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physica status solidi (b)

Radiative Coupling in Single Quantum Wells and Bragg Structures

Dirk Ammerlahn, J. Kühl, Bernd Grote, S. W. Koch, G. Khitrova, H. M. Gibbs, R. Hey, Klaus Ploog

Published Sep 1, 2000• 2 citations
Publisher

Abstract

Time-integrated four-wave mixing experiments reveal strong influence of the cladding layer thickness d1, its refractive index and the reflectivity of the sample–air interface on the radiative dephasing time Trad of excitons in single quantum wells and multiple quantum well structures. A cladding layer thickness of λ/2 and λ/4 decreases and increases, respectively, Trad. Furthermore, 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. All findings agree fairly well with solutions of the semiconductor Maxwell-Bloch equations.

DOI
10.1002/1521-3951(200009)221:1<101::aid-pssb101>3.0.co;2-t

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Time-integrated four-wave mixing experiments reveal strong influence of the cladding layer thickness d1, its refractive index and the reflectivity of the sample–air interface on the radiative dephasing time Trad of excitons in single quantum wells and multiple quantum well structures. A cladding layer thickness of λ/2 and λ/4 decreases and increases, respectively, Trad. Furthermore, 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. All findings agree fairly well with solutions of the semiconductor Maxwell-Bloch equations.
Due to the large mismatch in the refractive index of semiconductor material and air, time-integrated and spectrally resolved four-wave mixing experiments reveal strong influence of the cladding layer thickness, its refractive index, and the reflectivity of the sample-air interface on the radiative dephasing time of excitons in single quantum wells and multiple quantum well structures. A cladding layer thickness of \ensuremath{\lambda}/2 and \ensuremath{\lambda}/4 enhances and decreases, respectively, the radiative contribution to the exciton linewidth and causes radiative shifts to higher and lower energies, respectively. All our experiments are well described by solutions of the semiconductor Maxwell-Bloch equations.
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.
The theoretically predicted rapid superradiant decay of coherent 2D excitons on a time scale of approximately 10 ps [1] is expected to be strongly enhanced in multiple QW (MQW) Bragg structures consisting of N identical QWs separated by (Ga,Al)As barriers the thickness of which was adjusted so that the QWs had a distance d equal to one half of the heavy-hole exciton resonance wavelength λ in the medium [2]. This enhancement originates from efficient radiative coupling of excitons excited in different wells via the exchange of transverse photons. Recently we have published [3] degenerate-four-wave-mixing experiments with fs optical pulses on GaAs QW Bragg structures which demonstrate that the radiative lifetime in high-quality GaAs single QWs (SQW) is approximately 5 ps and decreases to less than 2 ps in Bragg samples with N=10. These studies revealed that radiative recombination provides the dominant contribution to the homogenous linewidth of the 2D exciton in high-quality samples and exceeds nonradiative contributions caused by scattering with sample imperfections in contrast to previous assumptions.
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.
The influence of radiative coupling on the four-wave-mixing signals of multiple-quantum-well structures is investigated theoretically for excitation at the excitonic resonance. It is shown that amplitude and shape of the FWM signals depend strongly on the number of quantum wells N in the sample and on the periodicity of the structure. For a fixed delay time τ12, the signal amplitude of a Bragg structure increases quadratically with N due to constructive interference as long as the radiative decay rate Nγrad is small compared to the inverse delay time τ—112. For large N, if the enhanced radiative decay rate exceeds the inverse delay time, superradiant emission leads to a decrease of the observed signals with increasing N. The signals of anti-Bragg structures with an odd number of quantum wells decrease with increasing N due to destructive interference effects whereas anti-Bragg structures with an even number of quantum wells behave similarly to Bragg structures.
Time-integrated and spectrally resolved degenerate-four-wave mixing experiments at liquid helium temperature on the heavy- hole exciton resonance of a wedged (In,Ga)As/GaAs quantum well Bragg structure reveal a strong dependence of the dynamic and amplitude of the coherent nonlinear optical response in dependence on sample position. In the vicinity of the Bragg resonance the signal amplitude depends on both the rapid dephasing due to enhanced superradiant decay of the excitons and on the constructive interference of the signal amplitude in the backward Bragg reflection direction. We find that even in the presence of moderate inhomogeneous broadening of the excitonic resonance the superradiant decay dominates the excitonic nonlinearity at Bragg resonance. Our experimental results can be fairly well described by solutions based on the semiconductor Maxwell-Bloch equations taking disorder into account.