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 -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.
Highlights
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We show that dissipative chaos exist in this model and that it is intimately related to Shilnikov homoclinic bifurcations
While bistability can be encountered in one-cavity systems, spontaneous Z2-symmetry breaking requires coupled cavities with mirror symmetry; this is the case for the Bose Hubbard model (2) and spontaneous symmetry breaking phase transitions are known to exist in the form of pitchfork bifurcations [27, 30]
Summary
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. We present the phase diagram of the mean-field driven-dissipative Bose-Hubbard dimer model.
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