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International Journal of Modern Physics B

SPATIALLY DEPENDENT AMPLIFICATION OF AN EXCITONIC BOSE-EINSTEIN CONDENSATE IN Cu 2 O

Emery Fortin, Mathieu Massé

Published Dec 10, 2001• 2 citations
Publisher

Abstract

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.

DOI
10.1142/s021797920100824x

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arXiv:0907.3612•Journal of Experimental and Theoretical Physics Letters•Sep 1, 2009•16 citations
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.
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.
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.
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).
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.
Correlations of the luminescence intensity (the second-order correlation function g (2)(τ)), where τ is the delay time between the photons detected in pairs) under the conditions of the Bose-Einstein condensation (BEC) of dipolar excitons has been studied in a temperature range of 0.45–4.2 K. Photoexcited dipolar excitons have been accumulated in a lateral trap in a GaAs/AlGaAs Schottky diode with a 25-nm wide single quantum well with an electric bias applied across the heterolayers. Two-photon correlations have been measured with the use of a two-beam intensity interferometer with a time resolution of }~0.4 ns according to the well-known classical Hanbury-Brown-Twiss scheme. The photon bunching has been observed at the onset of Bose-Einstein condensation manifested by the appearance of a narrow exciton condensate line in the luminescence spectrum at an increase in the optical pumping (the line width near the threshold is ≲200 μeV). At the same time, the two-photon correlation function itself obeys the super-Poisson distribution, g (2)(τ) > 1, at time scale τc ≲ 1 ns of the system coherence. The photon bunching is absent at a pumping level substantially below the condensation threshold. The effect of bunching also decreases at pumping significantly above the threshold, when the narrow exciton condensate line starts to dominate in the luminescence spectra, and finally disappears with the further increase in the optical excitation. In this region, the distribution of pair photon correlations is a Poisson distribution manifesting the united quantum coherent state of the exciton condensate. Under the same conditions, the first-order spatial correlation function g (1)(r) determined from the interference pattern of the luminescence signals from the spatially separated parts of the condensate at constant pumping remains noticeable at distances of no less than 4 μm. The discovered effect of photon bunching is very sensitive to temperature and decreases by several times with a temperature increase in the range of 0.45–4.2 K. Assuming that the luminescence of the dipolar excitons directly reflects the coherence properties of the gas of interacting excitons, the discovered photon bunching at the onset of condensation, where the fluctuations of the exciton density and, consequently, of the luminescence intensity are most significant, indicates a phase transition in the interacting Bose gas of excitons, which is an independent way of detecting the Bose-Einstein condensation of excitons.