VOLUME 73, NUMBER 8 P H Y S ICAL RE V IE% LETTERS 22 AUcUsT l994 Rabi Flopping in Semieondnetors S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, and E. O. Gobel Fachbereich Physik und Wt'ssenschaftliches Zentrum fur Materialwissenschaften, Philipps Universitat Ma-rburg, Renthof .&. D-35032 Marburg, Germany H. Nickel Deutsche Bundespost Telekom Fernmeldetechnisches Zentra)amt, D-64295 Darmstadt, Germani (Received 14 March l 994) 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. PACS numbers: 78.47. +p, 42. 50.Md Laser excited intrinsic excitations in a semiconductor provide a prototype for an interacting many-body sys- tem and, in particular, the coherent phenomena of the intrinsic excitations can yield extensive insight into the underlying many-body physics. The intrinsic excitations, however, display very short dephasing times, on the or- der of hundreds of femtoseconds or less, making the use of laser pulses with similar temporal durations necessary. Now that such pulses are routinely available, many of the optical measurements that were performed in atomic or molecular systems can be performed in semiconductors [1]. However, due to the many-body nature of a laser excited semiconductor, it is not a priori certain that co- herent phenomena, such as free polarization decay, pho- ton echo, quantum beats, self-induced transparency, etc. , should even be observable, and if so whether they will be modified in a many-body system as compared to atoms or molecules. Consequently, if they are observed, any such modifications provide a powerful tool for studying the many-body interactions themselves. One coherent phe- nomenon that is theoretically predicted to occur in a semi- conductor with many-body modifications [2], but that has not been directly experimentally observed, is the Rabi "Hopping" of the optically induced excitation density, i.e. , the induced excitation density is driven through a maxi- mum by the incident field. The oscillation of a two level system between the ground and excited states in the presence of a strong resonant driving field, often called transient nutation or Rabi Aopping, is a basic quantum mechanical effect and a textbook topic today [3]. It was first treated by Rabi in the context of molecular beam magnetic resonance experiments [4] where it was also observed [5]. Later it was observed in magnetic resonance experiments in bulk material [6]. With the advent of the laser many of the resonance effects first studied in magnetic experiments were reproduced in optical experiments on atomic and molecular systems, including Rabi Hopping [7]. The observation of density flops in semiconductors has been hindered by not only the rapid dephasing. but also by the fact the dephasing times are even shorter at elevated densities. And, to make matters worse in semiconductors, employing shorter pulses increases the hot carrier density. also increasing the dephasing. As a consequence, Rabi Hopping in semiconductors has not been previously reported. An important aspect of Rabi flopping is that it is a manifestation of the coupling between the optically induced coherence and the induced excitation density. As a consequence, it is sensitive to aspects of many-body phenomena that are not apparent in previously reported experiments in semiconductors, which have primarily focused only on the decay of the optically induced coherence (e.g. , four wave mixing) [8]. For example„ the theoretically expected enhancement of the Rabi flopping frequency by the internal field arising from many-body effects [2] is not observable in an experiment that is sensitive to the decay of the coherence alone. The experimental technique presented here for observ- ing density Hops is based on measuring the modification of the shape of a femtosecond pulse that has propagated through a thin semiconductor film, similarly to the first studies in molecules [7]. However, because the effect is weaker and on a femtosecond time scale, more elaborate techniques are necessary. The pulse shape modification is observed via cross correlation with a reference pulse, as in experiments which have observed linear pulse propagation effects [9, 10], however, this alone is not sufficient, The critical ingredient is the comparison of the pulse modi- fication after propagation through an unexcited sample to that in a weakly excited sample. This is achieved by a weak copropagating prepulse, which is chopped, and per- forming differential detection via a lock-in amplifier [as depicted schematically in the inset in Fig. 1(a)]. To show that this technique is sensitive to the polariza- tion (proportional to the temporal derivative of the exci- tation density), let us consider the cross-correlation signal detected by the lock-in„which is the difference between 1178 0031-9007/94/73(8)/li711(4)$06. 00 1994 The American Physical Society