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Physical review. B, Condensed matter

Wannier exciton superradiance in a quantum-well microcavity

Gunnar G. Bjork, Stanley Pau, Joseph M. Jacobson, Y. Yamamoto

Published Dec 15, 1994• 63 citations
Publisher

Abstract

Excitonic superradiance has been predicted to induce a rapid decay rate of coherently excited excitons in thin quantum wells and microspheres. In this paper we revisit this problem and derive the enhancement factor of the radiative decay due to superradiant effects. In a GaAs quantum well, the excitonic superradiant radiative decay can be roughly 320 times faster than the decay of a free electron-hole pair. The exciton decay rate depends strongly on the lateral size of the wave function when the size is smaller than the inverse of the wave vector of the emitted light. In a GaAs quantum well this corresponds to a distance of \ensuremath{\approxeq}365 \AA{}. Therefore, it is predicted that localization and elastic phonon scattering may lead to decay rates substantially smaller than that predicted for an ideal quantum well. It is also shown that if the quantum well is placed inside a microcavity, the decay rate can be enhanced even further since the cavity modifies the available density of radiation states in a way that matches the superradiant emission. It is predicted that in a matched dielectric cavity the decay rate can be enhanced by an additional factor of 100, but that inhomogeneous broadening may in practice limit the possible enhancement.

DOI
10.1103/physrevb.50.17336

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Excitonic superradiance has been predicted to induce a rapid decay rate of coherently excited excitons in thin quantum wells and microspheres. In this paper we revisit this problem and derive the enhancement factor of the radiative decay due to superradiant effects. In a GaAs quantum well, the excitonic superradiant radiative decay can be roughly 320 times faster than the decay of a free electron-hole pair. The exciton decay rate depends strongly on the lateral size of the wave function when the size is smaller than the inverse of the wave vector of the emitted light. In a GaAs quantum well this corresponds to a distance of \ensuremath{\approxeq}365 \AA{}. Therefore, it is predicted that localization and elastic phonon scattering may lead to decay rates substantially smaller than that predicted for an ideal quantum well. It is also shown that if the quantum well is placed inside a microcavity, the decay rate can be enhanced even further since the cavity modifies the available density of radiation states in a way that matches the superradiant emission. It is predicted that in a matched dielectric cavity the decay rate can be enhanced by an additional factor of 100, but that inhomogeneous broadening may in practice limit the possible enhancement.
Rapid superradiant decay of coherently excited excitons in thin quantum wells (QWs) on a time scale of approximately 10 ps has been theoretically predicted by several groups [1], however, the experimental observation of this ultrafast radiative recombination is still the subject of controversial discussions. A recent theoretical paper [2] concludes, that this radiative decay rate should be strongly enhanced in multiple QW (MQW) Bragg structures due to radiative coupling of excitons excited in different wells via the exchange of transverse photons.
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Time- and spectrally resolved reflectivity measurements on multiple-quantum-well structures excited by ultrashort laser pulses are presented. In Bragg structures, where the interwell distance amounts to half the optical wavelength at the exciton resonance, superradiant coupling of the polarization dynamics within different quantum wells leads to an enhancement of the reflectivity strength and linewidth. We show that the superradiance is not limited to the heavy-hole exciton but can be observed even on excited and light-hole exciton states as well as on correlated electron-hole pair states. These coupling effects grow with the number of quantum wells. For our samples containing 60 and 30 quantum wells, pronounced superradiant enhanced reflectivity is present even at high excitation intensities and high temperatures, showing the insensitivity of radiative coupling with respect to incoherent scattering processes. Our findings are in good agreement with solutions of the semiconductor Maxwell-Bloch equations.
Linear time-resolved reflection on the heavy-hole exciton transition of high-quality multiple GaAs quantum-well Bragg samples reveals enhanced radiative emission and accelerated decay of the coherent optical polarization due to radiative interwell coupling. It is shown that this superradiant mode gradually vanishes with increasing excitation intensity. Microscopic calculations attribute this decoupling to the carrier-carrier Coulomb interaction in the individual quantum wells leading to excitation-induced dephasing. The intricate density dependence is discussed comparing computed results for the excitation-dependent decay in single quantum wells and multiple-quantum-well Bragg structures.
Quantum-well exciton superradiance and exciton cavity polarization formation both require a substantial spatial coherence area in order to become the dominant exciton field interaction. In both interaction processes the quantum-well (in-plane) momentum is conserved. Momentum scattering, which is due, e.g., to interaction with a phonon reservoir, quickly localizes an initially delocalized exciton and randomizes the excitation momentum. We take a close look at how momentum scattering influences measurements of excitonic superradiance and of exciton cavity polariton splitting. An important conclusion is that, in general, measurements of the emitted light do not correspond to the evolution of the system as a whole. Therefore, e.g., the measured decay rates do not correspond to the true decay rate of the system.
We want to make the best use of the mesoscopic or macroscopic transition dipolemornent of excitons by controling the size and dimension of the materials. First, the semiconductor microcrystallites embedded in insulators or glasses are shown to have the mesoscopic transition dipolemoment of excitons1 . As a result, the exciton in CuC1 microcrystallite with the radius 80 A superradiatively decays in 100 pico-second2. Futhermore, the exciton-exciton interaction and the decay and relaxation of the exciton work effectively in deviating the excitons in the microcrystallite from ideal bosons and this system shows the large third-order optical susceptibility"3 of an order of iO esu when we assume the 0.1% packing of the CuC1 microcrystallites. These predictions have been confirmed expriment ally4'5. Second, the two-dimensional excitons in quantum wells can superradiatively decay in the direction perpendicular to the surfaces2 . This brings about the quick response and the deviation of the excitons from ideal bosons at the same time. The latter effect as well as the two-dimensional macroscopic enhancement of the exction transition dipolemoment enhance the third-order optical susceptibility3. Both the superradiative decay rate and increase as does the coherent length, which is inversely proportional to the square root of the exciton line width6.