Recent two-beam four-wave-mixing experiments on GaAs using pulses of 15 fs in duration have exhibited unusual line shapes that simultaneously show narrow spectral lines with a width of 1 meV and decays in the time-delay domain on a scale of 10 fs. This observation appears to violate time-energy uncertainty and has not been explained so far. Here we present three-beam four-wave-mixing experiments under identical conditions. The data are compared with a model of exciton-continuum coupling that explains the signatures of the threebeam data as well as the two-beam data. ͓S0163-1829͑96͒52332-5͔In a two-beam four-wave-mixing ͑FWM͒ experiment, the diffracted signal in direction 2q ជ 2 Ϫq ជ 1 is measured as a function of the time-delay t 21 between the two incident optical pulses with wave vectors q ជ 1 and q ជ 2 , respectively. Such measurement is commonly used to obtain information on the phase relaxation time T 2 of elementary excitations in solids and liquids. 1 Recent experiments on Fano resonances in GaAs under high magnetic fields, however, have shown a response that is completely governed by the autocorrelation of the laser pulses, while the FWM spectrum is much narrower than the laser spectrum, 2 equivalent to a slow real-time behavior. 2 This observation, which has been interpreted as a unique property of Fano resonances, 2 has later also been observed in experiments that resonantly excite the 1s exciton in bulk GaAs at 77 K without magnetic field, however, using much shorter ͑15 fs͒ optical pulses. 3 This strongly suggests that the underlying physics is more general and related to the coupling between the discrete 1s-exciton state and the continuum of states. For completeness, these previously published two-beam data 3 are depicted in Fig. 1.The fast decay is not a simple interference between the exciton and the continuum, 4 a process that is described by the semiconductor Bloch equations. 4 The semiconductor Bloch equations 5 -together with a phenomenological T 2 time-show a strict correlation between the decay in the time-delay domain and the width of the FWM spectrum when solved for conditions corresponding to the above experiments. This statement is also true for the optical Bloch equations, 1 the so-called local field model 6 and the so-called excitation-induced dephasing. 7 Clearly, in a situation where a photon echo occurs, the FWM spectrum can be ͑much͒ broader than the inverse of the decay in the time-delay domain. The opposite behavior described above, however, is highly unusual and remains to be explained.In this paper we present experimental three-beam FWM data that exhibit a characteristic line shape. In addition, we discuss a simple phenomenological model that reproduces most of the salient features of both the two-beam and the three-beam FWM experiments.The experimental setup is similar to the one previously employed 8 except for the extension to three beams of comparable intensity. The sech 2 -shaped incident pulses have a temporal full width at half maximum ͑FWHM͒ of 15 fs and a typical time-b...
The quantum kinetics of optically excited crystal electrons coupled to a bath of dispersionless phonons is studied in the regime of strong electron-phonon coupling. Four wave-mixing experiments on a thin film of bulk ZnSe using 13 fs blue pulses give evidence for corresponding effects that are distinctly different from those found for GaAs which has proven to be a model system for the weak-coupling regime. The experimental results on ZnSe are compared with solutions of a simple model Hamiltonian of electron-phonon interaction suitable for both GaAs and ZnSe. Exact analytic solutions of this model for arbitrary electron-phonon coupling strengths are compared with numerical solutions of the same model following the usual approach in terms of an infinite hierarchy of correlation functions. Virtues and limitations of the simple model Hamiltonian with respect to the experiment are discussed. ͓S0163-1829͑99͒10441-7͔
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