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IEEE Journal of Quantum Electronics

Possibility of coherent light emission from Bose condensed states in quantum-well systems

Tadashi Fukuzawa, T. Kenneth Gustafson, 栄三郎 山田

Published May 1, 1990• 5 citations
Publisher

Abstract

The possibility of coherent light emission in systems with a pairing of electrons and holes in a double quantum well spatially separated by a thin barrier (separated electron hole pairs (SEHPs)) is predicted. Bose condensation of excitons formed from SEHPs in GaAs/Al/sub x/Ga/sub (1-x)/As double quantum wells of approximately 10 AA size are possible at relatively high temperatures. Coherent recombination emission due to the transfer of coherence from the Bose-condensed SEHPs to the photon field is expected.>

DOI
10.1109/3.55516

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Journal of Experimental and Theoretical Physics Letters•Sep 1, 2001•7 citations
The possibility of coherent light emission in systems with a pairing of electrons and holes in a double quantum well spatially separated by a thin barrier (separated electron hole pairs (SEHPs)) is predicted. Bose condensation of excitons formed from SEHPs in GaAs/Al/sub x/Ga/sub (1-x)/As double quantum wells of approximately 10 AA size are possible at relatively high temperatures. Coherent recombination emission due to the transfer of coherence from the Bose-condensed SEHPs to the photon field is expected.>
A theoretical study is reported of stimulated light scattering, including wave-vector reversal and anomalous transmission, by a coherent phase in electron-hole (e-h) systems of low and high charge-carrier density. For these two cases the coherent phase is taken to be a Bose-Einstein condensate of excitons or a BCS-like state of e-h pairs, respectively. The scattering mechanism is laser-induced coherent recombination of two excitons or two coherent e-h pairs, respectively. The e-h system is assumed to exist within a GaAs/AlGaAs double quantum well or bulk GaAs. The emission rate of two photons with antiparallel momenta is estimated. Multiphoton emission due to multiexciton coherent recombination is covered. Methods for detecting the effects predicted are proposed.
ABSTRACT The new effect stimulated light backstattering and anomalous light transmission in Bose-condensed excitonsystem are considered. The effects are connected with photoinduced coherent recombination of two excitonsfrom the condensate with production of two photons with opposite momenta. The effect of two-exciton coherentrecombination leads also to the appearence of the second order coherence in exciton luminescence connectedwith squeezing between photon states with opposite momenta. Coherent 3- and 4-photon emission processesstimulted by respectively two and three laser beams are also considered.Keywords: nanostructure, quantum well, nanooptics, exciton, Bose condensationThe great progress has been made in the study of exciton Bose-condensation of exciton systems in quantumwells (QW) and Cu20 (see, e. g. [1—7] and references therein). However, the study of various ways which excitoncondensate should unambiguously reveal itself by its optical properties is still vital [3, 4].We analyze the coherent coupling of photons with opposite momenta, originating from coherent recombina-tion of two excitons from the condensate. We reveal that this process leads to new effect — stimulated lightbackscattering on exciton condensate. This effect can be viewed as a photoinduced coherent recombination oftwo condensate excitons with production of two photons with opposite momenta. We also consider analagouscoherent many-photon processes.Before we analyse the system of quasi-2D excitons in QW let us first consider the simpler case of 3D excitonsin Cu20. Direct recombination of electron and hole in Cu20 is a forbidden process and an exciton decays mainlywith production of a photon as well as of an optical phonon (Fig. 1 (a)). The process of two exciton recombination( Fig. 1(b)) has extra vertex of exciton—photon interaction and, therefore, is substantially weaker.
We consider many-photon coherent emission governed by coherent recombination of many excitons from Bose condensate. Momentum conservation makes photons simultaneously created in the coherent recombination of several excitons from the condensate have zero sum momentum. Many-photon correlations in the processes of simultaneous many-photon production (photons squeezing) could be detected by photon counting experiments with several detectors spatially arranged in an appropriate way, i.e., by Hanbury-Brown-Twiss-like experiments. We analyze the stimulated processes of N-exciton coherent recombination from the condensate resonantly induced by $N\ensuremath{-}1$ external laser beams with momenta ${\mathbf{k}}_{1},{\mathbf{k}}_{2},\dots{},{\mathbf{k}}_{N\ensuremath{-}1}.$ Such stimulated processes must reveal themselves through a unidirectional beam with recoil momentum ${\mathbf{k}}_{N}=\ensuremath{-}{\ensuremath{\sum}}_{i=1}^{N\ensuremath{-}1}{\mathbf{k}}_{i}.$ In particular, two-exciton coherent recombination from the condensate stimulated by a laser beam effectively acts in a three-dimensional (3D) exciton system as a laser beam backscattering from exciton Bose condensate. For 2D coherent exciton systems besides the backscattering stimulated two-exciton coherent recombination has an additional manifestation---anomalous beam transmission with the only change in the sign of in-plane momentum component of inducing laser beam. We estimate the rates of many-photon coherent emission from a 3D system of Cu2O{\mathrm{Cu}}_{2}\mathrm{O}Cu2​O excitons and from a 2D exciton system in GaAs/AlGaAs coupled quantum wells. The estimations show that these nonlinear optical effects are experimentally observable.
We report on the transfer of coherence from a quantum-well electron-hole condensate to the light it emits. As a function of density, the coherence of the electron-hole-pair system evolves from being full for the low-density Bose-Einstein condensate to a chaotic behavior for a high-density BCS-like state. This degree of coherence is transferred to the light emitted in a damped oscillatory way in the ultrafast regime. Additionally, the photon field exhibits squeezing properties during the transfer time. Our results suggest a new type of ultrafast experiments for detecting electron-hole-pair condensation.
A new effect—light backscattering from exciton Bose-condensate—is considered. This effect is connected with the photoinduced coherent recombination of two excitons in the condensate with the production of two photons with opposite momenta. The effect of two-exciton coherent recombination leads also to the appearance of the second-order coherence in exciton luminescence connected with squeezing between photon states with opposite momenta. The estimations given for Cu 2 O and GaAs excitons show that the effect of stimulated light backscattering can be detected experimentally. Moreover, in the system of 2D excitons in coupled quantum wells, the effect of stimulated anomalous light transmission must also take place. Anologous effects can also take place in systems of Bose-condensed atoms in excited (but metastable) states.