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physica status solidi (b)

Coulomb Corrections to the Gain in the Optical Stark Effect of Semiconductors

Ch. Tanguy

Published Mar 1, 1998• 0 citations
Publisher

Abstract

Induced gain appears when a semiconductor is submitted to an intense monochromatic pump beam tuned below the exciton resonance. Because of the Coulomb interaction between excitons, the gain coefficient strongly departs from the dressed-atom value to which it reduces in the limit of very large detunings. We give the leading corrections to the large detuning expansion, in the case of two and three dimensions.

DOI
10.1002/(sici)1521-3951(199803)206:1<349::aid-pssb349>3.0.co;2-d

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Induced gain appears when a semiconductor is submitted to an intense monochromatic pump beam tuned below the exciton resonance. Because of the Coulomb interaction between excitons, the gain coefficient strongly departs from the dressed-atom value to which it reduces in the limit of very large detunings. We give the leading corrections to the large detuning expansion, in the case of two and three dimensions.
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.
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.
When a direct-gap semiconductor is irradiated in the transparency region, the exciton line blue shifts. This so-called optical Stark effect of the exciton is due to a coupling between the exciton and all biexcitonic states (bound or unbound). More precisely we show that the exciton shift results only from interactions between excitons (Coulomb interaction and Pauli exclusion). At large detuning, Pauli exclusion dominates, and the excitonic shift is the same as the dressed-atom blue shift. In material having a bound biexcitonic molecule, the excitonic blue shift, observed at large detuning, becomes a red shift at small detuning close to the exciton-biexciton resonance.
Excitonic resonances in direct-gap semiconductors have proved to exhibit similar optical non-linearities as in atoms. One example is the optical Stark effect [1] which occurs when the sample is excited by a strong pump field whose frequency is detuned from the optical transition. The optical Stark effect has been described as a coupling between the electromagnetic field and the resonance with no real absorption. It can also be seen as the creation of a virtual population in the excited state. A transient gain, quadratic in pump intensity, is associated to this effect as already observed in atomic systems [2]. This hyper-Raman process involves two pump photons and occurs at frequency 2ω p – ω0, where ω p and ω0 are the pump and atomic transition frequencies, respectively (see inset of Fig. 1).
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.