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Journal of Physics Condensed Matter

Polarisation effects of the dynamical Stark effect of excitons in quantum wells

J Schlosser, Á. Stáhl, I. Balslev

Published Jul 9, 1990• 9 citations
Publisher

Abstract

The authors study the polarisation properties of the dynamical Stark effect of excitons in semiconductor quantum wells. They start from a four-band density matrix theory involving the heavy- and light-hole band and the two lowest conduction subbands. The set of equations of motion contains the dynamics relevant for both Frohlich-type experiments (pumping with a carbon dioxide laser) and the case of pumping a few exciton rydbergs below the exciton line. The authors perform the relevant projections based on excitonic eigenstates and study the resulting 'few-level' systems. From this they calculate the change in the susceptibility tensor with respect to a weak probe beam caused by a pump beam with specified polarisation and frequency.

DOI
10.1088/0953-8984/2/27/005

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The authors study the polarisation properties of the dynamical Stark effect of excitons in semiconductor quantum wells. They start from a four-band density matrix theory involving the heavy- and light-hole band and the two lowest conduction subbands. The set of equations of motion contains the dynamics relevant for both Frohlich-type experiments (pumping with a carbon dioxide laser) and the case of pumping a few exciton rydbergs below the exciton line. The authors perform the relevant projections based on excitonic eigenstates and study the resulting 'few-level' systems. From this they calculate the change in the susceptibility tensor with respect to a weak probe beam caused by a pump beam with specified polarisation and frequency.
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.
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.
Optical interband excitonic absorption of semiconductor quantum wells (QW’s) driven by a coherent pump field is investigated on the basis of semiconductor Bloch equations. The pump field has a photon energy close to the intersubband spacing between the first two conduction subbands in the QW’s. An external weak optical field probes the interband transition. The excitonic effects and pump-induced population redistribution within the conduction subbands in the QW system are included. When the density of the electron–hole pairs in the QW structure is low, the pump field induces an Autler–Townes splitting of the exciton absorption spectrum. The split size and the peak positions of the absorption doublet depend not only on the pump frequency and intensity but also on the carrier density. As the density of the electron–hole pairs is increased, the split contrast (the ratio between the maximum and the minimum values) is decreased, because the exciton effect is suppressed at higher densities owing to the many-body screening.
A theoretical study of the coherently coupled heavy-hole--light-hole optical Stark effect in semiconductor quantum wells is presented. Based on a detailed investigation of the various many-body contributions to the Stark shifts, we identify a parameter regime in which the existence of intervalence band coherences (analogous to the nonradiative Raman coherence in three-level atoms) can be inferred from the coherently coupled heavy-hole--light-hole excitonic optical Stark shift. The analysis is performed for the third-order nonlinear optical regime $({\ensuremath{\chi}}^{3}$ regime), and is based on the dynamics-controlled truncation (DCT) formalism. It includes the relevant optical selection rules, excitonic and two-exciton-correlation (e.g., biexcitonic) effects.