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Physical review. B./Physical review. B

Exciton-light coupling in (In,Ga)As/GaAs quantum wells in a longitudinal magnetic field

Philipp S. Grigoryev, I. V. Ignatĭev, V. Davydov, Yu. P. Efimov, Sergei A. Eliseev, V. A. Lovtcius, Pavel Yu. Shapochkin, M. Bayer

Published Oct 3, 2017• 11 citations
Publisher

Abstract

We report on the observation of a significant increase of the radiative decay rates for exciton transitions in a wide (In,Ga)As/GaAs quantum well ($L=95$ nm) in magnetic fields up to 6 T applied along the growth axis of the heterostructure. The absolute values of the radiative decay rates are obtained from a quantitative analysis of resonant features in the experimentally measured reflectance spectra in the range of the optical transitions to the quantum-confined exciton states. High crystalline quality of the heterostructure allows us to observe the ground and several excited exciton transitions with the nonradiative broadening comparable to the radiative one. We employ a numerical procedure appropriate for the studied wide quantum well to model the increase of the radiative decay rate in magnetic field. The results of the modeling agree well with the experimental data.

DOI
10.1103/physrevb.96.155404

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We report on the observation of a significant increase of the radiative decay rates for exciton transitions in a wide (In,Ga)As/GaAs quantum well (L=95L=95L=95 nm) in magnetic fields up to 6 T applied along the growth axis of the heterostructure. The absolute values of the radiative decay rates are obtained from a quantitative analysis of resonant features in the experimentally measured reflectance spectra in the range of the optical transitions to the quantum-confined exciton states. High crystalline quality of the heterostructure allows us to observe the ground and several excited exciton transitions with the nonradiative broadening comparable to the radiative one. We employ a numerical procedure appropriate for the studied wide quantum well to model the increase of the radiative decay rate in magnetic field. The results of the modeling agree well with the experimental data.
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.
We calculate two-photon transition rates of exciton states in GaAs quantum wells for varying well widths. The exciton states are described in the effective-mass approximation and are obtained variationally assuming wave functions that are separable in the r coordinates. The two-photon transition rate is calculated taking explicitly into account the sum over all the intermediate states, using a variational procedure. We calculate transition rates of excitons of s symmetry as well as of p symmetry, which are allowed for polarization of the radiation beam along the growth axis and in the layer planes, respectively. From our calculations we find that transitions to s-type excitons have sufficiently large rates to be observable, whereas transitions to p-type excitons seem to have rates too small to be observable; these results are in agreement with experiment. The transition rate of s excitons increases significantly for decreasing well width, whereas the transition rate of p excitons is found to be almost independent of the well width. Moreover, our model allows us to calculate transition rates for photons of different energy. We have shown the resonant enhancement of the transition rate of s-type excitons when one of the photon energies approaches the energy of an intermediate state.
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.
The dynamics of biexciton radiative decay in semiconductor quantum wells is treated within the excitonic-molecule mode including super-radiance, exciton recoil, and nonzero photon momentum. For parameters describing GaAs/Alx{\mathrm{Al}}_{\mathit{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells, we find that the rate for the decay of the excitonic molecule (in the ground state of the relative motion between excitons) into an exciton and a photon is less than the decay rate characteristic of radiative free one-excitons.
We investigate a GaAs/(Ga,Al)As Fabry-P\'erot microcavity, into which (In,Ga)As quantum wells have been inserted. The cavity is wedge shaped, i.e., the detuning between the bare-exciton resonance and the bare optical cavity mode depends on the spatial position on the sample. Linear transmission spectra reveal a well-resolved Rabi splitting of 8 meV at resonance, an inhomogeneously broadened exciton transition of 4--5-meV width, and an 0.7-meV-wide Fabry-P\'erot mode. The time-resolved transmission exhibits deep beatings and a subpicosecond exponential decay: a behavior similar to that foreseen in the strong-coupling regime and in the absence of electronic disorder. Conversely, the four-wave mixing response appears weakly influenced by the cavity and not much different from what is expected for bare excitons. A photon echo, dephasing times as long as 50 ps, and only weak Rabi oscillations are observed. The experimentally observed features can be explained by a model based on the numerical solutions of the Maxwell-Bloch equations. This model confirms the dramatic influence structural disorder in the quantum wells has on the coherent nonlinear exciton-photon dynamics.
The optical response of radiatively coupled semiconductor multiple-quantum-well structures is investigated theoretically. It is shown that the transverse optical field leads to a coupling of exciton states within each well which causes a radiative decay and a mixing of excitonic resonances. Simultaneously, the field-induced long-ranged coupling between different wells leads to collective effects that are very sensitive to the detailed geometry of the structure. For a quantum-well spacing equal to an integer multiple of half the optical wavelength inside the medium, it is predicted that the collective effects cause a stimulated decay of electronic excitations that should be observable in either transmission or reflection geometry. On the other hand, in a quarter wavelength structure, the light-induced coupling causes an interwell energy transport and a splitting of the excitonic resonances, that should be observable as quantum beats in the time-resolved transmitted or reflected signal.