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physica status solidi (b)

Microscopic Theory of Rabi Flopping, Photon Echo, and Resonant Pulse Propagation in Semiconductors

Stephan W. Koch, A. Knorr, Rolf H. Binder, Markus Lindberg

Published Sep 1, 1992• 34 citations
Publisher

Abstract

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.

DOI
10.1002/pssb.2221730118

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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.
Femtosecond-pulse propagation in resonantly excited semiconductors is investigated by numerically solving the semiconductor Maxwell-Bloch equations for plane waves. For excitation at the exciton resonance, it is shown that the pulse absorption exhibits a strongly nonlinear dependence on the input pulse area. Very long propagation distances for strong pulses are observed, but even when all dephasing processes have been neglected, no lossless propagation (self-induced transparency) was found. The influence of the electron-hole many-body effects, nonequilibrium carrier relaxation, and optical dephasing on the pulse-propagation dynamics is studied. The exchange interaction in the electron-hole plasma is shown to support large propagation distances. For excitation of the continuum states, the dependence of the absorption on the intensity of the input pulse is reduced due to the rapid carrier relaxation into quasiequilibrium distributions.
The availability of femtosecond pulses in the optical-frequency regime allows the study of coherent effects in the interaction between semiconductors and light. Because the properties of the exciting pulses become important ingredients in spectroscopy, the theoretical analysis must treat the complete time dependence of the system. For this purpose we use the semiconductor Bloch equations (SBE),1-3 which are the coupled equations of motion for the interband polarization and the electron and hole populations for an interacting electron-hole system in the random-phase approximation. The equations describe the electron-hole Coulomb attraction leading to excitonic features; they contain phasespace filling and band-gap renormalization effects, as well as the dipole interaction with the applied light field.
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.
Summary form only. The development of high-intensity ultrashort optical pulses has lead to a number of fascinating nonlinear optical propagation studies including Rabi flopping, self-induced transparency, and photon echo, to name but a few. Common to the description of these effects, is that their propagation phenomena can be described quite adequately by employing the appropriate coupled matter-Maxwell equations within the slowly-varying-envelope approximation (SVEA), i.e., the envelopes of the electromagnetic field and polarization are assumed to vary little over an optical period and wavelength. However, for several-cycle optical pulses this approximation becomes seriously questionable.
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.
Summary form only given.Free-exciton resonances in semiconductors cannot be treated as bare two-level systems because Coulomb interaction and correlation/exchange effects between the carriers substantially modify the optical Bloch equations that describe the behavior of a two-level system under the influence of an external light field. The semiconductor Bloch equations (SBEs) give a more realistic description of the dynamic response of the system on ultrafast time scales. Therefore, the coherent transients known from two-level systems in atomic physics have been found to be substantially modified in semiconductors. Whereas self-induced transparency (SIT) on bound excitons, which are known to behave as atomiclike two-level systems, has been found, the question whether SIT could also appear on a free-exciton resonance is still subject of controversial discussions. We addressed this problem in a combined theory-experiment study.