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Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physics

Cover Picture: Phys. Status Solidi C 4/2011

Published Apr 1, 2011• 0 citations
Publisher

Abstract

Excitons in cuprous oxide are promising candidates for the observation of Bose–Einstein condensation. Based on a multi-component Hartree–Fock–Bogoliubov theory, Sobkowiak et al., pp. 1178ff., determined the density profiles and luminescence spectra of interacting para- and orthoexcitons in a stress induced potential trap. The cover figure shows the exciton densities (top) of a system with strong repulsion between the two ortho-species. The calculations suggest that the phase separation of the ortho-condensates is not directly observable in the respective spectra, but may be revealed by the W-shaped distortion in the spatially resolved spectrum of the thermal paraexcitons, which can be seen in the bottom figure. The experimental observation of this footprint would yield a minimum estimate of the relative strength of the respective interactions.

DOI
10.1002/pssc.201190010

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Excitons in cuprous oxide are promising candidates for the observation of Bose–Einstein condensation. Based on a multi-component Hartree–Fock–Bogoliubov theory, Sobkowiak et al., pp. 1178ff., determined the density profiles and luminescence spectra of interacting para- and orthoexcitons in a stress induced potential trap. The cover figure shows the exciton densities (top) of a system with strong repulsion between the two ortho-species. The calculations suggest that the phase separation of the ortho-condensates is not directly observable in the respective spectra, but may be revealed by the W-shaped distortion in the spatially resolved spectrum of the thermal paraexcitons, which can be seen in the bottom figure. The experimental observation of this footprint would yield a minimum estimate of the relative strength of the respective interactions.
Abstract For the observation of Bose–Einstein condensation, excitons in cuprous oxide are regarded as promising candidates due to their large binding energy and long lifetime. High particle densities may be achieved by entrapment in a stress induced potential. We consider a multicomponent 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 (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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
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.
Pulsed-laser excitation of naturally grown crystals of Cu2{\mathrm{Cu}}_{2}Cu2​O produces a dense gas of excitons, which exhibits Bose-Einstein quantum statistics. Both orthoexcitons and paraexcitons, split by a 12-meV electron-hole exchange energy, are formed. At high excitation levels, the time-resolved luminescence of orthoexcitons yields a density-temperature relation that follows the phase boundary for Bose-Einstein condensation, n=CT3/2{\mathit{CT}}^{3/2}CT3/2, but no striking evidence for a condensed fraction is observed. We have now measured the time-resolved spectrum of the lower-lying paraexcitons whose luminescence is 1500 times weaker than the orthoexciton luminescence. At intermediate power levels, the paraexciton distribution is more degenerate than the orthoexcitons. The relative intensities of the two species indicate that at high excitation levels the paraexciton density exceeds the critical density for condensation. At these high densities the paraexciton spectrum develops a structure that cannot be explained in terms of the thermalized Bose-Einstein distribution. Time-resolved spatial measurements of the luminescence indicate a rapid nondiffusive expansion of the gas at supersonic velocities that approach the expected ballistic velocities of the excitons. The rapid transport and the concurrent changes in the spectral distribution of paraexcitons may be the first observation of excitonic Bose-Einstein condensation and superfluidity.
The case of excitons as candidates for Bose–Einstein condensation is discussed, and experimental results in CuCl and Cu 2 O are presented. In CuCl, spectral analysis of the luminescence from biexcitons as a function of their density reveals a gradual evolution from classical statistics towards a quantum degenerate regime. The appearance of a sharp emission line below a critical temperature and above a critical density is attributed to the presence of a laser-induced Bose–Einstein condensate of excitonic molecules. This interpretation is supported by pump-probe experiments which show that additional particles injected in the presence of a biexciton condensate are drawn into it. In Cu 2 O, free exciton luminescence spectral analysis of ortho- and paraexcitons reveals a gradual evolution from a classical to a Bose quantum degenerate regime with increasing particle densities. Orthoexciton densities close to the critical density for condensation are obtained at high incoherent excitation. Under similar pumping, paraexciton densities exceeding the critical value are inferred from luminescence intensity ratios. Anomalous transport properties of paraexcitons, such as ballistic propagation over macroscopic distances and formation of soliton-like excitonic packets are discussed as evidence for excitonic superfluidity. Introduction Excitons The lowest electronically excited state of a non-metallic crystal corresponds to the promotion of one electron from the top of the highest fully occupied valence band to the bottom of the next empty conduction band. A correct evaluation of the required energy must include the Coulomb correlation between the promoted electron and all other electrons left behind in the valence band.
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.