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Phase separation of multicomponent excitonic Bose-Einstein condensates

S. Sobkowiak, D. Semkat, H. Stolz, Th. Koch, Holger Fehske

Published Jan 1, 2010• 2 citations
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Abstract

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

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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)

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Cover Picture: Phys. Status Solidi C 4/2011

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.

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Physical review. B, Condensed matter•Jun 1, 1990•122 citations
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
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)
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.
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.
We present a numerical study of a trapped binary Bose-condensed gas by solving the corresponding Hartree-Fock equations. The density profile of the binary Bose gas is solved with a harmonic trapping potential as a function of temperature in two and three dimensions. We find a symmetry breaking in the two-dimensional case where the two condensates separate. We also present a phase diagram in the three-dimensional case of the different regions where the binary condensate becomes a single condensate and eventually an ordinary gas as a function of temperature and the interaction strength between the atoms.
We investigate phase separation of Bose-Einstein condensates (BECs) of two-component atoms and one-component molecules with a homonuclear Feshbach resonance. We develop a full model for dilute atomic and molecular gases including correlation of the Feshbach resonance and all kinds of interparticle interactions, and numerically calculate order parameters of the BECs in spherical harmonic oscillator traps at zero temperature with the Bogoliubov's classical field approximation. As a result, we find out that the Feshbach resonance can induce two types of phase separation. The actual phase structures and density profiles of the trapped gases are predicted in the whole parameter region, from the atom-dominant regime to the molecule-dominant regime. We focus on the role of the molecules in the phase separation. Especially in the atom-dominant regime, the role of the molecules is described through effective interactions derived from our model. Furthermore we show that a perturbative and semiclassical limit of our model reproduces the conventional atomic BEC (single-channel) model.
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.