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arXiv:0912.2010 · Physical Review B

Unique signatures for Bose-Einstein condensation in the decay luminescence lineshape of weakly interacting excitons in a potential trap

H. Stolz, D. Semkat

Published Feb 8, 2010• 16 citations
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Abstract

We calculate the spatially resolved optical emission spectrum of a weakly interacting Bose gas of excitons confined in a three dimensional potential trap due to interband transitions involving weak direct and phonon mediated exciton-photon interactions. Applying the local-density approximation, we show that for a noncondensed system the spatiospectral lineshape of the direct process reflects directly the shape of the potential. The existence of a Bose-Einstein condensate changes the spectrum in a characteristic way so that it directly reflects the constant chemical potential of the excitons and the renormalization of the quasiparticle excitation spectrum. Typical examples are given for parameters of the lowest yellow excitons in ${\text{Cu}}_{2}\text{O}$.

DOI
10.1103/physrevb.81.081302

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We calculate the spatially resolved optical emission spectrum of a weakly interacting Bose gas of excitons confined in a three dimensional potential trap due to interband transitions involving weak direct and phonon mediated exciton-photon interactions. Applying the local-density approximation, we show that for a noncondensed system the spatiospectral lineshape of the direct process reflects directly the shape of the potential. The existence of a Bose-Einstein condensate changes the spectrum in a characteristic way so that it directly reflects the constant chemical potential of the excitons and the renormalization of the quasiparticle excitation spectrum. Typical examples are given for parameters of the lowest yellow excitons in Cu2O{\text{Cu}}_{2}\text{O}Cu2​O.
The system under consideration is a multicomponent gas of interacting paraexcitons and orthoexcitons confined in a three-dimensional potential trap. We calculate the spatially resolved optical emission spectrum due to interband transitions involving weak direct and phonon-mediated exciton-photon interactions. For each component, the occurrence of a Bose-Einstein condensate changes the spectrum in a characteristic way so that it directly reflects the constant chemical potential of the excitons and the renormalization of the quasiparticle excitation spectrum. Moreover, the interaction between the components leads, in dependence on temperature and particle number, to modifications of the spectra indicating phase separation of the subsystems. Typical examples of density profiles and luminescence spectra of ground-state paraexcitons and orthoexcitons in Cu2O{\text{Cu}}_{2}\text{O}Cu2​O are given.
Recent experimental studies by Wolfe, Snoke, and Lin have given strong evidence that paraexcitons in optically excited Cu2{\mathrm{Cu}}_{2}Cu2​O crystals form a Bose condensate. In these studies, the observed recombination decay luminescence line shape I(\ensuremath{\omega}) has been analyzed in terms of an ideal Bose-condensed gas. We derive a general expression for I(\ensuremath{\omega}) in terms of the exact single-particle spectral density A(k,\ensuremath{\omega}) of a Bose fluid. This expression is then used to calculate I(\ensuremath{\omega}) for a dilute, weakly interacting Bose gas. Our analytic results, based on the approximate theory due to Popov, are valid in the region just below the Bose-Einstein transition temperature. When formally extended down to T=0, they reproduce the well-known Bogoliubov approximation.
Abstract An unambiguous observation of the Bose-Einstein condensation (BEC) of excitons in a photoexcited bulk semiconductor and elucidation of its inherent nature have been longstanding problems in condensed matter physics. Here, we observe the quantum phase transition and a Bose-Einstein condensate appearing in a trapped gas of 1s paraexcitons in bulk Cu2O below 400 mK, by directly visualizing the exciton cloud in real space using mid-infrared induced absorption imaging that we realized in a dilution refrigerator. Our study shows that the paraexciton condensate is undetectable by conventional luminescence spectroscopy. We find an unconventionally small condensate fraction of 0.016 with the spatial profile of the condensate well described by mean-field theory. Our discovery of this new type of BEC in the purely matter-like exciton system interacting with a cold phonon bath could pave the way for the classification of its long-range order, and for essential understanding of quantum statistical mechanics of non-equilibrium open systems.
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 transverse spatial distribution of weakly interacting Bose gas in a narrow channel is found. The corresponding analytical solution of the Gross-Pitaevskii equation has the form of a cnoidal wave. The possible physical realization of the model is a system of cold atoms or quasiparticles, e.g., excitons, cavity photons, exciton polaritons. The obtained formula is used for the numerical calculation of the spectrum of excitations and the critical velocity of the condensate. These numerical results do not coincide with the Bogoliubov spectrum, and we show that the strongly inhomogeneous condensate density leads to larger values of the critical velocity. We also make numerical estimation of the critical velocity for various types of considered particles or quasiparticles.
For the observation of Bose–Einstein condensation, ex-citons in cuprous oxide are regarded as promising can-didates due to their large binding energy and long life-time. High particle densities may be achieved by entrap-ment in a stress induced potential. We consider a multi-component gas of interacting para- and orthoexcitons in cuprous oxide confined in a three-dimensional potential trap. Based on the Hartree–Fock–Bogoliubov theory, we calculate density profiles as well as decay luminescence spectra which exhibit signatures of the separation of the Bose-condensed phases. Copyright line will be provided by the publisher 1 Introduction The theoretical framework for trapped dilute interacting bosonic gases is well known from the theory of atomic condensates [1,2,3,4]. First applications