  We use optimal control in order to find the optimal shapes of pulses
maximizing the population transfer between two bound states which are coupled
via a continuum of states. We find that the optimal bounded controls acquire
the bang-interior and interior-bang form, with the bang part corresponding to
the maximum allowed control value and the interior part to values between zero
and the maximum. Then, we use numerical optimal control to obtain the switching
times and the interior control values. We compare our results with those
obtained using Gaussian STIRAP pulses, and find that the optimal method
performs better, with the extent of improvement depending on the effective
two-photon detuning and the size of incoherent losses. When we consider
effective two-photon resonance, the improvement is more dramatic for larger
incoherent losses, while when we take into account the effective two-photon
detuning, the improvement is better for smaller incoherent losses. We also
obtain how the transfer efficiency increases with increasing absolute value of
the Fano factor. The present work is expected to find application in areas
where the population transfer between two bound states through a continuum
structure plays an important role, for example coherence effects, like
population trapping and electromagnetically induced transparency, optical
analogs for light waves propagating in waveguide-based photonic structures, and
qubits coupled via a continuum of bosonic or waveguide modes.
