Photon and polariton fluctuations in arrays of QED-cavities

¹  International School for Advanced Studies (SISSA) - Via Beirut 2-4, I-34014 Trieste, Italy, EU
²  NEST-CNR-INFM & Scuola Normale Superiore - Piazza dei Cavalieri 7, I-56126 Pisa, Italy, EU
³  CNR-INFM Democritos National Simulation Center - Via Beirut 2-4, I-34014 Trieste, Italy, EU
⁴  International Centre for Theoretical Physics (ICTP) - P.O. Box 586, I-34014 Trieste, Italy, EU

Corresponding author: drossini@sissa.it

Received: 5 June 2008
Accepted: 4 July 2008

Abstract

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.