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Nonlinear THz spectroscopy of low-dimensional materials

Helm, M.; König-Otto, J.; Schmidt, J.; Dimakis, E.; Winnerl, S.; Schneider, H.

Abstract

Thanks to the development of powerful THz sources, both table-top and accelerator-based, highly nonlinear THz investigations of materials are possible today. Here we will present two recent examples of nonlinear spectroscopy on low-dimensional materials: resonant four-wave mixing in graphene under a magnetic field, and nonlinear THz spectroscopy of intersubband transitions in a semiconductor quantum well.
Graphene is predicted to be a highly nonlinear material due to its linear dispersion. Clear experimental observations are relatively scarce, however. In a magnetic field, the band structure splits up into non-equidistant Landau levels, giving rise to resonant behavior of the optical properties. We demonstrate resonantly enhanced four-wave-mixing (FWM) at a photon energy of 78 meV, resonant at a magnetic field of B = 4.5 T. The chi(3) character is clearly demonstrated by the power dependence of the four-wave-mixing signal and the narrower line shape as compared to the linear absorption. The FWM signal, proportional to the induced microscopic polarization, decays faster than the also measured pump-probe signal, beyond the time resolution of the experiment (4 ps).
Intersubband transitions in quantum wells, due to their similarities to atomic transitions, have been a playground for many fundamental optical and quantum mechanical effects as well as for novel devices for three decades. Nonlinear or quantum optical effects such as dressed states or electromagnetically induced transparency (EIT) were demonstrated, however, only in the mid-infrared range or probed in the near infrared. Here we employ our THz free-electron laser (FEL) in combination with THz time-domain spectroscopy to realize a true narrow-band pump – broad-band probe experiment: While pumping the 2-3 intersubband transition in a single GaAs/AlGaAs quantum well (at 3.5 THz = 15 meV), we probe the entire THz absorption up to 4 THz (including 1-2 and 2-3 transitions). The experiment allows one to extract the transmission change vs pump-probe time delay as well as the complete spectral shape of the transmission change at a specific time delay. We will discuss the observed spectra, including indications for the Autler-Townes splitting on the 1-2 transition.

Keywords: four-wave mixing; graphene; free-electron laser; pump-prbe; GaAs; quantum well; intersubband transition; Autler-Townes

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