Reproducing spin lattice models in strongly coupled atom-cavity systems

In an array of coupled cavities where the cavities are doped with an atomic V-system, and the two excited levels couple to cavity photons of different polarizations, we show how to construct various spin models employed in characterizing phenomena in condensed matter physics, such as the spin-1/2 Ising, XX, Heisenberg, and XXZ models. The ability to construct networks of arbitrary geometry also allows for the simulation of topological effects. By tuning the number of excitations present, the dimension of the spin to be simulated can be controlled, and mixtures of different spin types produced. The facility of single-site addressing, the use of only the natural hopping photon dynamics without external fields, and the recent experimental advances towards strong coupling, makes the prospect of using these arrays as efficient quantum simulators promising.Comment: 4 pages, 3 figures. v3: References adde

Photon and polariton fluctuations in arrays of QED-cavities

We propose to detect the Mott insulator-superfluid quantum phase transition in an array of coupled cavities by studying the polariton and photon fluctuations in a block of linear dimension M (in units of the lattice constant of the array). We explicitly show this for a one-dimensional array; the analysis can be however extended to higher dimensions. In the Mott phase polariton fluctuations are independent of the block size. In the superfluid phase they grow logarithmically with M, the prefactor being related to the compressibility of the system. In the case of photon fluctuations, the critical behaviour is encoded in the subleading scaling with the block dimension, while the leading behaviour is linear in M and non-critical. Our results have been obtained by means of the density matrix renormalization group numerical algorithm.Comment: 6 pages, 7 figure