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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Experimental observation of multiple excitonic optical Rabi oscillations in a semiconductor

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

Published May 24, 1999• 2 citations
Publisher

Abstract

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.

DOI
10.1117/12.349298

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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.
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.
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.
Exciton Rabi oscillations and Rabi splitting differ significantly from their atomic counterparts in part because Coulomb interactions between excitons strongly influence the exciton Rabi frequency.' While both exciton Rabi oscillations and Rabi splitting were demonstrated recently in quantum wells (QWs),'.l experimental investigation of how exciton-exciton interactions affect these coherent optical Q~OCCSS~S has been hindered bya number of complications. In time-domain studies, the Rabi frequencyvaries with time due to the changing electric field strength. In typ ical spectral domain studies, a spectrally-broad probe pulse is spectrally resolved after its transmission through the sample. The resulting pump-probe spectra are difficult to interpret due to the presence of coherent spectral oscillations and a sensitive dependence on the pump-probe delay. In this paper we report studies of exciton Rabi splitting where spectrally narrow pump and probe pulses were used. In this case, coherent spectral oscillations in pump-probe spectra can be avoided by tuning the central frequency of the probe pulse. The intensity dependence of the Rabi splitting obtained from these studies reveals a distinctly nonlinear relationship between the Rabi frequency and the applied electric field, in contrast to the linear dependence expected from mean-field bed theoretical models.' Pump-probe experiments were performed on a 130 A GaAs1AlGa.k multiple QW sample at 10 K. Figure I shows results of pump-probe meas
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.
Summary form only given. We report studies of exciton Rabi splitting where spectrally narrow pump and probe pulses were used. In this case, coherent spectral oscillations in pump-probe spectra can be avoided by tuning the central frequency of the probe pulse. The intensity dependence of the Rabi splitting obtained from these studies reveals a distinctly nonlinear relationship between the Rabi frequency and the applied electric field, in contrast to the linear dependence expected from mean-field based theoretical models. Pump-probe experiments were performed on a 130 /spl Aring/ GaAs/AlGaAs multiple QW sample at 10 K.
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.