{
  "id": "1709.03762",
  "version": "v1",
  "published": "2017-09-12T09:38:26.000Z",
  "updated": "2017-09-12T09:38:26.000Z",
  "title": "Spatial correlations in driven-dissipative photonic lattices",
  "authors": [
    "Matteo Biondi",
    "Saskia Lienhard",
    "Gianni Blatter",
    "Hakan E. Tureci",
    "Sebastian Schmidt"
  ],
  "comment": "12 pages, 6 figures, submitted to New Journal of Physics (Focus issue on Many-body Physics with Photons and Polaritons) on August 22nd, 2017",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "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 ($\\sim 1/z$) 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-12T09:38:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "driven-dissipative photonic lattices",
      "spatial correlations",
      "xy model",
      "large density fluctuations",
      "inverse coordination number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}