Spatial correlations in driven-dissipative photonic lattices. (22nd December 2017)

• Record Type: Journal Article
• Authors: Biondi, Matteo; Lienhard, Saskia; Blatter, Gianni; Türeci, Hakan E; Schmidt, Sebastian
• Is Part Of: New journal of physics. Volume 19:Number 12(2017:Dec.)
• Publication Date: 2017-12-22
• Subjects: quantum simulations -- cavity arrays -- cavity QED -- circuit QED -- many-body physics with photons; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/aa99b2
• Languages: English
• ISSNs: 1367-2630

Abstract

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 ( ∼ 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.