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We show that the coherent response of semiconductor band-to-band continuum transitions at room temperature, excited by 11 fs pulses at elevated carrier densities, deviates substantially from that expected for an ideal photon echo. A microscopic non-Markovian quantum kinetic theory of both electron-electron and electron-LO-phonon scattering reproduces these unusual experimental observations qualitatively and, furthermore, the famous scaling of the decay time t with carrier density n eh according to Consider a dense gas of electrons and holes generated at random places in pairs with opposite momentum in coherent quantum states in a semiconductor. It is clear that the particles will move in such a way that they screen their mutual Coulomb interaction. How long does it take that screening is built up and that scattering has destroyed the initially quantum mechanically coherent state? About one decade ago, Shank et al. addressed this fundamental question when they studied the variation of the Coulomb scattering in a dense gas of optically excited crystal electrons and holes [1,2] with density n eh using ഠ10 fs pulses and a photon echo technique. They reported that the decay time t of the photon echo signal at room temperature scales approximately according to t~n 21͞D eh , where D is the dimension of either bulk GaAs ͑D 3͒ or GaAs quantum wells ͑D 2͒. At that time, it was tempting and appealing to interpret this seemingly simple result in terms of the nearest-neighbor scattering of D-dimensional hard spheres in which case it is simple to show that the average time between different collisions scales~n 21͞D eh indeed. Today, a number of important questions are still unanswered. (i) Is it a photon echo? In analogy with a spin echo this would mean that a first short pulse excites the system, a second pulse arrives after time delay t 21 , and the coherent collective response of the system, the photon echo, peaks at yet another time delay t 21 later. Without real-time resolution [1,2], however, one only measures the energy of the echo signal versus t 21 and its decay time t. For a phenomenological dephasing time T 2 it is known that T 2 4t holds for a four-wave mixing (FWM) geometry under these conditions. Not a single experiment, however, has shown directly that the coherent real-time response of semiconductor band-to-band continuum transitions under these conditions is a photon echo indeed. Under quite different conditions (T 4 K, 100 fs pulses, and much lower carrier densities), Ref. [3] showed that the total response is not a photon echo. Only after spectral filtering (behind the sample) of those components of the FWM-signal resonant with the band-to-band continuum, were they able to isolate a contribution which corresponded to an echo. The position of this signal shifted with time delay as expected [4], its width was constant (150 fs) and given by the time resolution of their setup for all conditions. The picosecond response of inhomogeneously broadened excitonic transitions [5] as well as the response of modulation-...

We observe a triplet around the third harmonic of the semiconductor band gap when exciting 50 -100 nm thin GaAs films with 5 fs pulses at 3 10 12 W=cm 2 . The comparison with solutions of the semiconductor Bloch equations allows us to interpret the observed peak structure as being due to a twoband Mollow triplet. This triplet in the optical spectrum is a result of light-induced gaps in the band structure, which arise from coherent band mixing. The theory is formulated for full tight-binding bands and uses no rotating-wave approximation. DOI: 10.1103/PhysRevLett.92.217403 PACS numbers: 78.20.Bh, 42.50.Md, 42.65.Re, 78.47.+p When an intense light field at frequency ! 0 excites band-to-band transitions in a semiconductor, additional energy gaps can evolve within the original bands [ Fig. 1(b)]. These so-called light-induced gaps [1][2][3][4][5] are the analog of the induced doublets, split by the Rabi frequency R , in a resonantly excited two-level system [ Fig. 1(a)]. Here, two out of the four possible optical transitions are energetically degenerate. Hence, the optical spectrum consists of three peaks -the famous Mollow triplet for atoms [6,7] or excitons [8,9]. In the semiconductor band case, the light-induced gap in, e.g., the conduction band arises because the original conduction band and the one-photon sideband of the valence band lead to an avoided crossing. The corresponding Hopfield coefficients [1] determine the amount of conduction band admixture. It is crucial to note that this admixture can be finite even far away from the fictitious crossing point. This statement becomes particularly important for Rabi energies h R approaching the photon energy h! 0 , while it can be neglected for small Rabi energies. The latter case is tacitly assumed in previous graphical representations of calculated light-induced gaps. Importantly, as a result of this finite admixture, optical transitions between the induced bands are possible throughout an appreciable fraction of momentum space. Consequently, the transitions acquire considerable spectral weight. Again, two out of the four sets of possible optical transitions are energetically degenerate and a triplet results, which we will refer to as the two-band Mollow triplet in what follows.Light-induced gaps in semiconductor bands have not unambiguously been observed yet. In order to observe the splitting, it clearly has to be larger than the damping. As typical electron dephasing times under relevant conditions are on the order of 10 fs or less, the Rabi oscillation period has to be shorter than this value. This brings one close to Rabi frequencies approaching the frequency of light -a regime which has previously been referred to as carrier-wave Rabi flopping [10]. In this regime, a splitting in the third-harmonic spectra has been observed [11]. However, as the measurements have been compared only with calculations on the basis of two-level systems [11], skepticism has been expressed whether this interpretation was correct indeed. Furthermore, later theoretical work [12...

