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Physical Review Letters

Collective Excitations and the Dynamical Stark Effect in a Coherently Driven Exciton System

Stefan Schmitt-Rink, D. S. Chemla

Published Nov 24, 1986• 323 citations
Publisher

Abstract

We consider a semiconductor of arbitrary dimension subject to a strong monochromatic laser beam in the transparency region below the exciton resonance. We calculate the spectrum of collective excitations and explain the recently observed dynamical Stark effect of the exciton. For the first time, we derive from first principles the nonresonant nonlinear susceptibility ${\ensuremath{\chi}}^{(3)}$ including exciton correlations.

DOI
10.1103/physrevlett.57.2752

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We consider a semiconductor of arbitrary dimension subject to a strong monochromatic laser beam in the transparency region below the exciton resonance. We calculate the spectrum of collective excitations and explain the recently observed dynamical Stark effect of the exciton. For the first time, we derive from first principles the nonresonant nonlinear susceptibility \ensuremathχ(3){\ensuremath{\chi}}^{(3)}\ensuremathχ(3) including exciton correlations.
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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.
The three-level optical Stark effect is due to a dynamical coupling of two excited states by an intense laser field. This effect has been observed on the heavy and light hole excitons in multiple quantum wells (MQW) and the dipole allowed 2 P exciton in Cu20. In this contribution new results on the dipole forbidden but quadrupole allowed 1 S exciton in Cu20 are reported. The experimental results are analyzed in terms of a nonlinear susceptibility which takes into account the dynamical coupling between the excited states to all orders.
The first observation of the optical Stark effect of electron-hole continuum states in addition to the bound-exciton states is reported under femtosecond excitation conditions chosen to minimize the generation of real carriers. The experimental results agree well with calculations using the generalized semiconductor Bloch equations. The theory shows that the commonly used adiabatic approximation is correct only for pulses which are longer than the coherence decay time. For shorter pulses coherent dynamic effects strongly influence the spectral changes.
Summary form only given. In the excitonic ac Stark shift in quantum wells the excitonic absorption line is blueshifted by shining on the sample an intense laser pulse, whose frequency is lower than the exciton transition frequency. The effect is bigger when the laser spectrum approaches the resonance with the excitonic absorption. But if the laser and excitonic absorption spectra sensibly overlap, a great amount of electronic population is excited and consequently the Coulomb nonlinearities due to the interaction between excited carries or excitons dramatically increase. One prominent effect under these conditions is the excitation- induced dephasing which can destroy the coherence of the electronic system and therefore the coupling between excitons and light, which is inherently coherent. Some evidence for the resonant Stark effect was already reported, but the direct observation of the spectral splitting was still missing. This observation demonstrates that the coherent exciton light coupling in semiconductors can be strong enough to survive the fast dephasing, and that therefore an efficient ultrafast manipulation of the exciton absorption in the coherent transient is possible. In order to magnify the ac Stark effect and its visibility a special sample was designed: a single In/sub 0.04/Ga/sub 0.96/As quantum well is grown on the top of an AlAs/AlGaAs distributed Bragg reflector; two /spl lambda//2 spacers separate the quantum well from the mirror and from the air. In this configuration the light field incident on the sample and the one reflected by the mirror constructively interfere at the quantum well position, giving a high effective absorption.
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.