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The exchange of collective modes has been demonstrated to be a powerful toolfor inducing superconductivity and superfluidity in various condensed matterand atomic systems. In this article, we study the mediated interactions ofcollective excitations in an ultracold gas of hard-core bosons. We show thatthe induced interaction supports two-body states with energies, symmetries, anda number of bound states strongly dependent on the properties of the hard-coreboson gas. The ability to control the nature of the two-body bound statesmotivates the study of superfluid phases, which we address within the BKTtheory. We demonstrate how the superfluid parameters and critical temperaturescan be tuned in our system. Our findings may pave the way for futuretheoretical and experimental studies with ultracold gases and solid-statesystems.

Collective excitations of a Bose-Einstein condensate of hard-core bosons  and their mediated interactions: from two-body bound states to mediated  superfluidity