In the context of quantum mechanical calculations, the properties of non-adiabatic coupling in a small system, the Shin-Metiu model, is investigated. The transition from adiabatic to non-adiabatic dynamics is elucidated in modifying the electron-nuclear interaction. This allows the comparison of weakly correlated electron-nuclear motion with the case where the strong correlations determine the dynamics. The studies of the model are extended to include spectroscopical transitions being present in two-dimensional and degenerate four-wave mixing spectroscopy. Furthermore, the quantum and classical time-evolution of the coupled motion in the complete electron-nuclear phase space is compared for the two coupling cases. Additionally, the numerically exact electron flux within the weak coupling case is compared to the Born-Oppenheimer treatment. In the last part of the thesis, the model is extended to two dimensions. The system then possesses potential energy surfaces which exhibit a typical 'Mexican hat'-like structure and a conical intersection in the adiabatic representation. Thus, it is possible to map properties of the system onto a vibronic coupling (Jahn-Teller) hamiltonian. Exact wave-packet propagations as well as nuclear wave-packet dynamics in the adiabatic and diabatic representation are performed.

This thesis describes novel concepts for the measurement of the static and dynamic properties of the electronic structure of molecules and nanocrystals in the liquid phase by means of coherent fluorescence-detected spectroscopy in two and three frequency dimensions. These concepts are based on the systematic variation ("phase cycling") of a sequence of multiple time-delayed femtosecond excitation pulses in order to decode a multitude of novel nonlinear signals from the resulting phase-dependent fluorescence signal. These signals represent any permutation of correlations between zero-, one-, two-, and three-quantum coherences. To this end, two new phase-cycling schemes have been developed which can simultaneously resolve and discriminate several nonlinear signals of sixth order, including those of the fourth order of nonlinearity. By means of the sixth-order signals recorded in this work, static properties of highly excited electronic states in molecules such as their energies, transition dipole moments, and relative displacement of electronic potential surfaces, as well as dynamic properties in terms of their relaxation kinetics, can be ascertained. Furthermore, it was shown that these signals are suitable for the characterization of exciton-exciton correlations in colloidal quantum dots and for the measurement of ultrafast exciton-exciton annihilation in molecular aggregates. The experiments performed in this thesis mark an important step towards the complete characterization of the nonlinear response of quantum systems. In view of this, the concept of fluorescence-detected multiple-quantum coherence multidimensional spectroscopy introduced here offers a unified, systematic approach. In virtue of the technical advantages such as the use of a single excitation beam and the absence of nonresonant contributions, the measurement protocols developed here can be directly transferred to other incoherent observables and to sample systems in other states of matter. Furthermore, the approaches presented here can be systematically extended to higher frequency dimensions and higher orders of nonlinearity.