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Investigation of Bose-Einstein condensation effects with excitons in Cu₂2O.

Mathieu Massé

Published Jan 1, 2001• 0 citations
Publisher

Abstract

Experimental observations are presented on Bose-Einstein condensation of excitons in Cu2O at low temperatures. These observations deal with traveling exciton packets in a high quality natural crystal. The properties of the exciton packets are examined using two different excitation depths of formation of the excitons (affecting the size of initial exciton cloud). The properties of the condensate include for example: the amplitude, the velocity of the exciton packet, the critical conditions for condensation and phase diagram. Interference effects of two coherent packets are also studied using these different initial excitation depths. Stimulated emission of particles into the exciton packet by injection of thermal excitons in the crystal volume is investigated in greater detail as well as the attenuation of the lateral laser beam (used to create the thermal excitons that trigger the amplification phenomenon).

DOI
10.20381/ruor-16254

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International Journal of Modern Physics B•Dec 10, 2001•2 citations
Experimental observations are presented on Bose-Einstein condensation of excitons in Cu2O at low temperatures. These observations deal with traveling exciton packets in a high quality natural crystal. The properties of the exciton packets are examined using two different excitation depths of formation of the excitons (affecting the size of initial exciton cloud). The properties of the condensate include for example: the amplitude, the velocity of the exciton packet, the critical conditions for condensation and phase diagram. Interference effects of two coherent packets are also studied using these different initial excitation depths. Stimulated emission of particles into the exciton packet by injection of thermal excitons in the crystal volume is investigated in greater detail as well as the attenuation of the lateral laser beam (used to create the thermal excitons that trigger the amplification phenomenon).
Experimental results are presented on excitonic effects related to the Bose-Einstein condensation (BEC) of excitons in Cu2O. Such effects include resonant light polarization dependent absorption, exciton creation and diffusion by absorption of scattered light, and resonant high density exciton packet induced absorption. These results are then utilized, in conjunction with similar results on excitonic BEC, to develop a plausible model for condensate amplification. Condensates are initially created at T = 1.8K with high intensity ND:YAG pulses (lambda = 532 nm) and then stimulated by a secondary source tuned around the 1S orthoexciton resonance (lambda = 609.51 nm); the latter induces the observed condensate amplification. By careful analysis of the various interactions between the secondary light source, the crystal, and the condensate itself, an improved understanding of how the secondary pulse excitations interact with the passage of a high density exciton packet is obtained.
Experiments investigating the process of Bose-Einstein condensation of excitons in Cu2O will be reviewed. The exciton flux reaching the back surface of mm thick single crystals is investigated following creation of a high density of excitons close to the front surface with a pulsed laser. An anomalous propagation regime is observed at. sufficiently low crystal temperatures and sufficiently high particle densities, in the form of a ballistic packet progressing at a velocity close to the crystal sound velocity. The ballistic packet is attributed to an excitonic superfluid, the result of a Bose-Einstein Condensation (BEC). Conditions for appearance of the ballistic excitonic transport are found to be in good agreement with the predictions of the weakly interacting Bose gas model.
Experimental results acquired with various methods used to optically probe an excitonic Bose-Einstein condensate are presented. The condensate is initially created by a high-intensity pulsed laser illumination (lambda = 532 nm) incident on a high-quality natural single crystal of Cu2O (at T = 1.8 K), having (100) symmetry. The travelling condensate is laterally probed by a laser pulse tuned at the 1S orthoexciton resonance (lambda = 609.51 nm), where significant condensate amplification is observed. Correspondingly, the resonant probing beam is additionally attenuated upon being transmitted through the excitonic packet. In an attempt to measure the condensate's lateral and longitudinal dimensions, the additional attenuation (NDA) is determined at various probing beam positions relative to the perpendicularly propagating packet. A three-dimensional representation of the exciton packet was constructed with spatially dependent NDA measurements. Highly detailed continuous spectra of the 1S line were taken with the use of a tunable dye laser, permitting the observation of never before seen features in the 1S line. The wavelength dependance of both the condensate amplification and the lateral pulse's additional attenuation were studied using this technique. The onset of a secondary exciton packet observed in various excitation geometries, further contributed to the amplification model proposed in previous work. Moreover, a strong correlation between electrical and all-optical measurements was found, providing reassurance on the validity of past interpretations based on electrical measurements.
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.
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.
Experimental results are presented on the spatial dependence of amplification of a travelling Bose-Einstein condensate of excitons in Cu 2 O . The exciton condensate is created at T = 1.8 K by high intensity pulsed laser illumination (λ = 532 nm). Amplification of the moving condensate is triggered by the local, time-delayed injection of thermal excitons created by a lateral laser pulse tuned at the 1S orthoexciton resonance (λ = 609.48 nm), perpendicular to the path of the condensate. The amplification factor depends on the trigger time of the lateral laser pulse and is related to the stimulated scattering into the condensate of non-condensed excitons present in the crystal volume. A spatial correlation is also observed between the amplification factor and the optical attenuation of the lateral laser radiation induced by the passing condensate.