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Physical review. B, Condensed matter

Three-band excitonic Rabi oscillations in semiconductor quantum wells

Rolf H. Binder, Markus Lindberg

Published Jan 15, 2000• 14 citations
Publisher

Abstract

Optical Rabi oscillations in atomic two-level systems and excitonic Rabi oscillations in two-band semiconductors are already well established. In contrast to two-level (or two-band) Rabi oscillations, three-level (or three-band) Rabi oscillations offer a rich variety of oscillation dynamics involving both radiative and nonradiative (Raman) transitions. We analyze excitonic three-band Rabi oscillations in semiconductor quantum wells and study, in particular, the role of band-coupling effects and Coulomb effects.

DOI
10.1103/physrevb.61.2830

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Summary form only given. We investigate theoretically the relation between generalized Rabi oscillations involving optical transitions in three band systems and Raman coherences. The system under consideration is a conventional GaAs semiconductor quantum well in which only the lowest subband of the conduction, the heavy hole bands need to be taken into account. We consider two simultaneous, strong sub-picosecond pulses (770 fs) of opposite circular polarization, spectrally centered at the hh and the lh-excitons respectively.

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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.

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•Jan 1, 2003•0 citations
Optical Rabi oscillations in atomic two-level systems and excitonic Rabi oscillations in two-band semiconductors are already well established. In contrast to two-level (or two-band) Rabi oscillations, three-level (or three-band) Rabi oscillations offer a rich variety of oscillation dynamics involving both radiative and nonradiative (Raman) transitions. We analyze excitonic three-band Rabi oscillations in semiconductor quantum wells and study, in particular, the role of band-coupling effects and Coulomb effects.
Summary form only given. We investigate theoretically the relation between generalized Rabi oscillations involving optical transitions in three band systems and Raman coherences. The system under consideration is a conventional GaAs semiconductor quantum well in which only the lowest subband of the conduction, the heavy hole bands need to be taken into account. We consider two simultaneous, strong sub-picosecond pulses (770 fs) of opposite circular polarization, spectrally centered at the hh and the lh-excitons respectively.
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 studied the semiconductor response with respect to high intensity resonant excitation on short-time scale when the contribution of the Fermi statistics of the electrons and holes prevails. We studied both the single- and double-pulse excitations. For the latter case we considered the time evolution of the multiwave mixing exciton polarization. The main difference between the excitation by a single pulse or by two noncollinear pulses is that the Rabi oscillations of the multiwave mixing response are characterized by two harmonics. Analyzing the operator dynamics governed by the external excitation we found that there are three invariant spin classes, which do not mix with the evolution of the system. Two classes correspond to the bright exciton states and one contains all dark states. We found that the dynamics of the classes are described by six frequencies and the Rabi frequencies are only two of them (one for each bright class). We discuss the effect of the dispersion of the electrons and holes and the Coulomb interaction describing the semiconductor by the semiconductor Bloch equation (SBE). We show that if initially the system is in the ground state then the SBE preserves the invariant spin classes, thus proving the absence of the dark excitons in the framework of this description. We found that due to the mass difference between holes of different kind additional Rabi frequencies, two of those present in the operator dynamics should appear in the evolution of the exciton polarization.
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
This dissertation addresses both fundamental aspects of Coulomb correlations in semiconductor quantum wells and more practical aspects of theoretical analysis of semiconductor optoelectronic devices. After introducing the subject, we present and evaluate a state-of-the-art theory of the third order coherent optical response of a semiconductor quantum well based on the Dynamics Controlled Truncation (DCT) scheme. Already in the third order (the so-called chi (3)) regime, semiconductors exhibit a number of many-body Coulomb correlation effects. Their manifestation in various multi-pulse experimental configurations, customarily used in ultrafast semiconductor spectroscopy, has been an important component of this thesis. Coherent optical effects in a semiconductor 3-band system based on the heavy-hole, light-hole and conduction bands were investigated. The quantum beats in the time-integrated differential transmission signal were analyzed and compared with experimental data obtained at the University of Iowa. Fundamental differences from corresponding quantum beats in atomic 3-level systems were found. Also, the analysis of experimental data (obtained at the University of Arizona) of the coupled heavy-hole-light-hole optical Stark shift revealed evidence of intervalence band coherences, an analog of Raman coherences in atomic 3-levels systems. A scheme for realization of electromagnetically-induced transparency (EIT) based on the interference of excitonic and biexcitonic coherences was proposed. Corresponding experiments performed at the University of Oregon showed indeed a considerable coherent reduction of excitonic absorption. Furthermore, an extension of the chi(3) analysis revealed an energy renormalization of the biexciton, in good agreement with the corresponding experiment. A microscopic analysis of polarization dynamics in time-resolved four-wave mixing signals was performed, revealing interesting implications for the biexciton dephasing in addition to the significance of many-body correlations. In the case of four-wave mixing in semiconductor microcavities, our theoretical analysis in conjunction with experimental data obtained at the University of Tokyo gave us indications for a significant shortcoming of the second Born approximation (2nd BA) applied to two-exciton Coulomb correlations in a thin semiconductor quantum well, in agreement with the general knowledge of the qualitative failure of the 2nd BA in systems with short-range interaction in two dimensions. We also analyzed a novel all-optical switching technique based on the nonlinear polarization rotation. Apart from identifying the many-particle processes relevant for the switch operation in the chi(3) regime, we proposed ways to further optimize the switch.