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Physical Review B

Coherent dynamics and parametric instabilities of microcavity polaritons in double-well systems

Davide Sarchi, Iacopo Carusotto, Michiel Wouters, Vincenzo Savona

Published Mar 19, 2008• 134 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.77.125324

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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.
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.
The polarization dependence of nonequilibrium transitions in a multistable cavity-polariton system is studied under nanosecond-long resonant optical excitation at normal and magic angle incidences with various polarizations of the pump beam. The temporal correlations between the frequency, intensity, and optical polarization of the intracavity field, which all undergo sharp threshold-like changes due to the spin-dependent interaction of cavity polaritons, are visualized. The observed dynamics cannot be reproduced within the conventional semiclassical model based on the Gross-Pitaevskii equations. To explain the observed phenomena, it is necessary to take into account the unpolarized exciton reservoir that brings on an additional blue shift of bright excitons, the same for the ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ polarization components. This model explains the effect of polarization instability under both pulsed- and continuous-wave resonant excitation conditions, consistently with the spin ring pattern formation that has recently been observed under Gaussian-shaped excitation.
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.
The polariton dynamics in a microcavity in the parametric oscillator mode, when two pump polaritons are transformed into signal and idler polaritons and vice versa, has been studied. A nonlinear differential equation is obtained, which describes the temporal evolution of pump-polariton density, the solution of which is expressed in terms of the Jacobi elliptical functions. The amplitude and period of polaritondensity oscillations are determined by the initial polariton densities and the resonance detuning. The possibility of self-trapping in exciton-polariton dynamics is predicted.
Dynamics of stimulated scattering of quasi-two-dimensional exciton polaritons in a semiconductor microcavity is considered theoretically. A system possessing a bistable response to coherent excitation is studied. Being a system of weakly interacting Bose particles under strongly nonequilibrium conditions, it exhibits a complex dynamics of the development of condensate modes. It is shown that multimode instability can arise in a threshold way in the system under a smooth increase in pump intensity. In this case, rapid populating of a multitude of unstable modes leads to stochastization of scattering, and evolution to a quasi-steady macrostate is performed as self-organization in an open nonequilibrium system. Arising fluctuations lead to the occurrence of a spatial nonuniformity of the distribution of scattered states.
Excitons-polaritons of semiconductor microcavities are quasiparticles originating from the dressing of optical cavity photons by the interactions between quantum well electron-hole pairs. In planar geometry, their belonging to the family of quantum fluids has been many times demonstrated through the observation of macroscopic coherence phenomena, such as superfluidity and Bose-Einstein condensation. Like ultracold atoms, polaritons support on their surface a set of collective excitations, the Bogoliubov modes, whose spectrum encompasses the key information to describe the dynamics of quantum fluids. In this thesis, we present a wide variety of results concerning the detection and control of such modes in different configurations. Thanks to the development of a new high-resolution coherent spectroscopy method, we carried out a detailed study of the spectrum of polariton collective excitations. In particular, we highlighted the effects of the driven-dissipative nature of the system on the fundamental dynamics of the fluid, by investigating the interplay between the Bogoliubov modes and the polariton bistability under coherent pumping. This was the opportunity to reveal, in addition to the well-known phonon-type excitations, precursors of dynamical instability and the so-called ghost branch. Moreover, we studied the behavior of out-of-equilibrium phase transitions: first, via the effect of the system dimension on the bistability and, second, with the onset of a Goldstone mode, as a result of a spontaneous symmetry breaking in a parametric oscillation regime. Finally, we designed a pumping geometry that directly controls the instability modes between dark solitons of a pair guided by an intensity channel, leading to the formation of vortex-antivortex streets in the density.