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Physical Review Letters

Rabi Flopping in Semiconductors

Steven T. Cundiff, A. Knorr, Jochen Feldmann, S. W. Koch, Ernst Otto Göbel, Heinrich. Nickel

Published Aug 22, 1994• 159 citations
Publisher

Abstract

By examining the interaction of two copropagating ultrafast optical pulses in a semiconductor multiple quantum well, we experimentally determine the temporal dependence of the induced polarization. Based on this technique we observe that the optically induced density goes through a maximum at sufficiently high excitation intensity. Microscopic calculations show that the observed phenomena are a manifestation of Rabi flopping in semiconductors.

DOI
10.1103/physrevlett.73.1178

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By examining the interaction of two copropagating ultrafast optical pulses in a semiconductor multiple quantum well, we experimentally determine the temporal dependence of the induced polarization. Based on this technique we observe that the optically induced density goes through a maximum at sufficiently high excitation intensity. Microscopic calculations show that the observed phenomena are a manifestation of Rabi flopping in semiconductors.
Abstract The optically induced excitation density in a semiconductor multiple quantum well is experimentally observed to go through a maximum at sufficiently high excitation intensity. This is achieved by using the interaction of two copropagating ultrafast optical pulses to extract the temporal dependence of the optically induced polarization, which is proportional to the temporal derivative of the excitation density. Solutions to the Maxwell semiconductor Bloch equations show that the observations are a manifestation of Rabi flopping in semiconductors. The results confirm the presence of many‐body modifications to the Rabi flopping for the excitation conditions used in the experiment.
The ready availability of sub-picosecond pulses from mode locked lasers has led to a large number of experiments being performed on the coherent interaction between light and extended electronic states in semiconductors and semiconductor heterostructures [1]. In tandem with these experimental efforts the theoretical understanding of these phenomena has also made significant strides [2]. However, one theoretical prediction which has not been directly experimentally observed is the phenomenon of Rabi-flopping in semiconductors [3]. Rabi-flopping is the oscillation of the excited state population induced by a strong light field. Here we present experimental results based on the nonlinear interaction of two copropagating pulses and show that in the theoretical treatment the observed behavior arises from the occurrence of a Rabi flop.
Summary form only given. Illuminating a semiconductor with a constant light intensity can lead to a periodic oscillation of the inversion, a phenomenon which is known as Rabi flopping. Using pulsed excitation, Rabi flopping has been observed on semiconductors and exhibited periods in the range from 100 fs to 1 ps. Hughes (Phys. Rev. Lett. vol. 81, p. 3363, 1998) theoretically investigated the question of what happens when the light intensity becomes so high that the period of one Rabi oscillation becomes comparable with that of only one cycle of light, 2.7 fs for the band edge of GaAs, and predicted a new phenomenon: carrier-wave Rabi flopping. During a carrier-wave Rabi oscillation, the optical polarization becomes strongly distorted, which can lead to a double-peak structure (the Fourier-transform of the Rabi oscillation) in the third-harmonic (3/spl omega/) spectra. This characteristic shape is quite different from the well-known off-resonant third-harmonic generation. Importantly, resonant effects contain information on the dynamics of electronic resonances-potentially on the timescale of a single optical cycle. It is clear that, under these conditions, the usual envelope approximation breaks down, i.e. both the rotating wave approximation (RWA) as well as the slowly varying envelope approximation (SVEA) must not be used. This paper investigates carrier-wave Rabi flopping experimentally.
We demonstrate that the temporal pulse phase remains essentially unaltered before separate phase characteristics are developed when propagating high-intensity pulses coherently on the exciton resonance of an optically thick semiconductor. This behavior is a clear manifestation of self-induced transmission and pulse breakup into soliton-like pulses due to Rabi flopping of the carrier density. Experiments using a novel fast-scan cross-correlation frequency-resolved optical gating (XFROG) method are in good agreement with numerical calculations based on the semiconductor Bloch equations.
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.