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International Conference on Ultrafast Phenomena

Collinear Transient Four-Wave-Mixing and Rabi Flopping in Semiconductors

Steven T. Cundiff, A. Knorr, Jochen Feldmann, B. Spill, W. Stolz, Stephan W. Koch, Ernst Otto Göbel

Published Jan 1, 1994• 0 citations
Publisher

Abstract

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.

DOI
10.1364/up.1994.tud.2

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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.
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 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.
Summary form only given. Optical interactions in semiconductor microcavities embedded with quantum wells enter a nonperturbative regime when the dipole coupling rate between the exciton and the cavity mode exceeds relevant decay rates. In this regime, coherent energy exchange between the exciton and the cavity mode, i.e. normal mode oscillation (NMO), takes place when the cavity mode is excited impulsively by a short laser pulse. Similar coherent oscillations have also been observed in transient four-wave mixing (FWM) responses. In this paper, we present experimental and theoretical studies on the nature of oscillations in these transient FWM responses. We show that, in contrast to earlier beliefs, oscillations in time-integrated transient FWM do not correspond to NMO of the exciton or photon populations. Theoretical studies further reveal that FWM arising from different physical mechanisms including band filling, excitation-induced dephasing, and renormalized electric fields is characterized by highly distinct coherent dynamics. Oscillations in transient FWM reflect interference between these coherent optical processes and can be used as a unique probe for exciton many-body interactions in the nonperturbative regime.
Using laser pulses of duration comparable to semiconductor relaxation and dephasing times, the coherent phenomena common to two-level systems have been demonstrated in II-VI and III-V semiconductors. These light-matter interactions are characterized by electrons and holes in their initially excited states and/or a macroscopic polarization that persists after the excitation. A nonthermal carrier distribution was observed in bulk CdSe, demonstrating the extremely fast energy relaxation possible when carrier-LO-phonon scattering is included. Quantum-confined CdSe microcrystallites were then employed to limit the available decay avenues. The one and two-pair transitions were characterized, and using spectral hole-burning, energy relaxation was shown to be substantially slower than in bulk. Dipole dephasing remained very rapid. Persistent macroscopic polarization was demonstrated in semiconductors through pump and probe experiments conducted on time scales faster than the inverse linewidth of the exciton. In the first set of experiments, it was found that the exciton optical Stark shift deviates from that predicted by a steady-state theory. The shift is smaller than expected and lasts longer than the pump pulse. Both effects are explained by free evolution of the exciton's polarization. Transient exciton bleaching is observed and shown to be a result of adiabatic following. In a second study of coherent polarization, spectral oscillations at negative delay times were studied. Oscillations were measured in a wide variety of semiconductors, temporally preceding several different pump-probe phenomena. By comparison with a semiclassical theory, it was shown that spectral oscillations in the spectral region of the exciton are evidence of persistent exciton polarization. Oscillations in the band are due to four wave mixing of the pump and probe beams.