  We examine the collective scattering of a superfluid droplet impinging on a
mesoscopic Bose-Einstein condensate (BEC) as a target. The BEC consists of an
atomic gas with two internal electronic states, each of which is trapped by a
finite-depth external potential. An off-resonant optical laser field provides a
localized coupling between the BEC components in the trapping region. This
mesoscopic scenario matches the microscopic setup for Feshbach scattering of
two particles, when a bound state of one sub-manifold is embedded in the
scattering continuum of the other sub-manifold. Within the mean-field picture,
we obtain resonant scattering phase shifts from a linear response theory in
agreement with an exact numerical solution of the real time scattering process
and simple analytical approximations thereof. We find an energy-dependent
transmission coefficient that is controllable via the optical field between 0
and 100%.
