  The exchange of collective modes has been demonstrated to be a powerful tool
for inducing superconductivity and superfluidity in various condensed matter
and atomic systems. In this article, we study the mediated interactions of
collective excitations in an ultracold gas of hard-core bosons. We show that
the induced interaction supports two-body states with energies, symmetries, and
a number of bound states strongly dependent on the properties of the hard-core
boson gas. The ability to control the nature of the two-body bound states
motivates the study of superfluid phases, which we address within the BKT
theory. We demonstrate how the superfluid parameters and critical temperatures
can be tuned in our system. Our findings may pave the way for future
theoretical and experimental studies with ultracold gases and solid-state
systems.
