  We investigate the effect of periodic driving by an external field on systems
with attractive pairing interactions. These include spin systems (like the
ferromagnetic XXZ model) as well as ultracold fermionic atoms described by the
attractive Hubbard model. We show that a well-known phenomenon seen in
periodically driven systems--the renormalization of the exchange coupling
strength--acts selectively on bound-pairs of spins/atoms, relative to
magnon/bare atom states. Thus one can control the direction and speed of
transport of bound-pair relative to magnon/unpaired atom states, and thus
coherently achieve spatial separation of these components. Applications to
recent experiments on transport with fermionic atoms in optical lattices which
consist of mixtures of bound-pairs and bare atoms are discussed.
