Fully quantum scalable description of driven dissipative lattice models

Abstract

Methods for modeling large driven dissipative quantum systems are becoming increasingly urgent due to recent experimental progress in a number of photonic platforms. We demonstrate the positive-P method to be ideal for this purpose across a wide range of parameters, focusing on the archetypal driven dissipative Bose-Hubbard model. Notably, these parameters include intermediate regimes where interactions and dissipation are comparable, and especially cases with low occupations for which common semiclassical approximations can break down. The presence of dissipation can alleviate instabilities in the method that are known to occur for closed systems, allowing the simulation of dynamics up to and including the steady state. Throughout the parameter space of the model, we determine the magnitude of dissipation that is sufficient to make the method useful and stable, finding its region of applicability to be complementary to that of truncated Wigner. We then demonstrate its use in a number of examples with nontrivial quantum correlations, including a demonstration of solving the urgent open problem of large and highly non-uniform systems with even tens of thousands of sites.

17 pages, 14 figures

References in corpus (19)

• Quantum fluids of light
• Quantum trajectories and open many-body quantum systems
• Cavity QED with a Bose-Einstein condensate
• Single photons from coupled quantum modes
• On the origin of strong photon antibunching in weakly nonlinear photonic molecules
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• Critical dynamical properties of a first-order dissipative phase transition
• Observation of the photon-blockade breakdown phase transition
• Stochastic classical field model for polariton condensates
• Spontaneous microcavity-polariton coherence across the parametric threshold: Quantum Monte Carlo studies
• Twist of generalized skyrmions and spin vortices in a polariton superfluid
• Violation of the Cauchy-Schwarz inequality with matter waves
• Polariton condensation in $S$- and $P$-flatbands in a two-dimensional Lieb lattice
• The stochastic projected Gross-Pitaevskii equation
• Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation
• Hybrid phase-space simulation method for interacting Bose fields
• Stationary discrete solitons in circuit QED
• Stochastic Differential Equations for Quantum Dynamics of Spin-Boson Networks
• Spatial correlations in driven-dissipative photonic lattices