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Physical review. B, Condensed matter

Theory of optical coherence for Wannier excitons: Application to photon echoes

Izo I. Abram

Published Sep 15, 1989• 18 citations
Publisher

Abstract

The coherent excitation of a Wannier-exciton system by a short resonant light pulse is described through a simple model that takes into account explicitly the phase-space-filling effects due to the fermion nature of the electrons and holes composing the excitons. This formalism can describe both coherent-transient experiments, such as photon echoes, and optical observations at time scales longer than dephasing, such as absorption saturation. At high excitation densities the optical response of hydrogenic excitons deviates significantly from the response of the two-level model used traditionally to describe resonant effects. This suggests that coherent-optical-transient experiments, such as photon echoes, may be used to probe exciton interactions due to their internal structure, in addition to the relaxation processes that they probe in traditional experimental arrangements.

DOI
10.1103/physrevb.40.5460

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Photon Echoes and the Structure of Wannier Excitons

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Abstract The coherent polarization of a Wannier exciton system, induced by a short incident resonant light pulse, is calculated within a formalism that takes into account explicitly the internal structure of excitions. By examining the phase‐space filling interactions among excitons, it is shown that the hydrogenic structure of excitions causes significant deviations in their coherent optical response when compared with the response of the traditional two‐level model of optical coherence. This suggests that photon echo experiments, which measure directly the coherent polarization, may provide information on the structure of Wannier excitons.

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Transient coherent effects in semiconductor three-state systems

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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.

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Summary form only given. Optical interactions in semiconductor microcavities embedded with quantum wells enter a nonperturbative regime when the dipole coupling rate between the exciton and the cavity mode exceeds relevant decay rates. In this regime, coherent energy exchange between the exciton and the cavity mode, i.e. normal mode oscillation (NMO), takes place when the cavity mode is excited impulsively by a short laser pulse. Similar coherent oscillations have also been observed in transient four-wave mixing (FWM) responses. In this paper, we present experimental and theoretical studies on the nature of oscillations in these transient FWM responses. We show that, in contrast to earlier beliefs, oscillations in time-integrated transient FWM do not correspond to NMO of the exciton or photon populations. Theoretical studies further reveal that FWM arising from different physical mechanisms including band filling, excitation-induced dephasing, and renormalized electric fields is characterized by highly distinct coherent dynamics. Oscillations in transient FWM reflect interference between these coherent optical processes and can be used as a unique probe for exciton many-body interactions in the nonperturbative regime.

