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arXiv:1704.04446 · Physical review. B./Physical review. B

Localization and self-trapping in driven-dissipative polariton condensates

Frank Bello, P. R. Eastham

Published Jun 23, 2017• 4 citations
arXivHTMLPDF

Abstract

We study driven-dissipative Bose-Einstein condensates in a two-mode Josephson system, such as a double-well potential, with asymmetrical pumping. We investigate nonlinear effects on the condensate populations and mode transitions. The generalized Gross-Pitaevskii equations are modified in order to treat pumping of only a single mode. We characterize the steady-state solutions in such a system as well as criteria for potential trapping of a condensate mode. There are many possible steady states, with different density and/or phase profiles. Transitions between different condensate modes can be induced by varying the parameters of the junction or the initial conditions, or by applying external fields.

DOI
10.1103/physrevb.95.245312

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We study driven-dissipative Bose-Einstein condensates in a two-mode Josephson system, such as a double-well potential, with asymmetrical pumping. We investigate nonlinear effects on the condensate populations and mode transitions. The generalized Gross-Pitaevskii equations are modified in order to treat pumping of only a single mode. We characterize the steady-state solutions in such a system as well as criteria for potential trapping of a condensate mode. There are many possible steady states, with different density and/or phase profiles. Transitions between different condensate modes can be induced by varying the parameters of the junction or the initial conditions, or by applying external fields.
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 Bose-stimulated self-organization of a quasi-two-dimensional nonequilibrium Bose-Einstein condensate in an in-plane potential is proposed. We obtained the solution of the nonlinear, driven-dissipative Gross-Pitaevskii equation for a Bose-Einstein condensate trapped in an external asymmetric parabolic potential within the method of the spectral expansion. We found that, in sharp contrast to previous observations, the condensate can spontaneously acquire a solitonlike shape for spatially homogeneous pumping. This condensate soliton performs oscillatory motion in a parabolic trap and, also, can spontaneously rotate. Stability of the condensate soliton in the spatially asymmetric trap is analyzed. In addition to the nonlinear dynamics of nonequilibrium Bose-Einstein condensates of ultracold atoms, our findings can be applied to the condensates of quantum well excitons and cavity polaritons in semiconductor heterostructure, and to the condensates of photons.
We investigate the physics of coherent polaritons in a double-well configuration under a resonant pumping. For a continuous wave pump, bistability and self-pulsing regimes are identified as a function of the pump energy and intensity. The response to an additional probe pulse is characterized in the different cases and related to the Bogoliubov modes around the stationary state. Under a pulsed pump, a crossover from Josephson-like oscillations to self-trapping is predicted for increasing pump intensity. The accurateness of the effective two-mode model is assessed by comparing its predictions to a full solution of the non-equilibrium Gross-Pitaevskii equation.
We investigate the physics of coherent polaritons in a double-well configuration under a resonant pumping. For a continuous-wave pump, bistability and self-pulsing regimes are identified as a function of the pump energy and intensity. The response to an additional probe pulse is characterized in the different cases and related to the Bogoliubov modes around the stationary state. Under a pulsed pump, a crossover from Josephson-like oscillations to self-trapping is predicted for increasing pump intensity. The accurateness of the effective two-mode model is assessed by comparing its predictions to a full solution of the nonequilibrium Gross--Pitaevskii equation.
The dynamics of Bose-Einstein condensates in a double-well magnetic trap is studied using the Gross-Pitaevskii equation (GPE) and a two-mode approximation. The self-trapping instability occurs when a sufficiently high potential barrier is formed in the centre of the trap. Close to the instability threshold, the GPE is reduced to a simple amplitude equation. In the case where weakly dissipative effects are taken into account, the condensate exhibits aperiodic oscillations which can be described by the Lorenz thermal convection model.