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Physical Review Letters

Direct Observation of Excitonic Rabi Oscillations in Semiconductors

Axel Schülzgen, Rolf H. Binder, Michael E. Donovan, Markus Lindberg, Kai Wundke, H. M. Gibbs, G. Khitrova, Nasser N. Peyghambarian

Published Mar 15, 1999• 189 citations
Publisher

Abstract

We observe multiple excitonic optical Rabi oscillations in a semiconductor quantum well. Up to eight oscillation periods of the heavy-hole exciton density on a subpicosecond time scale are observed. An approximate linear dependence of the oscillation frequency on the light field amplitude is established. The experiment is based on a two-color detection scheme which allows for the observation of the heavy-hole exciton density via transmission changes at the light-hole exciton. The observations are in good agreement with theoretical computations based on multiband semiconductor Bloch equations.

DOI
10.1103/physrevlett.82.2346

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Physical review. B, Condensed matter•Dec 15, 2000•27 citations
We observe multiple excitonic optical Rabi oscillations in a semiconductor quantum well. Up to eight oscillation periods of the heavy-hole exciton density on a subpicosecond time scale are observed. An approximate linear dependence of the oscillation frequency on the light field amplitude is established. The experiment is based on a two-color detection scheme which allows for the observation of the heavy-hole exciton density via transmission changes at the light-hole exciton. The observations are in good agreement with theoretical computations based on multiband semiconductor Bloch equations.
Data are presented which show eight excitonic density (Rabi) oscillations in an In0.1Ga0.9As/GaAs multiple quantum well at 5 K. Our time resolved, two-color pump-probe experimental technique for observing these oscillations is described. The quantum well sample geometry and linear spectrum are shown along with data characterizing the pump and probe pulses. Experimental data is shown to be in excellent agreement with our theoretical calculation of exciton density versus time, verifying the important affect of the Coulomb interaction between carriers in renormalizing the Rabi frequency. The theoretical calculations include the two-fold degenerate light-hole, heavy-hole, and valence bands in the Hartree-Fock form of the semiconductor Block equations, with all variables selected to conform to the experiment.
The number of complete Rabi oscillations of the electron-hole density induced by square optical pulses with area 2\ensuremath{\pi} is studied using the coherent part of the semiconductor Bloch equations. It is shown that the frequency of the density oscillations depends strongly on the exciton binding frequency, detuning, and the Rabi frequency of the light pulse. The well known doubling of the density oscillation frequency is only observed if the Rabi frequency and exciton binding frequency are approximately of the same order of magnitude. However for strong and weak excitation the semiconductor exhibits properties of atomic systems.
A theoretical study of excitonic Rabi oscillations in semiconductor quantum wells is presented. Fundamental differences between excitonic Rabi oscillations and optical Rabi oscillations in ideal atomic or molecular 2-level systems are due to the existence of the continuous 1-particle spectrum in solids (energy bands) and the resulting strong effects of the Coulomb interaction, such as the attractive electron-hole interaction and the repulsive exchange interaction. In spite of these fundamental differences, Rabi-like oscillations of the excited electron-hole densities are computed for the case of resonant optical pumping of excitons. We compare our theoretical results with our recent experimental observation of excitonic Rabi oscillations.
The coherent response of a semiconductor three-state system to one or two intense light pulses is investigated experimentally on a 100 fs time scale. Three experiments constitute this dissertation: observation of excitonic Rabi oscillations, measurement of two-exciton coupled Stark shifting, and an attempt to observe dark states. Basic concepts of time-resolved ultrafast semiconductor spectroscopy are explained, followed by an analysis of semiconductor two- and three-state systems. Pure two- and three-state dynamics are derived from first principles, followed by the development of the appropriate semiconductor Bloch equations (SBE). Two-color pump-probe, two-color pump-pump, and pump-pump-probe techniques are explained in the context of three-state semiconductor experiments. The experimental setup is explained in detail. Resonant two-color pump-probe measurements resulted in the first observation of multiple excitonic Rabi oscillations. The common conduction band shared by the light-hole and heavy-hole excitons of an InGaAs multiple quantum well allowed us to measure hh-exciton density (Rabi) oscillations by probing lh-exciton absorption. By studying the intensity dependence of the Rabi frequency, we showed the important role of many-body effects in renormalizing the dipole energy. The shared conduction band also causes the lh-exciton resonance to Stark shift when the hh exciton is Stark shifted. We measured a transient Stark shifting of both resonances due to virtual hh-exciton transitions. We observed that the ratio of the hh-exciton shift to lh-exciton shift was 2:1 at large pump-exciton detuning, as predicted from a simple three-state dressed exciton picture. For smaller detunings we saw an increase in the ratio and a redshift of the non-dipole coupled exciton state. Both of these observations are consistent with the most recent theories and experiments on excitonic Stark shifting. For strong near-resonant pumping of both lh- and hh-exciton transitions, an intervalence-band Raman-type coherence follows from the SBE that results in a transparent eigenstate (dark state) when both pumps are equally detuned from resonance. The existence of this coherence is well-known in atomic-optical systems, but has been elusive in semiconductors. Our inconclusive experimental result is presented along with an evaluation of experimental shortcomings. In brief, the expected change is absorption was too small to see.
We demonstrate the presence of strong exciton-exciton correlations in GaAs-AlGaAs multiple quantum wells by using the polarization selection rules for four-wave mixing and a test that was originally designed to distinguish between quantum beats and polarization interference. We show that, when the four-wave-mixing signal is produced by two pulses that have the same circular polarization, dynamic beating behavior is observed at the heavy-hole-light-hole frequency that provides evidence of Coulomb-induced correlations that go beyond those expected from the semiconductor Bloch equations in the Hartree-Fock approximation and beyond the local field corrections used in simple phenomenological models. Moreover, this behavior cannot be explained by invoking biexcitonic effects. We demonstrate that this dynamic excitonic coupling can be explained in terms of a competition between quantum-beat-like and polarization-interference-like behavior, and we show that such behavior can be used to place quantitative limits on the coupling strength. In addition, we use a simple phenomenological model to show that excitation-induced-dephasing can produce such correlations.
Ultrafast pump-probe measurements evidence the dynamical Stark splitting in the exciton absorption spectrum of a single semiconductor quantum well. The intensity of the Stark sidebands in the spectrum is comparable to the linear absorption and their separation scales as the pump field amplitude. In the time domain the Rabi oscillations are observed. The semiconductor Bloch equations solved in the Hartree-Fock approximation demonstrate that the coherent exciton-light coupling dominates over the many-body dephasing.