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-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.

12 pages, 6 figures, submitted to New Journal of Physics (Focus issue on Many-body Physics with Photons and Polaritons) on August 22nd, 2017

References in corpus (38)

• The density-matrix renormalization group in the age of matrix product states
• Quantum fluids of light
• Imaging topological edge states in silicon photonics
• The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
• Quantum trajectories and open many-body quantum systems
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Bosonic Condensation and Disorder-Induced Localization in a Flat Band
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• Circuit QED lattices: towards quantum simulation with superconducting circuits
• Nonlinear response of the vacuum Rabi resonance
• Quantum Simulation with Interacting Photons
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Collective quantum jumps of Rydberg atoms
• Steady-state phases and tunneling-induced instabilities in the driven-dissipative Bose-Hubbard model
• Variational principle for steady states of dissipative quantum many-body systems
• Photon solid phases in driven arrays of nonlinearly coupled cavities
• Dynamical phases and intermittency of the dissipative quantum Ising model
• Observation of the photon-blockade breakdown phase transition
• Observation of a Dissipation-Induced Classical to Quantum Transition
• Emergent equilibrium in many-body optical bistability
• A Matrix-Product-Operator Approach to the Nonequilibrium Steady State of Driven-Dissipative Quantum Arrays
• Non-equilibrium dynamics of coupled qubit-cavity arrays
• Strong coupling theory for the Jaynes-Cummings-Hubbard model
• Corner space renormalization method for driven-dissipative 2D correlated systems
• Perturbative approach to Markovian open quantum systems
• Beyond mean-field bistability in driven-dissipative lattices: bunching-antibunching transition and quantum simulation
• Auxiliary master equation approach within matrix product states: Spectral properties of the nonequilibrium Anderson impurity model
• Engineering topological materials in microwave cavity arrays
• Nonequilibrium gas-liquid transition in the driven-dissipative photonic lattice
• Bose-Hubbard Model: Relation Between Driven-Dissipative Steady-States and Equilibrium Quantum Phases
• Emergence of coherence in the Mott--superfluid quench of the Bose-Hubbard model
• Collective phases of strongly interacting cavity photons
• Incompressible polaritons in a flat band
• Self-Consistent Projection Operator Theory for Quantum Many-Body Systems
• Exploring Interacting Quantum Many-Body Systems by Experimentally Creating Continuous Matrix Product States in Superconducting Circuits
• Sauter-Schwinger like tunneling in tilted Bose-Hubbard lattices in the Mott phase
• Truncated correlation hierarchy schemes for driven-dissipative multimode quantum systems
• A tunable, nonlinear Hong-Ou-Mandel interferometer

Cited by in corpus (11)

• Spectral theory of Liouvillians for dissipative phase transitions
• Multistability of Driven-Dissipative Quantum Spins
• Mean-field validity in a dissipative critical system: Liouvillian gap, $\mathbb{PT}$-symmetric antigap, and permutational symmetry in the $XYZ$ model
• Theory of classical metastability in open quantum systems
• Fully quantum scalable description of driven dissipative lattice models
• Dynamical hysteresis properties of the driven-dissipative Bose-Hubbard model with a Gutzwiller Monte Carlo approach
• Correlation-induced steady states and limit cycles in driven dissipative quantum systems
• Emergent light crystal from frustration and pump engineering
• Quantum stabilization of photonic spatial correlations
• Transition between vacuum and finite-density states in the infinite-dimensional Bose-Hubbard model with spatially inhomogeneous dissipation
• A solvable model for strongly interacting nonequilibrium excitons