Laboratory observation of quantum control level sets

In controlled quantum dynamics, a level set is defined as the collection of control fields that produce a specific value for a particular observable. This paper explores the relationship between individual solutions to a control problem, and presents the first experimentally observed quantum control level sets, which are found to be continuous submanifolds. Level sets are observed for two photon transitions where the control is the spectral phase function, which is expressed as a fourth-order polynomial. For the systems studied here, the level sets are shown to be closed surfaces in the spectral phase control space. A perturbation analysis provides insight into the observed topology of the level set, which is shown to be preserved by the low-order polynomial phase representation. Each of the multiple control fields forming a level set preserves the observable value by its own distinct manipulation of constructive and destructive quantum interferences. Thus, the richness of quantum control fields meeting a particular observable value is accompanied by an equally diverse family of control mechanisms.