Theory of multidimensional spectroscopy and excitation transfer processes in nanostructures

Advances in the manufacturing of semiconductor-based hybrid nanostructures draws attention towards possible optoelectronic and quantum computational applications. The present work develops theoretical models to study the coherent couplings and excitation transfer mechanisms in nanostructures and aims at a microscopic understanding of the underlying Coulomb-mediated processes, thus, laying the foundation to access the full functionality of the studied quantum systems. A rich and versatile theoretical toolbox is developed capable of describing a variety of semiconductor nanostructures. Nonlinear four-wave mixing spectroscopy in its various realizations depending on the specific temporal and spatial configuration and polarization of the pulse sequence is a valuable tool to infer the excitonic structure and dynamics of different kinds of quantum systems. In particular, the combination of polarization-resolved nanooptical excitation with two-dimensional double quantum coherence spectroscopy is employed to derive a quantum state tomography protocol for Förster coupled, spin-degenerate two-level quantum emitters (e.g., quantum dots). The here suggested reconstruction scheme makes it possible to resolve the internal structure of the probed quantum system by decomposing the collective optical response into the contributions from the single quantum emitters. Photon echo spectroscopy, a different four-wave mixing technique, is simulated to evidence coherent couplings in monolayer transition-metal dichalcogenides and, thus, the formation of strongly correlated higher-order states without direct analogue in conventional semiconductors. A thorough implementation of the valleyand spin-dependent optical selection rules and separation of the involved quantum pathways in the presented calculations allows to identify different types of intervalley biexcitons in measured two-dimensional spectra. A theoretical treatment including electrostatic Coulomb couplings and fine-structure splitting is developed to analyze the two-dimensional spectra measured in a two-beam four-wave mixing experiment of individual quantum dots and quantum dot molecules in rephasing and doublequantum pulse configurations. The spectral signatures can be traced back to the underlying coupling mechanisms and strengths that determine the singleand double-excitonic resonances, yielding a good agreement between theory and experiment. Using a density-matrix equation technique, the geometry-dependent excitation transfer across a semiconductor/molecule hybrid interface is studied within physically reasonable parameter ranges. For this purpose, Förster-type non-radiative coupling is modeled microscopically using a partial charge technique, and the case of creating excitons in an optically active, highly ordered layer of organic molecules by strong electrical pumping of the semiconductor substrate is considered. It is found that the interlayer coupling efficiency is highly sensitive to changes in the resonance energy detuning, the molecular coverage, the charge carrier temperature and concentration in the semiconductor quantum well, the interlayer separation, and the spatial orientation of the flat-lying molecules on top of the substrate. Finally, the theoretical framework for these hybrid inorganic/organic systems is extended to treat the Coulomb coupling between Wannier excitons in the semiconductor substrate including interface roughness, acoustic phonon scattering, and radiative recombination, and Frenkel excitons in the disordered organic film including intermolecular Coulomb interaction and the coupling to vibrational modes. For this purpose, a perturbative approach is chosen to derive the transition amplitudes between exciton densities in the hybrid system, and a cumulant expansion technique is used to describe the coupling to vibrational modes in the organic layer, which constitutes the main dephasing mechanism in such systems.