Semidefinite Programming and Reachable Sets of Dissipative Bilinear Control Systems

In this manuscript, we investigate optimal control problems arising in connection with manipulation of dissipative quantum dynamics. These problems motivate the study of a class of dissipative bilinear control systems. For these systems it is shown that the optimal solution and the reachable set can be found by solving a semidefinite program. In practice, solutions to these problems generate optimal methods for control of quantum mechanical phenomena in presence of dissipation. In the area of coherent spectroscopy, this translates into the maximum signal that can be obtained in a spectroscopy experiment.