Fully quantum scalable description of driven dissipative lattice models

TL;DR

This paper demonstrates the effectiveness of the positive-P method for simulating large, driven dissipative quantum lattice systems, especially the Bose-Hubbard model, capturing quantum correlations in regimes where semiclassical methods fail.

Contribution

It introduces the positive-P method as a scalable, stable approach for modeling complex driven dissipative quantum systems across a wide parameter range.

Findings

Positive-P method is effective for large systems with dissipation.

Dissipation can stabilize simulations that are unstable in closed systems.

Successfully modeled systems with tens of thousands of sites.

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.