# Driven Bose-Hubbard dimer under nonlocal dissipation: A bistable time crystal

## TL;DR

This paper explores how nonlocal dissipation induces multistability and time-crystalline behavior in a driven Bose-Hubbard dimer, revealing novel critical phenomena and symmetry-breaking in open quantum systems.

## Contribution

It demonstrates the emergence of a period-bistable time crystal and multistability due to nonlocal dissipation, combining semiclassical and quantum analyses.

## Key findings

- Identification of amplitude bistability and symmetry breaking.
- Formation of a period-bistable time crystal with Josephson-like oscillations.
- Spectral analysis of the Liouvillian reveals critical behavior in the open quantum system.

## Abstract

We investigate the critical behavior of the open coherently-driven Bose-Hubbard dimer under nonlocal dissipation. A conserved quantity arises from the nonlocal nature of the dissipation, rendering the dimer multistable. In the weak-coupling semiclassical limit, the displayed criticality takes the form of amplitude bistability and breaking of spatial and temporal symmetries. A period-bistable time crystal is formed, consisting of Josephson-like oscillations. Mean-field dynamics and quantum trajectories complement the spectral analysis of the Liouvillian in the approach to the semiclassical limit.