# Stabilization of prethermal Floquet steady states in a periodically driven dissipative Bose-Hubbard model

## TL;DR

This paper investigates how dissipation can stabilize prethermal Floquet steady states in a driven Bose-Hubbard model, preventing heating and enabling stable energy absorption from external drives.

## Contribution

It demonstrates that dissipation suppresses parametric instabilities, leading to stable steady states in a periodically driven Bose-Hubbard system, a novel insight into controlling heating in quantum many-body systems.

## Key findings

- Dissipation suppresses parametric instabilities.
- Stable steady states form when dissipation exceeds on-site interactions.
- Driven systems can emit energy to reservoirs, avoiding heating.

## Abstract

We discuss the effect of dissipation on heating which occurs in periodically driven quantum many body systems. We especially focus on a periodically driven Bose-Hubbard model coupled to an energy and particle reservoir. Without dissipation, this model is known to undergo parametric instabilities which can be considered as an initial stage of heating. By taking the weak on-site interaction limit as well as the weak system-reservoir coupling limit, we find that parametric instabilities are suppressed if the dissipation is stronger than the on-site interaction strength and stable steady states appear. Our results demonstrate that periodically-driven systems can emit energy, which is absorbed from external drivings, to the reservoir so that they can avoid heating.