Interactions mediated by atoms, photons, electrons, and excitons

Interactions between quasiparticles mediated by a surrounding environment are ubiquitous and lead to a range of important effects from collective modes of low temperature quantum gases, superconductivity, to the interaction between elementary particles at high energies. This perspective article is motivated by experimental progress in the fields of quantum degenerate atomic gases, cavity QED, and two-dimensional (2D) semi-conductors, which enable a systematic exploration of mediated interactions in new settings and regimes. We first describe how to microscopically calculate the quasiparticle interaction using perturbation theory, diagrammatics, and the path integral, highlighting the key role played by the quantum statistics of the quasiparticles. Recent theoretical and experimental insights into quasiparticle and mediated interactions in general obtained from atomic gases are then discussed, after which we focus on hybrid light-atom systems where a remarkable long range photon mediated interaction can be realised. Next, we describe new and puzzling results regarding the interaction between quasiparticles in 2D semiconductors. We then discuss how mediated interactions open up ways to realise new quantum phases in atomic and hybrid atom-photon systems as well as 2D semiconductors, and the perspective ends by posing some open questions and outlook.