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Physical Review B

Generation of ultracold paraexcitons in cuprous oxide: A path toward a stable Bose-Einstein condensate

Kosuke Yoshioka, Yusuke Morita, Kenta Fukuoka, Makoto Kuwata‐Gonokami

Published Jul 23, 2013• 30 citations
Publisher

Abstract

Cooling of a gas of trapped paraexcitons in Cu${}_{2}$O to 100 mK, close to the lattice temperature, is reported. We show that the activation of a transverse acoustic scattering mechanism by the applied stress is responsible for the production of ultracold excitons. This low temperature is indispensable to achieving a stable and pure Bose-Einstein condensate of three-dimensional excitons in a strongly inelastic environment.

DOI
10.1103/physrevb.88.041201

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In this paper we present a theoretical model to describe the dynamics of paraexcitons in cuprous oxide at ultralow temperatures inside potential traps. A possible condensate is described by a generalized Gross-Pitaevskii equation. The noncondensed excitons evolve under a set of hydrodynamic equations, which were derived from a quantum Boltzmann equation. The model takes into account the finite lifetime of the excitons, the pump laser, the Auger-like two-body decay, as well as exciton-exciton and exciton-phonon scattering. The numerical results show the strong influence of the Auger effect on exciton temperatures and densities not only at high pump powers but also at ultralow temperatures. Furthermore, the excitons do not cool down to very low bath temperatures $({T}_{\mathrm{B}}\ensuremath{\ll}0.5\phantom{\rule{0.28em}{0ex}}\mathrm{K})$ under continuous wave excitation. We also compare the results of the theoretical model with experimental data.

Physical Review B•Feb 26, 2015•6 citations
Cooling of a gas of trapped paraexcitons in Cu2{}_{2}2​O to 100 mK, close to the lattice temperature, is reported. We show that the activation of a transverse acoustic scattering mechanism by the applied stress is responsible for the production of ultracold excitons. This low temperature is indispensable to achieving a stable and pure Bose-Einstein condensate of three-dimensional excitons in a strongly inelastic environment.
Biexciton as a Feshbach resonance and Bose-Einstein condensation of paraexcitons in Cu2_{2}2​O
Paraexcitons, the lowest energy exciton states in Cu2_{2}2​O, have been considered a good system for realizing exciton Bose-Einstein condensation (BEC). The fact that their BEC has not been attained so far is attributed to a collision-induced loss, whose nature remains unclear. To understand collisional properties of cold paraexcitons governing their BEC, we perform here a microscopic consideration of the s-wave paraexciton-paraexciton scattering. We show its two-channel character with incoming paraexcitons coupled to a biexciton, which is a Feshbach resonance producing a paraexciton loss and a diminution of their background scattering length. The former elucidates the mechanism of the long-observed paraexciton loss, which turns out to be inefficient at temperatures near one Kelvin and below, whereas the latter makes the paraexciton scattering length in strain-induced traps negative under stress exceeding a critical value. Our rough estimates give this value of order of one kilobar, hence already moderate stress creates a serious obstacle to attaining a stable paraexciton BEC. Thus our results indicate that BEC of trapped paraexcitons might be achieved at a subkelvin temperature, but only under low stress.
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.
Paraexcitons, the lowest energy exciton states in Cu 2 O, have been considered a good system for realizing exciton Bose–Einstein condensation (BEC). The fact that their BEC has not been attained so far is attributed to a collision-induced loss, whose nature remains unclear. To understand collisional properties of cold paraexcitons governing their BEC, we perform a theoretical analysis of the s-wave paraexciton–paraexciton scattering at low temperatures. We show the two-channel character of the scattering, where incoming paraexcitons are coupled to a biexciton in a closed channel. Being embedded in the paraexciton scattering continuum, the biexciton is a Feshbach resonance giving rise to a paraexciton loss and a diminution of their background scattering length. In strain-induced traps, the biexciton effects generally increase with stress. Thus the scattering length a of trapped paraexcitons decreases monotonically with stress turning its sign as stress goes beyond a critical value. In the stress range with a < 0, the paraexciton loss increases with stress, whereas in that with a > 0 the loss is almost stress-independent. Importantly, that in the latter case the loss rate can be reduced to such small values that it has no effects on BEC by lowering temperatures to near one Kelvin and below. Our approximate calculations give the critical value of stress in the range just above one kilobar; thus BEC of strain-confined paraexcitons might be attained under low stress at a subkelvin temperature.
In this paper we present a theoretical model to describe the dynamics of paraexcitons in cuprous oxide at ultralow temperatures inside potential traps. A possible condensate is described by a generalized Gross-Pitaevskii equation. The noncondensed excitons evolve under a set of hydrodynamic equations, which were derived from a quantum Boltzmann equation. The model takes into account the finite lifetime of the excitons, the pump laser, the Auger-like two-body decay, as well as exciton-exciton and exciton-phonon scattering. The numerical results show the strong influence of the Auger effect on exciton temperatures and densities not only at high pump powers but also at ultralow temperatures. Furthermore, the excitons do not cool down to very low bath temperatures $({T}_{\mathrm{B}}\ensuremath{\ll}0.5\phantom{\rule{0.28em}{0ex}}\mathrm{K})$ under continuous wave excitation. We also compare the results of the theoretical model with experimental data.