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Journal of Experimental and Theoretical Physics Letters

On the Position-Dependent Effective Mass in Bose Condensates of Photons and Polaritons in an Optical Microcavity Trap

Nina S. Voronova, Yu. E. Lozovik

Published Dec 1, 2018• 5 citations
Publisher

Abstract

The effect of the particle position-dependent effective mass on the behavior of quasi-two-dimensional photon and exciton-polariton condensates in a parabolic trap in a semiconductor optical microcavity is investigated. It is demonstrated that the correct inclusion of the coordinate dependence of the effective mass in the kinetic-energy operator modifies the effective confining potential for the particles. Corrections to the energy and wavefunction of the photon Bose condensate are derived. For exciton-polaritons, it is shown that the choice of specific mirror geometry can lead to the change from repulsive to attractive particle–particle interaction.

DOI
10.1134/s0021364018240104

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Journal of Experimental and Theoretical Physics Letters•Dec 1, 2014•3 citations
The effect of the particle position-dependent effective mass on the behavior of quasi-two-dimensional photon and exciton-polariton condensates in a parabolic trap in a semiconductor optical microcavity is investigated. It is demonstrated that the correct inclusion of the coordinate dependence of the effective mass in the kinetic-energy operator modifies the effective confining potential for the particles. Corrections to the energy and wavefunction of the photon Bose condensate are derived. For exciton-polaritons, it is shown that the choice of specific mirror geometry can lead to the change from repulsive to attractive particle–particle interaction.
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.
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.
The condensate density profile of trapped two-dimensional gas of photons in an optical microcavity, filled by a dye solution, is analyzed taking into account a coordinate-dependent effective mass of cavity photons and photon–photon coupling parameter. The profiles for the densities of the superfluid and normal phases of trapped photons in the different regions of the system at the fixed temperature are analyzed. The radial dependencies of local mean-field phase transition temperature Tc0(r) and local Kosterlitz–Thouless transition temperature Tc(r) for trapped microcavity photons are obtained. The coordinate dependence of cavity photon effective mass and photon–photon coupling parameter is important for the mirrors of smaller radius with the high trapping frequency, which provides Bose–Einstein condensation and superfluidity for smaller critical number of photons at the same temperature. We discuss a possibility of an experimental study of the density profiles for the normal and superfluid components in the system under consideration.
We present a theoretical description of Bogolyubov-type excitations of exciton-polariton Bose-Einstein condensates (BECs) in semiconductor microcavities. For a typical two-dimensional (2D) BEC we focus on two limiting cases, the weak- and strong-coupling regimes, where a perturbation theory and the Thomas-Fermi approximation, respectively, are valid. We calculate integrated scattering intensity spectra for probing the collective excitations of the condensate in both considered limits. Moreover, in relation to recent experiments on optical modulation allowing localization of condensates in a trap with well-controlled shape and dimensions, we study the quasi-one-dimensional (1D) motion of the BEC in microwires and report the corresponding Bogolyubov excitation spectrum. We show that in the 1D case the characteristic polariton-polariton interaction constant is expressed as ${g}_{1}=3\ensuremath{\lambda}\mathcal{N}/(2{L}_{y})$ ($\ensuremath{\lambda}$ is the 2D polariton-polariton interaction parameter in the cavity, N\mathcal{N}N the number of the particles, and Ly{L}_{y}Ly​ the wire cavity width). We reveal some interesting features for 2D and 1D Bogolyubov spectra for both repulsive $(\ensuremath{\lambda}>0)$ and attractive $(\ensuremath{\lambda}<0)$ interactions.
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 first-order spatial correlation function g (1)(r 12) and the polariton density distribution in the condensate of quasi-two-dimensional exciton polaritons formed in a high-Q semiconductor microcavity pillar under nonresonant optical pumping are investigated. It is found that the correlation function in certain regions of the micropillar decreases abruptly with increasing condensate density. It is shown that this behavior of the correlation function is caused by the formation of a localized dark soliton in these regions. A deep minimum of the polariton density and a shift in the phase of the condensate wavefunction by π occur within the soliton localization area.