@article{176691,
  author = {Matteo Biondi and Saskia Lienhard and Gianni Blatter and Hakan T{\"u}reci and Sebastian Schmidt},
  title = {Spatial correlations in driven-dissipative photonic lattices},
  abstract = { We study the nonequilibrium steady-state of interacting photons in cavity arrays as described by the driven-dissipative Bose{\textendash}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{\textendash}liquid transition in the driven-dissipative Bose{\textendash}Hubbard model is characterized by large density fluctuations and bunched photon statistics. (ii) We study the antibunching{\textendash}bunching transition of the nearest-neighbor correlator in the driven-dissipative spin-1/2 XY model and provide a simple explanation of this phenomenon. },
  year = {2017},
  journal = {New Journal of Physics},
  volume = {19},
  pages = {125016},
  month = {12/2017},
  issn = {1367-2630},
  url = {https://iopscience.iop.org/article/10.1088/1367-2630/aa99b2},
  doi = {10.1088/1367-2630/aa99b2},
  language = {eng},
}