Abstract

The recent experimental realization of strong light matter interactions in cavity/circuit QED systems has triggered an immense interest in quantum condensed and coherent photonic systems. The addressibility of a cavity with external lasers, device integration, and high tunability make these optical systems ideally suited for quantum information and simulation tasks.

An exciting question in this emerging field is whether one can realize a Superfluid – Mott insulator transition of strongly correlated lattice polaritons. The Jaynes-Cummings-Hubbard Model (JCHM) has been introduced to describe such a quantum phase transition of light in an array of coupled QED cavities, each containing a single photonic mode interacting with a two-level system (qubit) [1]. In this talk we review recent theoretical results on the equilibrium phase diagram, elementary excitations and critical exponents of the JCHM [3,4] and discuss similarities and differences with the seminal Bose-Hubbard model (BHM) describing ultra-cold atoms in optical lattices.

[1] A. D. Greentree et al., Nature Phys. 466, 856 (2006).

[2] S. Schmidt and G. Blatter, Phys. Rev. Lett. 103, 086403 (2009).

[3] S. Schmidt and G. Blatter, Phys. Rev. Lett. 104, 216402 (2010).