  Using heterostructures that combine a large-polarization ferroelectric
(BiFeO3) and a high-temperature superconductor (YBa2Cu3O7-{\delta}), we
demonstrate the modulation of the superconducting condensate at the nanoscale
via ferroelectric field effects. Through this mechanism, a nanoscale pattern of
normal regions that mimics the ferroelectric domain structure can be created in
the superconductor. This yields an energy landscape for magnetic flux quanta
and, in turn, couples the local ferroelectric polarization to the local
magnetic induction. We show that this form of magnetoelectric coupling,
together with the possibility to reversibly design the ferroelectric domain
structure, allows the electrostatic manipulation of magnetic flux quanta.
