Quasiparticle descriptions are a powerful tool in condensed matter physics as they provide an analytical treatment of interacting systems. In this thesis we will apply this tool to theoretically describe two systems: a superconductor interacting with cavity photons and a flowing Bose-Einstein condensate forming a sonic black hole.

First we will consider a two-dimensional s-wave BCS superconductor coupled to microwave cavity photons. We show how a nonequilibrium occupation of the photons can induce a nonequilibrium distribution of superconductor Bogoliubov quasiparticles, yielding an enhancement of the superconducting gap. The analytic dependence of this enhancement is provided in terms of the photon spectral and occupation functions, offering a large parameter space over which enhancement exists.

Next, we analyze the equilibrium properties of a similar superconductor-cavity structure which has strong sub-dominant d-wave pairing interaction. In this case there is a collective mode known as the Bardasis-Schrieffer mode, which is essentially an uncondensed d-wave Cooper pair. We show that by driving an external supercurrent through the sample the Bardasis-Schrieffer mode can be hybridized with cavity photons, forming exotic Bardasis-Schrieffer-polaritons.

We then turn to consider a flowing Bose-Einstein condensate. In the presence of inhomogeneous flow, the long-wavelength motion of quasiparticles can be mapped onto the kinematics of matter fields in a curved spacetime. This mapping allows for the simulation of a black hole and its interactions with quantum fields via analogy. We show that in the case of a step-like jump in the condensate flow the emission of analogue Hawking radiation is accompanied by evanescent modes which are pinned to the event horizon.

Finally, we generalize this setup to include pseudo-spin half spinor Bose condensates. In this case, we show that the analogue spacetime the quasiparticles experience can be of the exotic Newton-Cartan type. Newton-Cartan gravity -- the geometric formulation of Newtonian gravity -- is realized when the Goldstone mode disperses quadratically as opposed to linearly. The nature of the analogue spacetime is controlled by the presence or absence of an easy-axis anisotropy in the boson spin-exchange interaction. We conclude by arguing that this Newton-Cartan spacetime can be experimentally realized in current platforms.