Photon and polariton fluctuations in arrays of QED-cavities

TL;DR

This paper proposes a method to detect the Mott insulator-superfluid phase transition in coupled cavity arrays by analyzing photon and polariton fluctuations, using numerical simulations.

Contribution

It introduces a fluctuation-based detection scheme for quantum phase transitions in cavity arrays, extending analysis to higher dimensions.

Findings

Polariton fluctuations are constant in the Mott phase and grow logarithmically in the superfluid phase.

Photon fluctuations show critical behavior in subleading scaling, with leading linear behavior being non-critical.

Results obtained via density matrix renormalization group simulations.

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.