Spatial correlations in driven-dissipative photonic lattices

Matteo Biondi, Saskia Lienhard, Gianni Blatter, Hakan E. Türeci, Sebastian Schmidt

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12 Scopus citations


We study the nonequilibrium steady-state of interacting photons in cavity arrays as described by the driven-dissipative Bose-Hubbard and spin-1/2 XY model. For this purpose, we develop a self-consistent expansion in the inverse coordination number of the array () to solve the Lindblad master equation of these systems beyond the mean-field approximation. Our formalism is compared and benchmarked with exact numerical methods for small systems based on an exact diagonalization of the Liouvillian and a recently developed corner-space renormalization technique. We then apply this method to obtain insights beyond mean-field in two particular settings: (i) we show that the gas-liquid transition in the driven-dissipative Bose-Hubbard model is characterized by large density fluctuations and bunched photon statistics. (ii) We study the antibunching-bunching transition of the nearest-neighbor correlator in the driven-dissipative spin-1/2 XY model and provide a simple explanation of this phenomenon.

Original languageEnglish (US)
Article number125016
JournalNew Journal of Physics
Issue number12
StatePublished - Dec 2017

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


  • cavity QED
  • cavity arrays
  • circuit QED
  • many-body physics with photons
  • quantum simulations


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