Systematic Foundations of Optimal Control with Photonic and Chemical Reagents

Abstract

Optimal control of quantum systems has far-reaching applications ranging from quantum computation to chemical reaction optimization. The wide success of controlling the dynamics of quantum systems in both simulations and experiments lies in the favorable ``trap-free'' topology of the {\it control landscape}, which describes the functional relationship between the physical objective and the control variables subject to optimization. This dissertation explores the consequences of a trap-free landscape topology for controlling quantum systems with the control variables describing external laser fields, as well as chemical reagents, catalysts, processing conditions, etc.

Part I considers numerical analysis of control landscapes for the preparation of quantum states and unitary transformations. Simulations that are carefully designed to avoid placing significant constraints on the control variables find no evidence of landscape traps over tens of thousands of individual optimizations. The scaling of optimization effort is found to be highly dependent on the structure of the target quantum system and can be quantitatively understood in terms of distance and structure metrics defined on the control landscape. Constraints on the control field are found to limit the attainable objective yields and/or introduce traps on the landscape.

The experiments in Part II connect the action of shaped ultrafast laser pulses as ``photonic reagents'' to the action of traditional chemical reagents by investigating the dissociative ionization reactions of a family of halomethanes. Unoptimized and optimized photonic reagents are found to produce systematic correlations between the photoproduct yields and both the chemical composition of the substrates and the photonic reagent structure. These optimal photonic reagents are found to be transferrable to a different laser system, reproducing both optimal product yields and systematic trends over the chemical family. Control landscapes relating photoproduct yields to three control variables are found to satisfy theoretical topology predictions.

Part III introduces ``OptiChem theory'' as a unifying fundamental principle for chemical/ material synthesis and property optimization based on a trap-free control landscape topology. Extensive experimental evidence for the validity of OptiChem theory is found in the literature, with over 100 experimental trap-free landscapes reported. Applications of OptiChem theory to both NMR chemical shift prediction and identification of novel structure-property relationships in spectroscopy are presented.