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arXiv:1206.0194 · Physical Review B

Turbulence in a Bose-Einstein condensate of dipolar excitons in coupled quantum wells

Oleg L. Berman, Roman Ya. Kezerashvili, G. V. Kolmakov, Yu. E. Lozovik

Published Jul 10, 2012• 23 citations
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Abstract

The nonlinear dynamics of a Bose-Einstein condensate (BEC) of dipolar excitons trapped in an external confining potential in coupled quantum wells is analyzed. It is demonstrated that under typical experimental conditions the dipolar exciton BEC can be described by a generalized Gross-Pitaevskii equation with the local interaction between the excitons, which depends on the exciton distribution function. It is shown that, if the system is pumped at sufficiently high frequencies, a steady turbulent state can be formed.

DOI
10.1103/physrevb.86.045108

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The nonlinear dynamics of a Bose-Einstein condensate (BEC) of dipolar excitons trapped in an external confining potential in coupled quantum wells is analyzed. It is demonstrated that under typical experimental conditions the dipolar exciton BEC can be described by a generalized Gross-Pitaevskii equation with the local interaction between the excitons, which depends on the exciton distribution function. It is shown that, if the system is pumped at sufficiently high frequencies, a steady turbulent state can be formed.
The properties of traps for exciton polaritons in a semiconductor microcavity with an embedded quantum well have been considered. The behavior of the two-component Bose-Einstein condensate of photons and excitons described by the coupled system of Gross-Pitaevskii equations has been investigated. The analytical solutions for weak-confinement traps have been found in the Thomas-Fermi approximation. In the case of strong confinement, the behavior of the condensate has been investigated and constraints on the possible values of the chemical potential of the system have been obtained. The wavefunctions and generally different spatial profiles of the coupled photon and exciton condensates have been found.
We apply the concepts of nonlinear guided-wave optics to a Bose-Einstein condensate (BEC) trapped in an external potential. As an example, we consider a parabolic double-well potential and derive coupled-mode equations for the complex amplitudes of the BEC macroscopic collective modes. Our equations describe different regimes of the condensate dynamics, including the nonlinear Josephson effect for any separation between the wells. We demonstrate macroscopic self-trapping for both repulsive and attractive interactions, and confirm our results by direct numerical solution of the Gross-Pitaevskii-equation.
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.
Considered as a fundamental step for the development of the atomic laser and quantum computing, as well as the theoretical explanation of super fluidity, the Bose- Einstein condensate (BEC) has emerged as one of the most important topics in modern physics. This project is devoted to the analysis of a condensate based on exciton-polaritons. This BEC is characterized by a high critical temperature of condensation (about 20 K) and non-equilibrium dynamics. A mathematical model called complex Gross- Pitaevskii equation (cGPE) is used to describe its behavior. The steady state solutions of the cGPE are studied and a numerical method based on a collocation method is proposed in order to find these solutions. Once the steady state solutions are found, a linear stability analysis is performed, demonstrating that the steady state solutions become unstable as the pumping spot radius increases. Finally, the manifestations of these instabilities are analyzed by direct simulation of the cGPE, using a second order time-splitting spectral method. As a result, it is possible to see the formation of quantum vortices, which increase in number as the pumping spot radius increases.
The formation of a dense Bose-Einstein condensate in dark spin states of two-dimensional dipolar excitons is shown to be driven by a dynamical transition to the long-lived dark states. The condensate is stabilized by strong dipole-dipole interactions up to densities high enough for a dark quantum liquid to form. The persistence of dark condensation was observed in recent experiments. A model describing the non-equilibrium dynamics of externally driven coupled dark and bright condensates reproduces the step-like dependence of the exciton density on the pump power or on temperature. This unique condensate dynamics demonstrates the possibility of observing new unexpected collective phenomena in coupled condensed Bose systems, where the particle number is not conserved.
The purpose of this paper is to study the dynamics of solutions to an extended Gross–Pitaevskii equation that models the formation of droplets in a dipolar Bose–Einstein condensate (BEC). The formation of these droplets has been recently discovered by driving the BEC into the strongly dipolar regime. Surprisingly, instead of collapsing, the system formed stable droplets. So far, no rigorous mathematical explanation has been proved. To the best of our knowledge, only experimental results have been obtained. The goal of this paper is to validate this breakthrough discovery. Many predictions/ conjectures properties of these droplets have been stated by some research groups in physics and engineering. In particular, it has been claimed that the stability of these droplets is a consequence of the presence of the damping term in the extended Gross–Pitaevskii equation under study. This term describes the three-body loss process. To accurately model the dynamics of formation of these droplets, it is necessary to consider a time-dependent harmonic trapping potential as well as other terms with different types of nonlinearity among them that describe the Lee–Huang–Yang (LHY). This presents some challenges that will be solved in this paper.