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arXiv:cond-mat/0408605 · Physical Review Letters

Study of Orthoexciton-to-Paraexciton Conversion in Cu2O by Excitonic Lyman Spectroscopy

Motoyoshi Kubouchi, Kosuke Yoshioka, Ryo Shimano, A. Mysyrowicz, Makoto Kuwata‐Gonokami

Published Jan 6, 2005• 66 citations
arXivHTMLPDF

Abstract

Using time-resolved 1s-2p excitonic Lyman spectroscopy, we study the orthoexciton-to-paraexciton transfer, following the creation of a high density population of ultracold 1s orthoexcitons by resonant two-photon excitation with femtosecond pulses. An observed fast exciton-density dependent conversion rate is attributed to spin exchange between pairs of orthoexcitons. Implication of these results on the feasibility of Bose-Einstein condensation of paraexcitons in Cu(2)O is discussed.

DOI
10.1103/physrevlett.94.016403

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•Sep 24, 2004•4 citations
Using time-resolved 1s-2p excitonic Lyman spectroscopy, we study the orthoexciton-to-paraexciton transfer, following the creation of a high density population of ultracold 1s orthoexcitons by resonant two-photon excitation with femtosecond pulses. An observed fast exciton-density dependent conversion rate is attributed to spin exchange between pairs of orthoexcitons. Implication of these results on the feasibility of Bose-Einstein condensation of paraexcitons in Cu(2)O is discussed.
Supercooled orthoexcitons are generated in Cu2O{\mathrm{Cu}}_{2}\mathrm{O}Cu2​O by resonant two-photon excitation with a femtosecond laser pulse. The excitonic Lyman series is systematically analyzed by time-resolved induced-absorption measurements. The decay time of orthoexcitons as well as the buildup and decay times of paraexcitons are found to be dependent on their respective densities. With these results, the two-body excitonic spin-exchange and the exciton dissociation processes are investigated. The collision-induced spin-exchange process is found to dominate in the early stage of photoexcitation. The conditions required to obtain a Bose-Einstein condensate with paraexcitons are discussed.
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.
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.
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.
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.
There is a 40-year long history in the search for Bose-Einstein condensation (BEC) of excitons in semiconductors. This thesis presents research directed toward this goal in bulk crystal Cu2O in three dimensions and in GaAs-based coupled quantum wells (CQW) in two dimensions.The Auger recombination process in Cu2O plays a major role in limiting the density of the excitons. We find that the rate for this process increases with applied stress and lattice temperature. We create paraexcitons in Cu2O through a resonant two-photon excitation in a harmonic potential trap with the Auger recombination process as small as possible (at low temperature and low stress), and find that the exciton creation efficiency in the resonant two-photon excitation is greater for one-beam excitation than for two colliding pulses, but the colliding pulse method may be useful for direct creation of a condensate in the ground state. The paraexciton density in this work is about thirty times less than the required density for BEC of paraexcitons. One promising direction for BEC of excitons in Cu2O is that with higher laser power from stronger IR laser sources, or at lower temperature, the critical density can be approached under one-beam two-photon excitation resonant with the paraexciton state.In two dimensions, the CQW structure has been modified with four design strategies: highest possible barriers, introducing into the barriers a superlattice of 60 angstrom GaAs wells, p-i-n doping, and wider quantum wells, which provides indirect excitons low disorder and high mobility. With a cold near-resonant excitation, we conclude that the excitons act as a free gas, travelling distances of hundreds of microns. We also present observations of a narrow beam of emitted light, when the indirect excitons are confined in a two-dimensional harmonic potential trap, in a way quite similar to the first observations of BEC in alkali atoms. A beam-like emission has been suggested as a telltale for BEC of excitons. This opens the door to a whole range of investigations, including attempts to observe coherence of the emitted light, proof of superfludity of the excitons, and other fascinating effects.