{O}Cu2​O are given.
This work is motivated by the active surge in research on ring Bose–Einstein condensates of exciton polaritons, including those with artificially created defects (barriers). Currently, such systems are primarily described within a one-dimensional approach, taking into account that the order parameter depends only on the azimuthal angle. In this work, the profiles of a polariton ring Bose–Einstein condensate in the stationary case have been numerically simulated using the two-dimensional Gross–Pitaevskii equation. The radial profiles of the ground-state wavefunction are obtained for ring confinement potentials of various depths and widths, which have been used to calculate effectively one-dimensional interaction constants for various particle densities in the condensate. The results have been compared with analytical expressions for the linear limit and for a ring of a large radius, and the validity range for these simplified analytical descriptions have been determined.