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Journal of Applied Physics

Dressed-band approach and Coulomb corrections to the light-induced exciton Stark shift

Humberto Siqueira Brandi, Andrea Latge, L. E. Oliveira

Published Oct 24, 2003• 3 citations

Abstract

In the present work, we perform a comparison of theoretical approaches involving Coulomb-interaction corrections within the Hartree–Fock approximation and the renormalized dressed-band scheme in the large detuning limit. We focus on the well-studied optical Stark shift of the exciton peak in bulk and GaAs–(Ga,Al)As semiconductor quantum wells. It is argued that the Hartree–Fock scheme has severe limitations concerning its application to real experimental situations, even in the simplest laser field–perturbative regime. It is also shown, through a comparison between experiments and a three-band Kane-dressed GaAs–(Ga,Al)As quantum well calculation, that a proper treatment of band structure and confinement effects due to the quantum well is of fundamental importance in a theoretical understanding of Stark shift experimental measurements, and that the renormalized dressed-band approach is a very convenient tool to treat, in the large detuning limit, processes involving the laser–semiconductor interaction in low-dimensional heterostructures.

DOI: 10.1063/1.1614863

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In the present work, we perform a comparison of theoretical approaches involving Coulomb-interaction corrections within the Hartree–Fock approximation and the renormalized dressed-band scheme in the large detuning limit. We focus on the well-studied optical Stark shift of the exciton peak in bulk and GaAs–(Ga,Al)As semiconductor quantum wells. It is argued that the Hartree–Fock scheme has severe limitations concerning its application to real experimental situations, even in the simplest laser field–perturbative regime. It is also shown, through a comparison between experiments and a three-band Kane-dressed GaAs–(Ga,Al)As quantum well calculation, that a proper treatment of band structure and confinement effects due to the quantum well is of fundamental importance in a theoretical understanding of Stark shift experimental measurements, and that the renormalized dressed-band approach is a very convenient tool to treat, in the large detuning limit, processes involving the laser–semiconductor interaction in low-dimensional heterostructures.

We extend the dressed-atom approach to treat the interaction of a laser field with a semiconductor system. The semiconductor is modeled via a simple Kane band-structure scheme and the interaction with the laser field is incorporate through the renormalization of the semiconductor energy gap and conduction/valence effective masses. Far from resonances, such one-body approach allows the study of the effects of laser fields on a variety of optoelectronic phenomena in semiconductor systems for which the effective-mass approximation provides a good physical description. We calculate the effects originated by the laser-dressing on the donor and exciton peack energies in quantum-well heterostructures, and show that they may be quite considerable and observable.

The role of Coulomb scattering is studied in the coherent transients of strongly driven exciton resonances in semiconductor quantum wells. Coulomb scattering is treated within the second Born approximation and the light-induced dressing of the electron–hole gas is consistently included. The light dressing is found to decrease the Coulomb collision efficiency and therefore the field-driven dynamics is close to the Hartree-Fock case. Indeed, Coulomb relaxation and dephasing are not strong enough to prevent a dynamical Stark splitting in the pump–probe absorption spectra.

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.

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.

Summary form only given. The optical Stark shift in semiconductors transient nonlinearity which helps to understand fundamental ultrafast microscopic processes. Studies of similarities and differences between optical Stark shifts in atomic two-level systems and those observed in semiconductors led to the understanding of semiconductor-specific many-body effects such as biexcitons and Coulomb memory effects. While the two-level analogies of Stark shifts in semiconductors have been successfully exploited, the question of what one can learn from a comparison of coherent atomic three-level effects with optical Stark shifts in semiconductors using the coherent coupling between heavy-hole (hh) and light-hole (lh) excitons has not been addressed so far. In atomic three-level systems, nonradiative or Raman coherences are the foundation of important nonlinear optical effects such as electromagnetically-induced transparency and lasing without inversion. We investigate these coherences in an InGaAs multiple quantum well utilizing coherently-coupled Stark shift measurements of the hh- and lh-exciton resonances.