Cavity polaritons: Crossroad between non-linear optics and atomic condensates

Polaritons are mixed light-matter particles arising from the strong coupling between excitons and photons confined in a two-dimensional semiconductor microcavity. Their bosonic nature along with the possibility to directly manipulate them in a semiconductor chip makes them an excellent workbench to study non-linear properties of interacting degenerate bosons in a dissipative system. In this chapter we review the basic properties of semiconductor microcavities in the strong coupling regime including the methods used to achieve polariton condensation and to observe quantum fluid effects. We then describe how the engineering of the planar cavity using different technological approaches allows confining polaritons in low dimensional structures with a large variety of geometries. We illustrate the fascinating physics that arise from these low dimensional microstructures choosing a few examples: periodically modulated wires, coupled micropillars and polariton lattices. Cavity polaritons thus appear as a versatile platform to implement non-linear Hamiltonians and to study non-linear topological excitations.