  We show that a time-dependent magnetic field inducing a periodically
modulated scattering length may lead to interesting novel scenarios for cold
gases in optical lattices, characterized by a nonlinear hopping depending on
the number difference at neighboring sites. We discuss the rich physics
introduced by this hopping, including pair superfluidity, exactly defect-free
Mott-insulator states for finite hopping, and pure holon and doublon
superfluids. We also address experimental detection, showing that the
introduced nonlinear hopping may lead in harmonically trapped gases to abrupt
drops in the density profile marking the interface between different superfluid
regions.
