Closed-loop quantum control utilizing time domain maps

Closed-loop laser control of quantum dynamics phenomena may be accomplished through frequency domain manipulations in the laboratory guided by a learning algorithm. This paper presents an alternative method based on the use of nonlinear input → output maps generated in the time domain, although the actual experiments and control optimization are carried out in the frequency domain. The procedure first involves the construction of input → output maps relating the field structure to the observed control performance. These maps are utilized as a substitute for actual experiments in the subsequent optimization stage in order to find the field that drives the system to a specified target. This closed-loop learning process is repeated with a sufficient number of maps until a control field is found that yields the target observable as best as possible. The overall algorithm is simulated with two model quantum systems. It is shown that excellent quality control can be achieved through this sequential learning procedure, even with individual maps that have only modest global accuracy.