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Physical Review Letters

Excitonic optical Stark redshift: The biexciton signature

Daniele Hulin, M. Joffre

Published Dec 31, 1990• 70 citations
Publisher

Abstract

We report the observation of an exciton redshift with a below-gap laser beam, linked to the presence of a bound two-pair state in CuCl. This change in the shift direction for the optical Stark effect in semiconductors relies upon the predominant creation of virtual biexcitons, as shown by the polarization selection rules. Our experiment demonstrates the importance of the biexciton in the description of the optical Stark effect.

DOI
10.1103/physrevlett.65.3425

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physica status solidi (b)•May 1, 1990•2 citations
We report the observation of an exciton redshift with a below-gap laser beam, linked to the presence of a bound two-pair state in CuCl. This change in the shift direction for the optical Stark effect in semiconductors relies upon the predominant creation of virtual biexcitons, as shown by the polarization selection rules. Our experiment demonstrates the importance of the biexciton in the description of the optical Stark effect.
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.
Nonequilibrium Theory of the Optical Stark Effect in the Excitonic Range of the Spectrum One of the most important applications of the theory of Bose condensation of excitons is the optical Stark effect, or “AC Stark effect, ” first demonstrated for excitons in Cu 2 O [1] and since seen in several semiconductors and semiconductor heterostructures (e.g., Refs. 2-5). This effect is a promising tool for the field of optical communications. One of the major interests in this field is the development of all-optical-switching methods, by which light signals are switched on or off directly by other light signals, just as in electronics, electrical signals switch other electrical signals. At the present, most optical communications systems use electrical signals (e.g., electro-optic or acousto-optic devices) to switch the light signals, which means that the limiting bandwidth of the system is controlled by that of the electrical signals, not the optical bandwidth. The optical Stark effect offers this possibility. When one laser beam impinges on a sample, it can drastically alter the excitonic absorption line shape. Therefore a second beam can see either a transparent or an absorbing medium, depending on the presence of the control beam. This is the optical equivalent of a transistor. The basic effect is shown in Fig. 6.1. When an intense laser is tuned to a photon energy that is just below the excitonic ground state, the exciton ground state is shifted in frequency and the oscillator strength is altered. This leads to a strong reduction in the optical absorption at the original wavelength of the exciton ground state.
There are two different models to explain the observed optical bistability (OB) in GaAs. Haken and Goll1 use the saturation of the two-level (electron and hole) atoms as the mechanism of OB, whereas the Stark shift of excitons is the dominant factor in the work by Koch and Haug.2 We analyze both models, including the local field effect.3 It is shown that the validity of each model depends very much upon the parameters involved. We also give a similar analysis for CuCℓ where the biexcitons are important. In contrast to the earlier work by Abram and Maruani,4 we find by careful analysis, including the origin of the background dielectric constant, that the local field correction is not important in this case. The contribution of the exciton and biexciton interaction, however, can be important and should be included in the calculation of OB given by Haug.5 The changes in the numerical results of Ref. 5, by including the exciton-biexciton interaction and the local field correction are to be represented.
Abstract The nonlinear optical phenomena associated with the formation of virtual biexcitons in direct gap semiconductors are studied. Relations are set up for real‐space two‐fermion operators using methods similar to those used when deriving a well known conservation law of k‐space operators for intraband and interband transitions. Restricting the analysis to the χ(3) level, or set of density matrix equations are obtained for the exciton‐biexciton system. Analytical solutions in the limit of small detuning show that the biexcitonic induced absorption and the dynamical Stark effect are closely related, and that the Stark shift as function of the pump frequency has a pole at the frequency of the exciton‐to‐biexciton transition.