Genetic algorithm with migration on topology conserving maps for optimal control of quantum systems

The laboratory implementation of molecular optimal control has to overcome the problem caused by the changing environmental parameters, such as the temperature of the laser rod, the resonator parameters, the mechanical parameters of the laboratory equipment, and other dependent parameters such as the time delay between pulses or the pulse amplitudes. In this paper a solution is proposed: instead of trying to set the parameter(s) with very high precision, their changes are monitored and the control is adjusted to the current values. The optimization in the laboratory can then be run at several values of the parameter(s) with an extended genetic algorithm (GA) which is tailored to such parametric optimization. The extended GA does not presuppose but can take advantage and, in fact, explores whether the mapping from the parameter(s) to optimal control field is continuous. Then the optimization for the different values of the parameter(s) is done cooperatively, which reduces the optimization time. A further advantage of the method is its full adaptiveness; i.e., in the best circumstances no information on the system or laboratory equipment is required, and only the success of the control needs to be measured. The method is demonstrated on a model problem: a pump-and-dump type model experiment on CsI.