Dynamical complexity of non-Gaussian many-body systems with dissipation

TL;DR

This paper analyzes the dynamical behavior of many-body bosonic and fermionic systems with non-Gaussian interactions and dissipation, revealing conditions for Gaussianity, separability, and classical simulability, and highlighting differences between fermionic and bosonic systems.

Contribution

It provides a comprehensive characterization of how noise and interactions influence the Gaussianity, entanglement, and classical simulability of many-body quantum systems.

Findings

Fermionic systems become convex-Gaussian when dephasing exceeds non-Gaussian interactions.

Bosonic systems remain separable if particle loss and gain rates surpass Gaussian couplings.

Above certain noise thresholds, systems can be efficiently simulated classically.

Abstract

We characterize the dynamical state of many-body bosonic and fermionic many-body models with inter-site Gaussian couplings, on-site non-Gaussian interactions and local dissipation comprising incoherent particle loss, particle gain, and dephasing. We first establish that, for fermionic systems, if the dephasing noise is larger than the non-Gaussian interactions, irrespective of the Gaussian coupling strength, the system state is a convex combination of Gaussian states at all times. Furthermore, for bosonic systems, we show that if the particle loss and particle gain rates are larger than the Gaussian inter-site couplings, the system remains in a separable state at all times. Building on this characterization, we establish that at noise rates above a threshold, there exists a classical algorithm that can efficiently sample from the system state of both the fermionic and bosonic models. Finally, we show that, unlike fermionic systems, bosonic systems can evolve into states that are not convex-Gaussian even when the dissipation is much higher than the on-site non-Gaussianity. Similarly, unlike bosonic systems, fermionic systems can generate entanglement even with noise rates much larger than the inter-site couplings.