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Physical Review Letters

Influence of Many-Body Interactions on the Excitonic Optical Stark Effect

Claudia Ell, J. F. Müller, K. El Sayed, H. Haug

Published Jan 16, 1989• 100 citations
Publisher

Abstract

Band-edge absorption spectra for a probe beam under the action of a nonresonant pump beam are calculated and analyzed within the Hartree-Fock theory. As a result of many-body interactions, one obtains an exciton optical Stark shift with a constant (2D) or slightly increasing (3D) exciton oscillator strength in agreement with several recent experiments and in striking contrast to corresponding atomic observations. Apparently, the deviating results of earlier semiconductor experiments were partly caused by dynamical effects and partly by the presence of real excitations.

DOI
10.1103/physrevlett.62.304

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Band-edge absorption spectra for a probe beam under the action of a nonresonant pump beam are calculated and analyzed within the Hartree-Fock theory. As a result of many-body interactions, one obtains an exciton optical Stark shift with a constant (2D) or slightly increasing (3D) exciton oscillator strength in agreement with several recent experiments and in striking contrast to corresponding atomic observations. Apparently, the deviating results of earlier semiconductor experiments were partly caused by dynamical effects and partly by the presence of real excitations.
We calculate the change in the absorption strength of excitonic lines induced by a pump beam tuned in the transparency region of a direct-band-gap semiconductor. We show that, in the large-detuning limit, and unlike what happens to the energy shift, this change does not simply take the dressed-atom value, but instead this value multiplied by a factor 1-d, where d is the space dimension. We also calculate the absorption strength for low-energy unbound excitonic states, and derive the absorption-amplitude change close to the band edge. Finally, we give the first correction to the large-detuning limit of the absorption strength, in the case of the lowest excitonic level.
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.
We theoretically analyze a pump–probe experiment to detect the optical Stark effect on impurity-bound excitons taking the quantization of the pump field into account. A density matrix approach allows the calculation of the probe absorption spectra with high accuracy. For bound excitons with low inhomogeneous broadening of several tens of μeV, the photon statistics of the pump field has a considerable influence on the lineshape of the Stark-shifted resonance. The effect should be clearly observable for broad photon number distributions and low pump detuning.
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.
We show that a laser beam, tuned in the transparency region of a direct-gap semiconductor, not only shifts but also splits the exciton levels. This splitting originates from the degeneracy of the valence band as the (${\ensuremath{\sigma}}_{+},{\ensuremath{\sigma}}_{\ensuremath{-}}$) parts of the light are not similarly coupled to the various exciton components. In the case of a fourfold-degenerate valence band, we find that, at large detuning, the shifts of the (2\ifmmode\times\else\texttimes\fi{}4) eightfold exciton are exactly the shifts of a (2+4) six-level atom. This is just the generalization of the simple band-structure case with one electron and one hole band in which the large detuning excitonic shift has the same value as that of the two-level (dressed) atom. We give the selection rules to observe the various shifted lines for typical pump-probe experiments. We also discuss the experimental conditions necessary to see an exciton red shift at the two-photon absorption threshold, when the molecular biexciton is stable.