Protecting coherence in Optimal Control Theory: State dependent constraint approach

Optimal control theory is developed for the task of obtaining a primary objective in a subspace of the Hilbert space while avoiding other subspaces of the Hilbert space. The primary objective can be a state-to-state transition or a unitary transformation. A new optimization functional is introduced which leads to monotonic convergence of the algorithm. This approach becomes necessary for molecular systems subject to processes implying loss of coherence such as predissociation or ionization. In these subspaces controllability is hampered or even completely lost. Avoiding the lossy channels is achieved via a functional constraint which depends on the state of the system at each instant in time. We outline the resulting new algorithm, discuss its convergence properties and demonstrate its functionality for the example of a state-to-state transition and of a unitary transformation for a model of cold Rb2.