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Physical Review Letters

Picosecond quantum-beat spectroscopy of bound excitons in CdS

H. Stolz, V. Langer, Erik Schreiber, Sergei A Permogorov, Wolf von der Osten

Published Aug 5, 1991• 61 citations
Publisher

Abstract

We report the first observation of quantum beats in the resonance fluorescence of a bound exciton in a semiconductor, the ionized-donor exciton complex in CdS. Measurements of the polarization behavior and magnetic-field dependence of the beats permitted a detailed investigation of strain effects and magneto-optical parameters of the states. From the damping of the beats, coherence times of the order of several hundreds of picoseconds are deduced. For the neutral-donor and -acceptor bound exciton states, very rapid dephasing with coherence times of the order of 20 ps is found.

DOI
10.1103/physrevlett.67.679

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We report the first observation of quantum beats in the resonance fluorescence of a bound exciton in a semiconductor, the ionized-donor exciton complex in CdS. Measurements of the polarization behavior and magnetic-field dependence of the beats permitted a detailed investigation of strain effects and magneto-optical parameters of the states. From the damping of the beats, coherence times of the order of several hundreds of picoseconds are deduced. For the neutral-donor and -acceptor bound exciton states, very rapid dephasing with coherence times of the order of 20 ps is found.
Pulse propagation experiments are performed with coherent picosecond laser pulses in resonance with the donor bound A-exciton (I2) state in CdS. Using bandwidth-limited time-resolved spectroscopy, we investigate the intensity of the transmitted laser pulse as a function of monochromator energy position and time. This method permits the determination of both the amplitude and the phase of the complex electric-field amplitude. Studying the dependence of pulse propagation on the input intensity, for small-area pulses we found at the rear of the sample the spectral hole formation and beating characteristic of a 0π pulse. At large pulse areas close to 2π the pulse propagates nearly unperturbed, showing no oscillatory reshaping or significant absorption losses. This provides clear evidence for self-induced transparency at an excitonic state in solids. Our interpretation is substantiated by an analysis within the framework of the combined Maxwell and optical Bloch equations.
The occurrence of quantum beats for an extended exciton state in a solid is demonstrated for the first time. They are observed as oscillations in the two-phonon resonance fluorescence decay of the indirect free exciton states in AgBr split in magnetic fields up to 1 T after excitation by picosecond laser pulses. The results are in agreement with calculations by a density-matrix formalism. From the beating frequencies the splitting of the exciton states can be obtained with high accuracy. Quantum dephasing times of several hundred picosecond are determined comparable to the energy relaxation time.
The propagation of small-area picosecond pulses of coherent light in resonance with the I 2 bound-exciton line in CdS is investigated. The observed strong reshaping of the pulses in form of propagation beats is consistent with the concomitantly measured hole formation in the pulse spectrum. By employing transform-limited time-resolved spectroscopy the complex amplitude of the transmitted optical field can be reconstructed. This allows to identify the beats as amplitude oscillations and phase changes by π characteristic of 0π pulse formation.
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.
We report experimental studies of coherent spin dynamics of donor-bound electrons in high-purity GaAs by using transient differential transmission. The donor-bound exciton transitions, which are not visible in the linear absorption spectrum, are spectrally resolved in the nonlinear differential transmission spectra. The spin beats in the transient differential transmission response, arising from electron spin precession in an external magnetic field, are investigated with the pump and probe coupling to various donor-bound exciton transitions. The spectral dependence of the spin beats provides important information on the polarization selection rule for the underlying donor-bound exciton transitions. The polarization selection rules deduced from these experiments indicate that contributions from higher-energy donor-bound exciton transitions can severely limit the effectiveness of optical spin control using mechanisms such as polarization-dependent optical Stark shifts.
Abstract Measuring the transform‐limited time‐resolved spectrum of a coherent laser pulse allows one to determine the amplitude and phase of the pulse electric field. From the reshaping of pulses transmitted through a thin semiconductor platelet in resonance with an exciton transition in case of the donor bound exciton in CdS the effects of coherent exciton–photon interaction for different laser intensities can be studied. While at low intensities the expected polariton beating connected with the formation of a 0π‐pulse is observed, at sufficiently high intensities changes in the pulse shape occur that are ascribed to self‐induced transparency of the bound exciton states.