The ultrafast transition of an optical phonon resonance to a coupled phonon-plasmon system is studied. After 10-fs photoexcitation of i-InP, the buildup of coherent beats of the emerging hybrid modes is directly monitored via ultrabroadband THz spectroscopy. The anticrossing is mapped out as a function of time and density. A quantum kinetic theory of microscopic carrier-carrier and carrier-LO-phonon interactions explains the delayed formation of the collective modes. The buildup time is quantitatively reproduced to scale with the oscillation cycle of the upper branch of the coupled resonance.

We predict a carrier-density dependent oscillation, which is superimposed on the decay of the coherent control photon echo signal of a semiconductor. It reflects the oscillatory transfer of excitation back and forth between electrons and a mixed plasmon-phonon mode. This signature provides obvious and unique evidence for the finite duration of the interaction process, i.e., evidence for the collective Coulomb quantum kinetics. The theoretical predictions for the model semiconductor GaAs are reproduced in corresponding experiments. PACS numbers: 78.47. +p, 42.50.Md, 42.65.Re, 63.20.Kr Dissipation and relaxation processes in solid state physics can often be thought of as a transfer of excitation from a part of the problem, "the system," to the rest, "the bath." For the well-studied example of electron-phonon interaction in semiconductors, this separation into system and bath is obvious. Yet, it has only been recently that quantum kinetics has revealed the rich real-time quantum mechanical details of this transfer process [1][2][3]. The main new point of quantum kinetics -as compared to semiclassical Boltzmann kinetics -is that two time scales are involved: the mean time between collisions and the duration of an interaction process. One signature of this finite duration is a coherent oscillation which results from a combined electron-phonon coherence, i.e., the excitation oscillates back and forth between system and bath for a short time span, the memory time. The analog of this process for a molecule or a quantum dot, where one has discrete states rather than energy bands, would be a quantum beating between an electronic state and its vibrational sideband [4].These concepts of quantum kinetics reach far beyond solid state physics. They are currently also discussed for heavy-ion collisions, for nonequilibrium nuclear matter, and for plasmas in strong electromagnetic fields (for a recent survey, see, e.g., Ref.[5]).For the case of electron-electron interaction in semiconductors, a separation of the complete problem into system and bath contributions is not obvious at all. As a result, many groups have addressed various aspects of this fundamental problem in the dilute limit [6][7][8], where memory effects due to biexcitonic correlations do occur indeed [8], as well as for elevated carrier densities [9][10][11][12][13][14][15], where plasma screening becomes important. Intuitively, one would expect that the collective excitation of the electron gas, the plasmon, could play the role of the phonon in the above example. In analogy to the electron-phonon quantum kinetics, one should then be able to observe an oscillation corresponding to the transfer of excitation back and forth between individual electrons (the system) and the collective mode of the electrons, i.e., the plasmons (the bath). This combined electron-plasmon coherence, which must not be confused with coherent plasmons [16], has neither been observed experimentally, nor has any realistic theoretical suggestion been made as to how it could be measured.In t...

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