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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Optical coherent transient effects in GaAs/GaAlAs quantum well structure

Sharmila Banerjee, Pratima Sen, Pranay K. Sen

Published Apr 28, 1999• 0 citations
Publisher

Abstract

Using semiclassical time-dependent perturbation approach, we have analyzed one of the important optical coherent transient effects viz., the Stark shift and Stark broadening (also known as self energy correction) by incorporating the higher excitonic states in GaAs/GaAlAs quantum well structures irradiated by an ultrashort pulsed laser. It has been found that both Stark shift as well as Stark broadening get modified when we take into account multiple excitonic states.

DOI
10.1117/12.347933

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Using semiclassical time-dependent perturbation approach, we have analyzed one of the important optical coherent transient effects viz., the Stark shift and Stark broadening (also known as self energy correction) by incorporating the higher excitonic states in GaAs/GaAlAs quantum well structures irradiated by an ultrashort pulsed laser. It has been found that both Stark shift as well as Stark broadening get modified when we take into account multiple excitonic states.
Using straightforward time-dependent perturbation treatment, transient coherent radiation-semiconductor interaction mechanisms are investigated analytically in a quantum well structure (QWS) duly irradiated by a moderate power femtosecond laser with photon energy slightly less than the crystal bandgap energy. The transition energy is calculated by recognizing the finite potential well depth of the QWS. The effects of higher excitonic states on the Stark shift and self-energy correction are examined in GaAs/AlGaAs QWS. The study shows a red shift with increasing excitation intensity and the shift is also found to be less when all the discrete excitonic states below the band edge are considered together. An increased self-energy correction accompanies this red shift.
Summary form only given. The optical Stark shift in semiconductors transient nonlinearity which helps to understand fundamental ultrafast microscopic processes. Studies of similarities and differences between optical Stark shifts in atomic two-level systems and those observed in semiconductors led to the understanding of semiconductor-specific many-body effects such as biexcitons and Coulomb memory effects. While the two-level analogies of Stark shifts in semiconductors have been successfully exploited, the question of what one can learn from a comparison of coherent atomic three-level effects with optical Stark shifts in semiconductors using the coherent coupling between heavy-hole (hh) and light-hole (lh) excitons has not been addressed so far. In atomic three-level systems, nonradiative or Raman coherences are the foundation of important nonlinear optical effects such as electromagnetically-induced transparency and lasing without inversion. We investigate these coherences in an InGaAs multiple quantum well utilizing coherently-coupled Stark shift measurements of the hh- and lh-exciton resonances.
The coherent response of a semiconductor three-state system to one or two intense light pulses is investigated experimentally on a 100 fs time scale. Three experiments constitute this dissertation: observation of excitonic Rabi oscillations, measurement of two-exciton coupled Stark shifting, and an attempt to observe dark states. Basic concepts of time-resolved ultrafast semiconductor spectroscopy are explained, followed by an analysis of semiconductor two- and three-state systems. Pure two- and three-state dynamics are derived from first principles, followed by the development of the appropriate semiconductor Bloch equations (SBE). Two-color pump-probe, two-color pump-pump, and pump-pump-probe techniques are explained in the context of three-state semiconductor experiments. The experimental setup is explained in detail. Resonant two-color pump-probe measurements resulted in the first observation of multiple excitonic Rabi oscillations. The common conduction band shared by the light-hole and heavy-hole excitons of an InGaAs multiple quantum well allowed us to measure hh-exciton density (Rabi) oscillations by probing lh-exciton absorption. By studying the intensity dependence of the Rabi frequency, we showed the important role of many-body effects in renormalizing the dipole energy. The shared conduction band also causes the lh-exciton resonance to Stark shift when the hh exciton is Stark shifted. We measured a transient Stark shifting of both resonances due to virtual hh-exciton transitions. We observed that the ratio of the hh-exciton shift to lh-exciton shift was 2:1 at large pump-exciton detuning, as predicted from a simple three-state dressed exciton picture. For smaller detunings we saw an increase in the ratio and a redshift of the non-dipole coupled exciton state. Both of these observations are consistent with the most recent theories and experiments on excitonic Stark shifting. For strong near-resonant pumping of both lh- and hh-exciton transitions, an intervalence-band Raman-type coherence follows from the SBE that results in a transparent eigenstate (dark state) when both pumps are equally detuned from resonance. The existence of this coherence is well-known in atomic-optical systems, but has been elusive in semiconductors. Our inconclusive experimental result is presented along with an evaluation of experimental shortcomings. In brief, the expected change is absorption was too small to see.
Irradiation of a medium with non-resonant light leads to a shift of the energy levels in the system. This optical, or dynamical Stark effect has been studied for many years in atomic gases. It is only recently, however, that it could be detected for excitonic transitions in solids. This development has stirred considerable interest, because the optical Stark effect has inherent features which makes it well suited for applications such as in ultrafast all-optical data processing. Since the pump light beam falls in a transparency region of the medium, it experiences little loss, in contrast to optical non-linearities based on a saturation mechanism. Also, because virtual transitions are involved, the light-induced shift of exciton levels follows closely the pump pulse duration, making it possible to design ultrafast all-optical logic gates with subpicosecond switch-on and -off times.
We describe the first reported experimental observation of an extremely fast shift of the n = 1 exciton transition energy in GaAs quantum-well heterostructures. The shift is produced by optical pumping below the band gap and is not associated with a carrier or exciton population. We interpret the shift in terms of an optical Stark effect. We present a model for the Stark effect on the ground-state exciton in quantum wells and find good agreement between the predictions of the model and our experimental results.
Stark shift and self-energy correction in a non-centrosymmetric semiconductor have been studied by using the time-dependent perturbation technique and considering the diagonal elements of the transition dipole moment operator to be finite. The Stark shift obtainable from the Rabi frequency shows a time dependence. The analysis is applied to a sample of InSb duly irradiated by a near-resonant laser and it is found that the magnitude of Stark shift decreases while the magnitude of self-energy correction increases due to the incorporation of non-centrosymmetry.