Getting more out of quantum control

A problem is that one does not know what is the Hamiltonian of the system (this is not just true for a system as complex as a protein but even for a small organic molecule in the gas phase) is and so a priori one cannot predict what the optimal laser pulse sequence will be to steer the photochemical reaction. This might make the problem seem hopeless but in 1992 Judson and Rabitz proposed a very clever solution: to optimise the pulse sequence using a learning algorithm that iteratively improves the control scheme. This has now successfully been implemented by many experimental groups. A comprehensive review of what has been done in condensed phases is here.

Hence, the optimal (and anti-optimal) pulse sequence contains a significant amount of information about the system. I wonder is there a way to convert this into information about the Hamiltonian of the system? For example, details of the ground state and excited state potential energy surfaces. For example, for a reaction which passes through a conical intersection surely the optimal pulse sequence defines a wave packet at the Franck-Condon point on the excited state surface with a momentum that points in the direction towards the conical intersection, i.e., it tells us exactly which vibrational modes comprise the "reaction co-ordinate". The wave packet shape and speed may be optimised to minimise intersystem crossing at the conical intersection.

The figure below is taken from a paper by Hunt and Robb shows the relevant potential energy surfaces for photoisomerisation of a model cynanine dye.