Quantum many body physics with strongly interacting light-matter systems
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In the physics of strongly correlated quantum systems the electromagnetic
radiation has traditionally assumed the role of a spectroscopic probe 
and thus treated as a classical field. In recent years an increasing control
over light-matter interactions at the genuine quantum level
has been achieved due to experimental developments in quantum optics and
quantum electronics. This has brought forth a novel class of many body
systems where elementary excitations are made by single quanta of light 
and matter. These hybrid setups are currently attracting a great experimental 
and theoretical interest, for the unique features they offer to explore quantum 
many body physics in novel far from equilibrium regimes. 
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Motivated by the experimental effort, currently ongoing at Princeton, to realize
these correlated systems of photons and atoms using superconducting circuits, in
this talk I will discuss the physics of large arrays of microwave resonators
coupled to superconducting qubits via the elementary Rabi non-linearity. I will
argue that the very nature of photon field and its interaction with matter-like
excitations allows to stabilize finite-density quantum phases of correlated
photons out of the vacuum. I will discuss the properties of these phases and the
quantum phase transition occurring between them and highlight the differences
with the physics of interacting massive quantum particles.