Spatial correlations in driven-dissipative photonic lattices

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

doi:10.1088/1367-2630/aa99b2

Spatial correlations in driven-dissipative photonic lattices

Journal Article · Fri Dec 22 00:00:00 EST 2017 · New Journal of Physics

DOI:https://doi.org/10.1088/1367-2630/aa99b2· OSTI ID:1500093

Biondi, Matteo ^[1]; Lienhard, Saskia ^[2]; Blatter, Gianni ^[2]; Türeci, Hakan E. ^[3]; Schmidt, Sebastian ^[2]

ETH Zurich, Zurich (Switzerland); Institute for Theoretical Physics, Zurich, Switzerland
ETH Zurich, Zurich (Switzerland)
Princeton Univ., Princeton, NJ (United States)

In this paper, 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.

View Accepted Manuscript (DOE)

Research Organization:: Princeton Univ., Princeton, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division

Grant/Contract Number:: SC0016011

OSTI ID:: 1500093

Alternate ID(s):: OSTI ID: 22990760

Journal Information:: New Journal of Physics, Journal Name: New Journal of Physics Journal Issue: 12 Vol. 19; ISSN 1367-2630

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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