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Physical Review Letters

Ultrafast adiabatic following in semiconductors

Rolf H. Binder, Stephan W. Koch, Markus Lindberg, Nasser N. Peyghambarian, Wilfried Schäfer

Published Aug 13, 1990• 127 citations
Publisher

Abstract

The full semiconductor Bloch equations are solved to analyze the ultrafast exciton dynamics in semiconductors. Transient adiabatic following is obtained for large detunings and arbitrary intensities, leading to exciton Stark shift, bleaching, and recovery on the time scale of the pump pulse. The many-body Coulomb effects strongly influence the semiconductor response for resonant excitation conditions, almost doubling the effective Rabi frequency of the applied field.

DOI
10.1103/physrevlett.65.899

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The full semiconductor Bloch equations are solved to analyze the ultrafast exciton dynamics in semiconductors. Transient adiabatic following is obtained for large detunings and arbitrary intensities, leading to exciton Stark shift, bleaching, and recovery on the time scale of the pump pulse. The many-body Coulomb effects strongly influence the semiconductor response for resonant excitation conditions, almost doubling the effective Rabi frequency of the applied field.
A comprehensive numerical study of the optical Stark effect and associated phenomena in semiconductors is presented. The results are obtained from numerical solutions of the full semiconductor Bloch equations for bulk and quantum-well structures. Coherent oscillations, the optical Stark effect, and adiabatic following, i.e., ultrafast bleaching and recovery of the exciton, are discussed. The relative importance of the different contributions in the semiconductor Bloch equations is identified. Optical-absorption spectra are computed for different exciton dephasing models and a large variety of pump-probe excitation parameters.
The optical Stark effect of excitons in semiconductors, where the exciton resonance is blue shifted by an off-resonance light beam, has been actively studied. Here we report on the observation of a very fast recovery of the exciton bleaching for an off-resonance excitation condition in a quantum well sample at room temperature. The good agreement between the experimental results and our numerical calculations of the time-resolved absorption spectra suggests a coherent transient population buildup and decay occurring on the time scale of the pump pulse.
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.
Recent works in the area of ultrafast nonlinearities due to virtual carriers in semiconductor heterostructures have generated significant interest among researchers. It has been shown that excitons in QW's behave very much like conventional two-level atoms, to the extent that exciton-exciton interaction can be neglected. Therefore, fast coherent phenomena usually associated with two-level system may occur in excitonic QW transitions. Indeed, dynamic (AC) Stark effect in QW's have been demonstrated. When semiconductor QW's were pumped below the absorption edge there were a strong "blue" shift of the exciton resonance, accompanied by a strong bleaching.
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.