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Physical review. B, Condensed matter

Bose-Einstein statistics of orthoexcitons generated by two-photon resonant absorption in cuprous oxide

Toru Goto, Mengyan Shen, S. Koyama, Tomoyuki Yokouchi

Published Mar 15, 1997• 48 citations
Publisher

Abstract

Excitation by two-photon resonant absorption may be able to maintain the temperature of the orthoexcitonic system in ${\mathrm{Cu}}_{2}$O sufficiently low, resulting in an excitonic density high enough to allow us to study the quantum Bose-Einstein statistical properties of a nearly ideal Bose gas. The luminescence spectra show that the orthoexcitonic system consists of two parts. One follows the usual Bose-Einstein statistics with chemical potential \ensuremath{\mu}=0. The other is at an energy position corresponding to zero kinetic energy.

DOI
10.1103/physrevb.55.7609

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Phase separation of multicomponent excitonic Bose-Einstein condensates

S. Sobkowiak, D. Semkat, H. Stolz +2 more

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

•Jan 1, 2010•2 citations
Excitation by two-photon resonant absorption may be able to maintain the temperature of the orthoexcitonic system in Cu2{\mathrm{Cu}}_{2}Cu2​O sufficiently low, resulting in an excitonic density high enough to allow us to study the quantum Bose-Einstein statistical properties of a nearly ideal Bose gas. The luminescence spectra show that the orthoexcitonic system consists of two parts. One follows the usual Bose-Einstein statistics with chemical potential \ensuremath{\mu}=0. The other is at an energy position corresponding to zero kinetic energy.
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.
A comprehensive investigation of the optical properties of excitonic molecules in CuCl films is presented and discussed. The experimental work includes resonant two-photon absorption (TPA), observations of the resonantly excited biexciton emission, and optical pump-and-probe studies. The collision broadening of the TPA implies a collision rate \ensuremath{\sim}${10}^{\ensuremath{-}12}$ sec for the biexcitons, which is sufficiently rapid to establish a quasithermal equilibrium for the particles on a time scale that is short in comparison with the biexciton lifetime and the duration of the laser pump pulse. The biexciton luminescence line shapes obtained with resonant $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}=0$ two-photon excitation have been fitted using a Bose-Einstein thermal distribution of biexcitons. The chemical potential obtained from the fits goes to zero as the biexciton density is increased at a fixed lattice temperature or if the lattice temperature is decreased at fixed density. The sharp luminescence features that are observed at high densities and low temperatures with single-beam, two-photon excitation are interpreted as resulting from a Bose-Einstein---condensed state of the biexcitons at twice the wave vector of the laser pumping photons. Further evidence for a condensed state is obtained from optical-probe measurements in which a small number of probe biexcitons is injected into the sample, with and without the presence of a condensed state produced by an intense laser pump beam. The luminescence of these injected probe biexcitons is modified in the presence of the pump beam such that it exhibits the sharp features of the emission from the condensed state. Measurements of optical gain and stimulated emission in the presence of the pump beam show that the redistribution of the probe luminescence does not result from those processes, but must involve a preferential redistribution of the probe particles in momentum space via collisions. Such a redistribution is expected when additional particles are added to a condensed system of bosons.
In a first part, a brief review of some excitonic properties is presented, with the accent put on their relevance with respect to the possibility of Bose-Einstein condensation. In a second part, recent experimental evidence is described, which supports the idea that excitonic particles may form a highly quantum fluid. In Cu20, the analysis of the exciton decay spectrum shows a gradual evolution of the gas from a classical regime at low densities up to a strongly degenerate one at high densities, with a chemical potential µ ~ 0. In CuCl excitons are unstable against formation of molecules (biexcitons). It is possible to generate directly a high density gas of biexcitons with momentum K ~ 0 by giant two-photon absorption. At low excitation, the observed molecular emission is in agreement with Maxwell -Boltzmann statistics. At high densities, strong deviations occur. In particular, the appearance of a sharp emission line is attributed to the presence of a Bose-Einstein condensate of excitonic molecules.
Time-resolved spectral and spatial measurements of photoluminescence in Cu2{\mathrm{Cu}}_{2}Cu2​O at low temperatures suggest that the gas of paraexcitons undergoes Bose-Einstein condensation at high densities. As a result of the two-component nature of the gas (orthoexcitons and paraexcitons with different ground-state energies and spin multiplicities) and the nonequilibrium nature of photoproduced excitons, the condensation process is quite different from the simple ideal-gas case envisioned by Einstein.
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.
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