  We explore novel features of a nonrelativistic fermionic superfluid in which
the pairing interaction includes a contribution from the exchange of a
dynamical bosonic mode. We show that the dynamical boson exchange (DBE), which
causes a retarded pairing interaction and thus violates the Galilean invariance
of the fermion sector, generically leads to a quantum reduction of the
superfluid density and hence a nonzero normal fraction even at zero
temperature. For spin-singlet pairing, the DBE also leads to a nonvanishing
spin susceptibility at zero temperature, providing a mechanism for the
coexistence of pairing and magnetization. While these effects are negligible
for weak pairing, they become sizable at strong pairing. For the double
superfluidity in ultracold Fermi-Bose mixtures, the superfluid density
reduction for the fermion sector induced by the DBE just gives rise to the
Andreev-Bashkin drag effect, indicating a strong entrainment between the two
superfluid components. The DBE may also provide a new source for the superfluid
fraction reduction of neutron matter, which is crucial for models of neutron
star glitches based on neutron superfluidity.
