Understanding adaptive laser pulse-shaping control of two-photon emission and second harmonic generation

Adaptive control offers revolutionary possibilities for informing photophysical and photochemical research because it affords the ability to interrogate complex systems without any a priori knowledge of the Hamiltonian. However, the transitioning of adaptive control to liquid-phase applications---especially those prefaced by electronic excitations---has proven difficult. In particular, it is not clear to what extent the shorter lifetimes of quantum coherence phenomena and more complicated energy distributions limit the ability to control systems in condensed media.;This dissertation work focuses on developing methods for the purposes of establishing controllability and characterizing latent control mechanisms in liquid-phase solutions that will serve as a blueprint for future applications of the adaptive methodology. The starting place for this work is the development and characterization of a prototype control experiment based on the adaptive manipulation of emission derived from two-photon excitation of liquid solutions containing dye molecules (TPE) relative to the second-harmonic generation (SHG) of the fundamental.;Using this experiment, a general framework for the dimension reduction of adaptive control experiments is developed. This work shows that an original control problem composed of several hundred control variables can be robustly understood in as little as one dimension. Additionally, this work provides experimental evidence that the control surface admits a simple topology that resembles a multidimensional 'hill'.;The topology of these control experiments is further investigated by devising a simple theoretical approximation of the control problem. With this model, novel one and multidimensional Fourier transform correlation spectroscopy techniques based on amplitude and phase switching are derived. These spectroscopies provide experimental methodologies to establish controllability and interrogate latent control mechanisms. Lastly, this methodology is abstracted to develop a description of the topologies of control surfaces in terms of Fourier transform spectroscopy. From this, a description of how the reduced dimension subspaces reveal latent control mechanisms is developed.