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Physical Review Letters

Excitonic Stark Shift: A Coupling to "Semivirtual" Biexcitons

Monique Combescot, R. Combescot

Published Jul 4, 1988• 160 citations
Publisher

Abstract

The optical Stark shift of the exciton is due to a coupling between the exciton and "semivirtual" biexcitonic states (bound and unbound). We show that at large detuning the excitonic shift is the same as the "dressed atom" blue shift. We predict that at small detuning the exciton-exciton interaction plays an important role and leads to an excitonic red shift at the two-photon absorption threshold when the molecular biexciton is stable.

DOI
10.1103/physrevlett.61.117

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The optical Stark shift of the exciton is due to a coupling between the exciton and "semivirtual" biexcitonic states (bound and unbound). We show that at large detuning the excitonic shift is the same as the "dressed atom" blue shift. We predict that at small detuning the exciton-exciton interaction plays an important role and leads to an excitonic red shift at the two-photon absorption threshold when the molecular biexciton is stable.
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.
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. Since the original discovery of the excitonic optical Stark effect, substantial progress has been made in the understanding of this ultrafast nonlinear optical effect. Recently, a red shift of the excitonic absorption line has been reported using low intensity excitation detuned 4.5 meV below the 1s-heavy-hole (hh) resonance and cross-circularly-polarized pulses. This was attributed to higher-order Coulomb correlations, interpretable as bound and unbound two-exciton states and memory effects. For co-circularly polarized pulses the well-known blue shift was found. Here we present a related effect occurring in the higher-intensity regime. Standard pump-probe experiments were performed on high-quality 8.5 nm-thick In/sub 0.04/Ga/sub 0.96/As multiple quantum well (MQW) samples.
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.