In the present book, we exploit the newly gained opportunity of growing artificial structures with spatial periodicity comparable to the wavelength of the confined quasiparticle, the exciton in our case, and their embedding in a microcavity. We theoretically investigate a system consisting of a planar lattice of quantum dots in a semiconductor microcavity. The peculiar symmetry of the system introduces a so called umklapp interaction between excitons and photons, leading to a discrete and finite set of photon modes that is coupled to a single exciton mode. The main idea now consists in tuning the exciton energy in such a way that at least two photon modes with different momentum are resonantly coupled to it due to the lattice symmetry. In the strong coupling regime this setting gives rise to a novel kind of quasi-particles (umklapp polaritons) with peculiar and very interesting properties, like their extraordinary light mass that makes them the lightest exciton-like quasi-particles in solids.

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