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

Abstract

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 &gt; 0) and coherent driving, we prove that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> -symmetry breaking, via pitchfork bifurcations with sizable extensions of the asymmetric solutions, require a negative tunneling parameter ( J &lt; 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.