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Physical review. B, Condensed matter

Various appearances of Rabi oscillations for 2π-pulse excitation in a semiconductor

Th. Östreich, A. Knorr

Published Dec 15, 1993• 32 citations
Publisher

Abstract

The number of complete Rabi oscillations of the electron-hole density induced by square optical pulses with area 2\ensuremath{\pi} is studied using the coherent part of the semiconductor Bloch equations. It is shown that the frequency of the density oscillations depends strongly on the exciton binding frequency, detuning, and the Rabi frequency of the light pulse. The well known doubling of the density oscillation frequency is only observed if the Rabi frequency and exciton binding frequency are approximately of the same order of magnitude. However for strong and weak excitation the semiconductor exhibits properties of atomic systems.

DOI
10.1103/physrevb.48.17811

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The number of complete Rabi oscillations of the electron-hole density induced by square optical pulses with area 2\ensuremath{\pi} is studied using the coherent part of the semiconductor Bloch equations. It is shown that the frequency of the density oscillations depends strongly on the exciton binding frequency, detuning, and the Rabi frequency of the light pulse. The well known doubling of the density oscillation frequency is only observed if the Rabi frequency and exciton binding frequency are approximately of the same order of magnitude. However for strong and weak excitation the semiconductor exhibits properties of atomic systems.
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.
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.
We studied the semiconductor response with respect to high intensity resonant excitation on short-time scale when the contribution of the Fermi statistics of the electrons and holes prevails. We studied both the single- and double-pulse excitations. For the latter case we considered the time evolution of the multiwave mixing exciton polarization. The main difference between the excitation by a single pulse or by two noncollinear pulses is that the Rabi oscillations of the multiwave mixing response are characterized by two harmonics. Analyzing the operator dynamics governed by the external excitation we found that there are three invariant spin classes, which do not mix with the evolution of the system. Two classes correspond to the bright exciton states and one contains all dark states. We found that the dynamics of the classes are described by six frequencies and the Rabi frequencies are only two of them (one for each bright class). We discuss the effect of the dispersion of the electrons and holes and the Coulomb interaction describing the semiconductor by the semiconductor Bloch equation (SBE). We show that if initially the system is in the ground state then the SBE preserves the invariant spin classes, thus proving the absence of the dark excitons in the framework of this description. We found that due to the mass difference between holes of different kind additional Rabi frequencies, two of those present in the operator dynamics should appear in the evolution of the exciton polarization.
The Rabi oscillation of the thin bulk semiconductor GaAs, which takes into account the effect of the local-field correction induced by the interacting excitons, is investigated by numerically solving the semiconductor Bloch equations. It is found, for a 2π few-cycle pulse excitation, that two incomplete Rabi-floppings emerge due to the competition between the Rabi frequency of the incident pulse and the internal-field matrices. Furthermore, for a sub-cycle 2π pulse excitation a complete Rabi-flopping can occur because of the absolute phase effect. We ascribe these characteristics of the Rabi oscillation to the renormalized Rabi frequency.
Abstract The phenomena of Rabi oscillations, resonant pulse propagation, and photon echo in semiconductors are investigated by numerically solving the full semiconductor Bloch equations for the example of bulk CdSe. The calculations are done for resonant femtosecond excitation at the exciton resonance. The many‐body modifications of Rabi flopping and semiconductor photon echo are discussed for a thin medium, whereas the propagation of weak and strong pulses is analyzed for an extended material. Rabi flopping of the density can lead to field reamplification and thus to long propagation distances of sufficiently strong pulses and to pulse break‐up. The area theorem known from self‐induced transparency (SIT) in atomic systems is generalized for the case of phase modulated fields and shown to be modified significantly in semiconductors. Even though no ideal SIT occurs, the Coulomb interacting electron–hole system nevertheless seems to support extremely long propagation distances of so‐called π‐pulses.
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.