Spectral properties of coupled cavity arrays in one dimension

The experimental progress in controlling quantum optical and atomic systems, which has been achieved over the last few years, prompted ideas for new realizations of strongly-correlated many body systems, such as ultracold gases of atoms trapped in optical lattices [1–3] or light-matter systems [4–6]. The latter consist of photons, which interact with atoms or atomic-like structures. Normally, the interaction between photons and atoms is very weak, since the interaction time is small. However, a strong interaction can be achieved when photons are confined within optical cavities. In this case, the coupling between photons and atoms leads to an effective repulsion between photons, which means that it costs energy to add additional photons to the cavity. The arrangement of such cavities on a lattice, see Fig. 1, allows the photons to “hop” between neighboring sites, provided the cavities are coupled. Quantum mechanically the coupling of adjacent cavities means that their photonic wave functions overlap. Due to the strong interaction between photons and atoms, and the introduction of a lattice of coupled cavities, a strongly-correlated phase emerges where photons are present. The light-matter models share some basic properties with the Bose-Hubbard (BH) model [7], such as the quantum phase transition from a Mott phase, where particles are localized on the lattice sites, to a superfluid phase, where par-