The nonlinear optical response of quantum well excitons is investigated experimentally using polarization resolved four wave mixing, optical-pump optical-probe, and optical-pump Terahertz-probe spectroscopy. The four-wave mixing data reveal clear signatures of coherent biexcitons which concur with straight-forward polarization selection rules at the Γ point. The type-I samples show the well-established time-domain beating signatures in the transients as well as the corresponding spectral signatures clearly. The latter are also present in type-II samples; however, the smaller exciton and biexciton binding energies in these structures infer longer beating times which, in turn, are accompanied by faster dephasing of the type-II exciton coherences. Furthermore, the THz absorption following spectrally narrow, picosecond excitation at energies in the vicinity of the 1s exciton resonance are discussed. Here, the optical signatures yield the well-established redshifts and blueshifts for the appropriate polarization geometries in type-I quantum well samples also termed “AC Stark Effect”. The THz probe reveals intriguing spectral features which can be ascribed to coherent negative absorption following an excitation into a virtual state for an excitation below the 1s exciton resonance. Furthermore, the scattering and ionization of excitons is discussed for several excitation geometries yielding control rules for elastic and inelastic quasiparticle collisions.
The nonlinear optical response of quantum well excitons excited by optical fields is analyzed by numerical solutions of the semiconductor Bloch equations. Differential absorption spectra are computed for resonant pumping at the exciton resonance and the dependence of the absorption changes on the polarization directions of the pump and probe pulses is investigated. Coherent biexcitonic many-body correlations are included in our approach up to third-order in the optical fields. Results are presented for spatially-direct type-I and spatiallyindirect type-II quantum well systems. Due to the spatial inhomogeneity, in type-II structures a finite coupling between excitons of opposite spins exists already on the Hartree-Fock level and contributes to the absorption changes for the case of opposite circularly polarized pump and probe pulses.
The semiconductor Bloch equations provide a very versatile and microscopic approach to compute and analyze optical and electronic properties of semiconductors. Here, we focus on high harmonic generation arising from the driving of crystalline systems with very strong optical and Terahertz pulses. Implementing a proper gauge allows us to solve the semiconductor Bloch equations in the length gauge. The length gauge turns out to be advantageous since it converges for a smaller number of bands than the velocity gauge and, in addition, enables a unique distinction between inter- and intraband contributions. Besides odd harmonics polarized parallel to the incoming field our approach also describes even harmonics which originate from the Berry curvature and are polarized perpendicular to the incident field. Next, we demonstrate that the electron and hole collision/recombination dynamics is mainly responsible for the anisotropy of the interband high harmonic generation. Our findings connect the electron/hole backward scattering to van Hove singularities and the forward scattering with critical lines in the band structure and we show that this dynamics can be controlled by properly designed two-color fields. Furthermore, we consider excitonic effects within a two-band model and show that they can strongly enhance the high harmonic emission intensity for suitably chosen incident pulses. When an odd-order harmonic corresponds to the energy of the 1s exciton this harmonic is several orders of magnitude larger than the emission from non-interacting electrons and holes.
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