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arXiv:1403.6247 · Physical Review B

Excited states of exciton-polariton condensates in 2D and 1D harmonic traps

C. Trallero‐Giner, M. V. Durnev, Y. Núñez-Fernández, Mikhail I. Vasilevskiy, Victor Lopez‐Richard, Alexey Vitalievich Kavokin

Published May 27, 2014• 6 citations
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Abstract

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, $\mathcal{N}$ the number of the particles, and ${L}_{y}$ 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.

DOI
10.1103/physrevb.89.205317

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•Jan 1, 2014•0 citations
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 g1=3\ensuremathλN/(2Ly){g}_{1}=3\ensuremath{\lambda}\mathcal{N}/(2{L}_{y})g1​=3\ensuremathλN/(2Ly​) (\ensuremathλ\ensuremath{\lambda}\ensuremathλ 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 (\ensuremathλ>0)(\ensuremath{\lambda}>0)(\ensuremathλ>0) and attractive (\ensuremathλ<0)(\ensuremath{\lambda}<0)(\ensuremathλ<0) interactions.
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.
Recent experiments have shown that it is possible to create an in-plane harmonic potential trap for a two-dimensional (2D) gas of exciton polaritons in a microcavity structure, and evidence has been reported of Bose-Einstein condensation of polaritons accumulated in this type of trap. We present here the theory of Bose-Einstein condensation (BEC) and superfluidity of the exciton polaritons in a harmonic potential trap. Along the way, we determine a general method for defining the superfluid fraction in a 2D trap, in terms of angular momentum representation. We show that in the continuum limit, as the trap becomes shallower, the superfluid fraction approaches the 2D Kosterlitz--Thouless limit, while the condensate fraction approaches zero, as expected.
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.
This thesis includes theoretical studies regarding stability and manipulation of Bose-Einstein condensates (BECs) of ultra-cold atoms in 2D trapping geometry, as well as formation of steady states of exciton-polariton Bose-Einstein condensates created in solid states. We analyze and numerically model the dynamics and localization of the condensates using mean-field model. Chapter 1 contains an introduction to the physics of ultra-cold atom BEC and excitonpolariton BEC which provides a framework for the work presented in later chapters. In Chapter 2, we consider a method for achieving dynamically controllable transport of highly mobile matter-wave solitons in an ultra-cold atom BEC with attractive interparticle interaction loaded into a driven two-dimensional optical lattice. Our numerical analysis based on the mean-field model and the theory based on the effective particle approach demonstrate that fast, time-periodic rocking of the two-dimensional optical lattice enables efficient stabilization and manipulation of spatially localized matter wave packets via induced reconfigurable mobility channels. Chapter 3 consists of an investigation of the instability - collapse of a BEC with attractive interactions. In this chapter we explore the influence of an orbital angular momentum on the collapse of vortex-free elliptic clouds of Bose-Einstein condensates trapped in a radially symmetric harmonic potential or a rotating elliptic potential. The results of our analysis show that the number of trapped ultracold atoms corresponding to the collapse threshold can be radically increased for such rotating nonlinear matter waves in a radially harmonic trap. The results corresponding to a BEC cloud confined in a rotating elliptic trap show that the elongated stationary states can be parallel or perpendicular to the long axis of the trap and display bistable nature. In Chapter 4, we examine spatial localization and dynamical stability of Bose-Einstein condensates of exciton-polaritons in microcavities under the condition of off-resonant spatially inhomogeneous optical pumping both with and without a harmonic trapping potential. We employ the open-dissipative Gross-Pitaevskii model for describing an incoherently pumped polariton condensate coupled to an exciton reservoir. We reveal that spatial localization of the steady-state condensate occurs due to effective self-trapping created by the polariton flows, regardless of the presence of the external potential. A ground state of the polariton condensate with repulsive interactions between the quasiparticles represents a dynamically stable bright dissipative soliton. We also investigate the conditions for sustaining spatially localized structures, with nonzero angular momentum, in the form of single-charge vortices. Chapter 5 consider the existence of novel spatially localized states of exciton-polariton Bose-Einstein condensates in semiconductor microcavities with fabricated periodic inplane potentials. Our theory shows that, under the conditions of continuous nonresonant pumping, localization is observed for a wide range of optical pump parameters due to effective potentials self-induced by the polariton flows in the spatially periodic system. We show that the self-localization of exciton-polaritons in the lattice may occur both in the gaps and bands of the single-particle linear spectrum, and is dominated by the effects of gain and dissipation rather than the structured potential, in sharp contrast to the conservative condensates of ultra-cold alkali atoms.