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arXiv:1404.5353 · Physical Review B

Effective interaction and condensation of dipolaritons in coupled quantum wells

Tim Byrnes, G. V. Kolmakov, Roman Ya. Kezerashvili, Y. Yamamoto

Published Sep 23, 2014• 45 citations
arXivHTMLPDF

Abstract

Dipolaritons are a three-way superposition of a photon, a direct exciton, and an indirect exciton that are formed in coupled quantum well microcavities. As is the case with exciton-polaritons, dipolaritons have a self-interaction due to direct and exchange effects of the underlying electrons and holes. Here we present a theoretical description of dipolaritons and derive simple formulas for their basic parameters. In particular, we derive the effective dipolariton-dipolariton interaction taking into account exchange effects between the excitons. We obtain a simple relation to describe the effective interaction at low densities. We find that dipolaritons should condense under suitable conditions, described by a dissipative Gross-Pitaevskii equation. While the parameters for condensation are promising, we find that the level of tunability of the interactions is limited.

DOI
10.1103/physrevb.90.125314

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Dipolaritons are a three-way superposition of a photon, a direct exciton, and an indirect exciton that are formed in coupled quantum well microcavities. As is the case with exciton-polaritons, dipolaritons have a self-interaction due to direct and exchange effects of the underlying electrons and holes. Here we present a theoretical description of dipolaritons and derive simple formulas for their basic parameters. In particular, we derive the effective dipolariton-dipolariton interaction taking into account exchange effects between the excitons. We obtain a simple relation to describe the effective interaction at low densities. We find that dipolaritons should condense under suitable conditions, described by a dissipative Gross-Pitaevskii equation. While the parameters for condensation are promising, we find that the level of tunability of the interactions is limited.
In this paper, we investigate the nonlinear optical properties and photon correlations in a cavity containing quantum wells and interacting with a third-order nonlinear medium. More precisely, we study the interaction of the photonic Kerr nonlinearity with polariton and dipolariton quasiparticles in thermal environments. The optical bistability, the intensity spectrum, and the squeezing spectrum of the transmitted radiation are analyzed. It is shown that the regime of the bistability is reached in the dipolariton cavity faster than attained by the polariton system. Furthermore, the increase of the coupling with the wells reduces the squeezing. More interestingly, it turns out that the additional interactions arising in the dipolariton cavity, between direct and indirect excitons, slow down the variation of the squeezing. As a consequence, dipolaritons offer a greater margin of squeezed light than polaritons, and also than the ${\ensuremath{\chi}}^{(3)}$ medium in the absence of quantum wells. Moreover, the dipolariton system is found to be much more robust against the bath temperature in the weak-coupling regime.
The properties of traps for exciton polaritons in a semiconductor optical microcavity with an embedded quantum well were considered. The two-component Bose condensate of photons and excitons was described by a coupled system of equations similar to the Gross-Pitaevskii equations, and analytical solutions in the Thomas-Fermi approximation were obtained for traps with weak exciton confinement. For strong confinement, condensate behavior was investigated numerically, and spatial profiles of coupled condensates of excitons and photons (which appear to be different in general case) were determined.
We study the behavior of exciton polaritons in an optical microcavity with an embedded semiconductor quantum well. We use a two-component exciton-photon approach formulated in terms of path integral formalism. In order to describe spatial distributions of the exciton and photon condensate densities, the two coupled equations of the Gross-Pitaevskii type are derived. For a homogeneous system, we find the noncondensate photon and exciton spectra, calculate the coefficients of transformation from the exciton-photon basis to the lower-upper polariton basis, and obtain the exciton and photon occupation numbers of the lower and upper polariton branches for nonzero temperatures. For an inhomogeneous system, the set of coupled equations of the Bogoliubov--de Gennes type is derived. The equations govern the spectra and spatial distributions of noncondensate photons and excitons.
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.
In this work, we study the exciton-polariton condensate phase transition in a microcavity matter-light system in which electron-hole Coulomb interaction and matter-light coupling effects are treated on an equal footing. In the framework of the unrestricted Hartree-Fock approximation applying the two-dimensional exciton-polariton model, we derive the self-consistent equations determining simultaneously the excitonic and the photonic condenstate order parameters. In the thermal-equilibrium limit, we find a condensed state of the exciton-polariton systems and phase diagrams are then constructed. At a given low temperature, the condensate by its nature shows a crossover from an excitonic to a polaritonic and finally photonic condensed state as the excitation density increases at large detuning. Without the detuning, the excitonic condensed state disappears whereas the polaritonic or photonic phases dominate. The crossover is also found by lowering the Coulomb interaction at a finite matter-light coupling. Lowering the Coulomb interaction or increasing the temperature, the excitonic Mott transition occurs, at which the exciton-polariton condensates dissociate to free electron-hole/photon. Depending on temperature and excitation density, the phase transition of the exciton-polariton condensates is also addressed in signatures of photoluminescence mapping to the photonic momentum distribution.
We derive the equation of motion for a Bose-Einstein condensate of photons in a dye-microcavity system, starting from Maxwell's equations. Our theory takes into account mirror shape, Kerr-type intensity-dependent refractive index and incoherent pumping and loss. The resulting equation is remarkably similar to the Gross-Pitaevskii equation for exciton-polariton condensates, despite the different microscopic origins. We calculate the incoherent photoluminescence spectrum of the photon condensate, which shows the Bogoliubov-type excitations around the mean field at thermal equilibrium. Both open- and closed-system models are presented to account for, respectively dissipation and inhomogeneities. Considering realistic parameters and experimental resolution, we estimate that by observing the angle-resolved spectrum of incoherent photoluminescence it is possible to resolve dimensionless interaction parameters of order ${10}^{\ensuremath{-}5}$, two orders of magnitude below current estimates. Thus we expect that this technique will lead to accurate measurements of the interactions in photon condensates.