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The increasing level of experimental control over atomic and

optical systems gained in recent years has paved the way

for the exploration of new physical regimes in quantum optics

and atomic physics. Some of these regimes are characterised

by the appearance of quantum many-body phenomena, originally

encountered only in condensed-matter physics, and the possibility

of experimentally accessing them in a more controlled manner.

In this talk I will try to give an overview over recent theoretical

studies concerning the use of cavity quantum electrodynamics to

create quantum many-body systems.

Based on recent experimental progress in the fabrication

of arrays of interacting micro-cavities and on their coupling

to atomic-like structures, several proposals for the realisation of

paradigmatic many-body models, such as the Bose-Hubbard

and anisotropic Heisenberg models have been developed.

Such arrays of coupled cavities offer interesting properties as

simulators of quantum many-body physics, including the full

addressability of individual sites and the accessibility of

inhomogeneous models.

This talk is part of the AMOP list series.

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