Principles for determining mechanistic pathways from observable quantum control data

Hamiltonian encoding (HE) methods have been used to understand mechanism in computational studies of laser controlled quantum systems. This work studies the principles for extending such methods to extract control mechanisms from laboratory data. In an experimental setting, observables replace the utilization of wavefunctions in computational HE. With laboratory data, HE gives rise to a set of quadratic equations for the interfering transition amplitudes, and the solution to the equations reveals the mechanistic pathways. The extraction of the mechanism from the system of quadratic equations raises questions of uniqueness and solvability, even in the ideal case without noise. Symmetries are shown to exist in the quadratic system of equations, which is generally overdetermined. Therefore, the mechanism is likely to be unique up to these symmetries. Numerical simulations demonstrate the concepts on simple model systems.