# Quantum behaviour of open pumped and damped Bose-Hubbard trimers

## TL;DR

This paper investigates the quantum behavior of three-well Bose-Hubbard models with pumping and damping, revealing entanglement, squeezing, and EPR paradox states, with potential for experimental demonstration.

## Contribution

It introduces and analyzes atom-based analogs of optical cavities using three-well Bose-Hubbard models with pumping and losses, highlighting quantum correlations and non-equilibrium phenomena.

## Key findings

- Observation of quadrature squeezing
- Detection of bipartite and tripartite entanglement
- States exhibiting the EPR paradox

## Abstract

We propose and analyse analogs of optical cavities for atoms using three-well inline Bose-Hubbard models with pumping and losses. With one well pumped and one damped, we find that both the mean-field dynamics and the quantum statistics show a qualitative dependence on the choice of damped well. The systems we analyse remain far from equilibrium, although most do enter a steady-state regime. We find quadrature squeezing, bipartite and tripartite inseparability and entanglement, and states exhibiting the EPR paradox, depending on the parameter regimes. We also discover situations where the mean-field solutions of our models are noticeably different from the quantum solutions for the mean fields. Due to recent experimental advances, it should be possible to demonstrate the effects we predict and investigate in this article.