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The superfluid to Mott insulator transition in cavity polariton arrays is analyzed using the variational cluster approach, taking into account quantum fluctuations exactly on finite length scales. Phase diagrams in one and two dimensions exhibit important non-mean-field features. Single-particle excitation spectra in the Mott phase are dominated by particle and hole bands separated by a Mott gap. In contrast to Bose-Hubbard models, detuning allows for changing the nature of the bosonic particles from quasi-localized excitons to polaritons to weakly interacting photons. The Mott state with density one exists up to temperatures $T/ggtrsim0.03$, implying experimentally accessible temperatures for realistic cavity couplings $g$.
Jaynes-Cummings-Hubbard lattices provide unique properties for the study of correlated phases as they exhibit convenient state preparation and measurement, as well as in situ tuning of parameters. We show how to realize charge density and supersolid
Recently, condensed matter and atomic experiments have reached a length-scale and temperature regime where new quantum collective phenomena emerge. Finding such physics in systems of photons, however, is problematic, as photons typically do not inter
We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons, and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter we develop a semiclas
We unveil a mechanism for generating oscillations with arbitrary multiplets of the period of a given external drive, in long-range interacting quantum many-particle spin systems. These oscillations break discrete time translation symmetry as in time
We investigate the non-equilibrium quantum dynamics of a canonical light-matter system, namely the Dicke model, when the light-matter interaction is ramped up and down through a cycle across the quantum phase transition. Our calculations reveal a ric