A hybrid local/global optimal control algorithm for dissipative systems with time-dependent targets: formulation and application to relaxing adsorbates

Open-system quantum optimal control theory for optical control of the dynamics of a quantum system in contact with a dissipative bath is used here for explicitly time-dependent target operators, O(t). Global and local control strategies are combined in a novel algorithm by defining a set of time slices, into which the total control time is subdivided. The optimization then proceeds locally forward in time from subinterval to subinterval, while within each subinterval global control theory is used with iterative forward-backward propagation. The subintervals are connected by appropriate boundary conditions. In the present paper, all operators are represented in the basis of the eigenstates of the field-free system Hamiltonian. The algorithm is first applied to and its computational performance tested for a two-level system with energy and phase relaxation, and later extended to a many-level model. Model parameters are chosen to represent the IR pulse excitation of the adsorbate-surface stretch mode of vibrationally relaxing CO on a Cu(100) surface. Various time-dependent targets are formulated to achieve (i) population inversion, (ii) the creation of a wavepacket, and (iii) overtone excitation by "ladder climbing."