# Optically bistable driven-dissipative Bose-Hubbard dimer: Gutzwiller approaches and entanglement

## TL;DR

This paper investigates the optical bistability of a driven-dissipative Bose-Hubbard dimer using Gutzwiller mean field methods, comparing different decoupling schemes and exploring entanglement via squeezing.

## Contribution

It introduces and compares various Gutzwiller approximation schemes for the system, highlighting the accuracy of wavefunction-based methods and reciprocal space decoupling.

## Key findings

- Wavefunction-based Gutzwiller approximation is more accurate.
- Decoupling in reciprocal space can outperform real space in certain regimes.
- Entanglement is evidenced by squeezing in reciprocal space.

## Abstract

We theoretically examine the driven-dissipative Bose-Hubbard dimer in the optical bistable regime. Various approximation schemes based on a Gutzwiller mean field decoupling are applied and compared. Depending on the system parameters we show that a decoupling with respect to the real space or to the reciprocal space can be more accurate. The Gutzwiller decoupling is applied both at the level of the density matrix and for the wavefunction during a quantum trajectory simulation. The latter is shown to be a more accurate approximation. A Gaussian approximation for the non-homogeneous anti-bonding mode is also explored. We also show that entanglement in this system is witnessed by squeezing in reciprocal space.