Quantum Electronics and Laser Science Conference•Jan 20, 2003•0 citations
The coherent excitation of a Wannier-exciton system by a short resonant light pulse is described through a simple model that takes into account explicitly the phase-space-filling effects due to the fermion nature of the electrons and holes composing the excitons. This formalism can describe both coherent-transient experiments, such as photon echoes, and optical observations at time scales longer than dephasing, such as absorption saturation. At high excitation densities the optical response of hydrogenic excitons deviates significantly from the response of the two-level model used traditionally to describe resonant effects. This suggests that coherent-optical-transient experiments, such as photon echoes, may be used to probe exciton interactions due to their internal structure, in addition to the relaxation processes that they probe in traditional experimental arrangements.
Abstract The coherent polarization of a Wannier exciton system, induced by a short incident resonant light pulse, is calculated within a formalism that takes into account explicitly the internal structure of excitions. By examining the phase‐space filling interactions among excitons, it is shown that the hydrogenic structure of excitions causes significant deviations in their coherent optical response when compared with the response of the traditional two‐level model of optical coherence. This suggests that photon echo experiments, which measure directly the coherent polarization, may provide information on the structure of Wannier excitons.
Based upon the time dependent perturbation theory for coherent radiation-semiconductor interaction, the possibility of occurrence of the phenomenon of two-pulse photon echo has been investigated analytically in a bulk direct-gap semiconductor under near resonant transition regime below the absorption edge of the crystal. The excitation intensity is chosen to be in the low-to-moderate power regime such that the photoinduced electron-hole pair density remains below the Mott transition limit and the weakly bound Wannier-Mott excitonic structure of the crystal absorption edge is manifested. The band gap renormalization effect is also taken into account. Numerical estimation of the transmitted intensity has been made for electron-hole transition to the 1s excitonic states in the bulk CdS crystal. The analytical results demonstrate the occurrence of photon echo in direct-gap semiconductors.
An overview on photon echo spectroscopy under resonant excitation of the exciton complexes in semiconductor nanostructures is presented. The use of four-wave-mixing technique with the pulsed excitation and heterodyne detection allowed us to measure the coherent response of the system with the picosecond time resolution. It is shown that, for resonant selective pulsed excitation of the localized exciton complexes, the coherent signal is represented by the photon echoes due to the inhomogeneous broadening of the optical transitions. In case of resonant excitation of the trions or donor-bound excitons, the Zeeman splitting of the resident electron ground state levels under the applied transverse magnetic field results in quantum beats of photon echo amplitude at the Larmor precession frequency. Application of magnetic field makes it possible to transfer coherently the optical excitation into the spin ensemble of the resident electrons and to observe a long-lived photon echo signal. The described technique can be used as a high-resolution spectroscopy of the energy splittings in the ground state of the system. Next, we consider the Rabi oscillations and their damping under excitation with intensive optical pulses for the excitons complexes with a different degree of localization. It is shown that damping of the echo signal with increase of the excitation pulse intensity is strongly manifested for excitons, while on trions and donor-bound excitons this effect is substantially weaker.
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.
This work presents new results of experimental studies of exciton relaxation in GaAs/AlGaAs multiple quantum well materials, using transient nonlinear laser spectroscopy techniques. In the low excitation regime, effective optical Bloch equations similar to the density matrix formalism of a two-level system describe the response. Solutions of these equations appropriate for three-pulse scattering studies are presented, along with a discussion of new experimental techniques used in this work. Non-ideal conditions present in the molecular beam epitaxy growth process introduce monolayer fluctuations in the quantum well thickness, leading to inhomogeneous broadening and exciton localization at sites of minimum energy. Localized excitons are separated in energy from extended, quasi-delocalized states by the mobility edge. Studies of localized exciton relaxation indicate that these excitons relax on a much slower timescale than delocalized excitons. The temperature dependence of the localized exciton relaxation rate shows that above 15K, the excitons are thermally activated to extended states above the mobility edge. Below 15K the excitons relax by phonon assisted migration between localization sites. For temperatures above 5K, and for exciton energies greater than 1 meV below line center, an extra dephasing mechanism characterizes the exciton relaxation. The inhomogeneous broadening of the exciton leads to the emission of stimulated photon echoes in the experimental geometry used in this work. The time-resolved emission demonstrates the stimulated photon echo nature at low excitation densities. At higher excitation densities, the decay dynamics is more complex. The time-resolved emission shows the presence of a stimulated photon echo and a free polarization decay. This unusual result suggests that both a homogeneous and an inhomogeneous exciton distribution comprise the exciton resonance. Exciton relaxation at low excitation densities represents the interaction of the exciton with the lattice. At higher excitation densities, exciton-exciton and exciton-free carrier interactions modify the relaxation rates. The dependence of the exciton relaxation rate on excitation density shows that many-body effects play an important role in the exciton physics. Free carrier interactions are more efficient at increasing the exciton relaxation rate; both types of interactions are more important in quantum well systems than in bulk materials.
Summary form only given. Optical interactions in semiconductor microcavities embedded with quantum wells enter a nonperturbative regime when the dipole coupling rate between the exciton and the cavity mode exceeds relevant decay rates. In this regime, coherent energy exchange between the exciton and the cavity mode, i.e. normal mode oscillation (NMO), takes place when the cavity mode is excited impulsively by a short laser pulse. Similar coherent oscillations have also been observed in transient four-wave mixing (FWM) responses. In this paper, we present experimental and theoretical studies on the nature of oscillations in these transient FWM responses. We show that, in contrast to earlier beliefs, oscillations in time-integrated transient FWM do not correspond to NMO of the exciton or photon populations. Theoretical studies further reveal that FWM arising from different physical mechanisms including band filling, excitation-induced dephasing, and renormalized electric fields is characterized by highly distinct coherent dynamics. Oscillations in transient FWM reflect interference between these coherent optical processes and can be used as a unique probe for exciton many-body interactions in the nonperturbative regime.