The driven-dissipative Bose-Hubbard dimer: phase diagram and chaos

Abstract

We present the phase diagram of the mean-field driven-dissipative Bose-Hubbard dimer model. For a dimer with repulsive on-site interactions ($U>0$) and coherent driving we prove that ${\mathbb{Z}}_2$-symmetry breaking, via pitchfork bifurcations with sizable extensions of the asymmetric solutions, require a negative tunneling parameter ($J<0$). In addition, we show that the model exhibits deterministic dissipative chaos. The chaotic attractor emerges from a Shilnikov mechanism of a periodic orbit born in a Hopf bifurcation and, depending on its symmetry properties, it is either localized or not.

arXiv comment5 pages and 3 figures

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• Quantum metrology via chaos in a driven Bose-Josephson system
• Dissipative Quantum Chaos unveiled by Stochastic Quantum Trajectories
• Forced Oscillatory Motion of Trapped Counter-Propagating Solitons
• Semiclassical bifurcations and quantum trajectories: a case study of the open Bose-Hubbard dimer
• Non-equilibrium steady states and critical slowing down in the dissipative Bose-Hubbard model
• Self-pulsing and chaos in the asymmetrically-driven dissipative photonic Bose-Hubbard dimer: A bifurcation analysis
• Dissipative phase transition: from qubits to qudits
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