Unconventional Condensation Phenomena from Superconductors to Polaritons

Systems with strongly interacting constituents can acquire macroscopic coherence and develop collective excitations at new energy scales that would be difficult to foresee from the microscopic ingredients. Bose-Einstein condensation and superconductivity are two paradigmatic examples of this kind of emergence. In this thesis I consider how these phenomena change in the presence of a cavity, broadly construed as some kind of field that is capable of mediating long-range forces across the system. I focus specifically on two examples: a kind of polariton in which strongly-interacting excitons on a lattice couple to photon field in a physical cavity, and forms a supersolid state in which the condensate coexists with spatial order; and superconductivity in strontium titanate, considered as a case in which the collective motions of the electron fluid and the lattice, respectively plasmons and optic phonons, hybridize to produce superconductivity mediated by long-range forces.