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Physical review. B, Condensed matter

Asymptotic analytic solution for Rabi oscillations in a system of weakly excited excitons

A. Knorr, Th. Östreich, Kurt Schönhammer, Rolf H. Binder, S. W. Koch

Published May 15, 1994• 21 citations
Publisher

Abstract

An asymptotic solution for light-induced exciton density oscillations in a semiconductor is calculated from the semiconductor Bloch equations in the low density limit (weak optical excitation). The analytic approximation is compared with a numerical solution of the full equations. It is shown that even for low area fields (\ensuremath{\ll}2\ensuremath{\pi}) density oscillations are caused by Coulomb exchange effects coupling the generated excitons and that the oscillation frequency and amplitude depend nonlinearly on the Rabi frequency of the incident field.

DOI
10.1103/physrevb.49.14024

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An asymptotic solution for light-induced exciton density oscillations in a semiconductor is calculated from the semiconductor Bloch equations in the low density limit (weak optical excitation). The analytic approximation is compared with a numerical solution of the full equations. It is shown that even for low area fields (\ensuremath{\ll}2\ensuremath{\pi}) density oscillations are caused by Coulomb exchange effects coupling the generated excitons and that the oscillation frequency and amplitude depend nonlinearly on the Rabi frequency of the incident field.
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We observe multiple excitonic optical Rabi oscillations in a semiconductor quantum well. Up to eight oscillation periods of the heavy-hole exciton density on a subpicosecond time scale are observed. An approximate linear dependence of the oscillation frequency on the light field amplitude is established. The experiment is based on a two-color detection scheme which allows for the observation of the heavy-hole exciton density via transmission changes at the light-hole exciton. The observations are in good agreement with theoretical computations based on multiband semiconductor Bloch equations.
The set of phenomenological model equations which we proposed to determine the scaling behavior of the low-density Rabi oscillations [Phys. Rev. B 48, 17 811 (1993)] is justified from the coherent part of the semiconductor Bloch equations in lowest order in the light-matter coupling. In contrast to similar short-time studies, it is shown that for resonant excitation of an excitonic state the Rabi oscillations can be described by a Ginzburg-Landau type equation which includes only the exciton-exciton interaction of the resonantly excited state but no state-filling terms or contributions from detuned excitonic or continuum resonances. Explicit calculations are performed for the bulk two-band jellium model and for a one-dimensional two-band Hubbard model.
We develop a theoretical model for slow light using excitonic population oscillation in a semiconductor quantum well. In a two-level system, if the resonant pump and the signal have a difference frequency within the range of inverse of the carrier lifetime, coherent population beating at this frequency will be generated. We analyze the excitonic population oscillation using an atomiclike model extended from semiconductor Bloch equations for both spin subsystems of the excitonic population and the electrical polarization density. The two spin subsystems are coupled by the excitation-induced dephasing rate, which depends on the net population difference in conduction and heavy hole quantized bands and the population exchange due to flip of the spins of electrons or holes. We present our theoretical results for the absorbance, the refractive index spectra, and the slowdown factor due to population oscillation at various pump intensities, and show very good agreement with experimental data. It is shown that a slowdown factor of $3.12\ifmmode\times\else\texttimes\fi{}{10}^{4}$ has been achieved for a semiconductor quantum-well structure. We also obtain analytical solutions from our theory and account for different response behaviors of the signal when its polarization is either parallel or orthogonal to that of the pump, which has also been confirmed by experiments.
A theoretical study of excitonic Rabi oscillations in semiconductor quantum wells is presented. Fundamental differences between excitonic Rabi oscillations and optical Rabi oscillations in ideal atomic or molecular 2-level systems are due to the existence of the continuous 1-particle spectrum in solids (energy bands) and the resulting strong effects of the Coulomb interaction, such as the attractive electron-hole interaction and the repulsive exchange interaction. In spite of these fundamental differences, Rabi-like oscillations of the excited electron-hole densities are computed for the case of resonant optical pumping of excitons. We compare our theoretical results with our recent experimental observation of excitonic Rabi oscillations.
We report on the optical response of a semiconductor microcavity featuring a strong exciton–photon coupling. The weak excitation regime is investigated experimentally by means of time-resolved transmission and four-wave mixing experiments. The influence of electronic disorder on the coherent exciton–photon dynamics is discussed in terms of the solutions of the Maxwell-Bloch equations. The high excitation regime is investigated by using transient sub-picosecond pump–probe experiments. Optical amplification of the probe beam (up to a factor of five), as well as a fundamental change of the optical spectra, have been found close to and above the exciton saturation density. The observed oscillations are corresponding to the Rabi frequency of the excitons in the pump field.