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EXCITONS AT HIGH DENSITY IN CUPROUS OXIDE AND COUPLED QUANTUM WELLS

Yingmei Liu

Published Sep 24, 2004• 4 citations
OpenAlex

Abstract

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.

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Experiments on Bose-Einstein condensation (BEC) of excitons in the semiconductor Cu2O started over 30 years ago, as one of the first serious attempts at exciton BEC. Early claims were based on spectroscopic signatures and transport data which have since been reinterpreted, in large part because the Auger recombination process for excitons was not well understood. Understanding of the Auger process has advanced, and recent experiments have made significant progress toward exciton BEC. We review the history of experiments on exciton BEC in Cu2O, the Auger recombination process, and the prospects for observing exciton BEC in this system in the near future.

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Summary form only given. In the dilute limit excitons behave as weakly interacting Bose particles and are expected to undergo the Bose-Einstein condensation (BEC). Because the exciton mass is very small at experimentally accessible exciton densities the critical temperature for exciton BEC should reach several Kelvins, i.e., about six orders of magnitude higher than the T/sub c/ for atom BEC. To create degenerate Bose-gas of excitons we propose quasi-2D gas of indirect excitons in coupled quantum wells (CQWs) which have two primary advantages for realizing a quantum degenerate exciton gas and, ultimately, the BEC-like phase transition: (i) the long lifetime of indirect excitons and (ii) the short exciton cooling time.

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Mathieu Massé

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).

•Jan 1, 2001•0 citations
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.
Experiments on Bose-Einstein condensation (BEC) of excitons in the semiconductor Cu2O started over 30 years ago, as one of the first serious attempts at exciton BEC. Early claims were based on spectroscopic signatures and transport data which have since been reinterpreted, in large part because the Auger recombination process for excitons was not well understood. Understanding of the Auger process has advanced, and recent experiments have made significant progress toward exciton BEC. We review the history of experiments on exciton BEC in Cu2O, the Auger recombination process, and the prospects for observing exciton BEC in this system in the near future.
Summary form only given. In the dilute limit excitons behave as weakly interacting Bose particles and are expected to undergo the Bose-Einstein condensation (BEC). Because the exciton mass is very small at experimentally accessible exciton densities the critical temperature for exciton BEC should reach several Kelvins, i.e., about six orders of magnitude higher than the T/sub c/ for atom BEC. To create degenerate Bose-gas of excitons we propose quasi-2D gas of indirect excitons in coupled quantum wells (CQWs) which have two primary advantages for realizing a quantum degenerate exciton gas and, ultimately, the BEC-like phase transition: (i) the long lifetime of indirect excitons and (ii) the short exciton cooling time.
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.
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.
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.
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).