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arXiv:1607.02578 · Physical Review A

Quantum entanglement in the spatial-symmetry-breaking phase transition of a driven-dissipative Bose-Hubbard dimer

Wim Casteels, Cristiano Ciuti

Published Jan 6, 2017• 79 citations
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Abstract

We theoretically explore the quantum correlation properties of a dissipative Bose-Hubbard dimer in the presence of a coherent drive. In particular, we focus on the regime where the semiclassical theory predicts a bifurcation with a spontaneous spatial symmetry breaking. The critical behavior in a well-defined thermodynamical limit of large excitation numbers is considered and analyzed within a Gaussian approach. The case of a finite boson density is also examined by numerically integrating the Lindblad master equation for the density matrix. We predict the critical behavior around the bifurcation points accompanied by large quantum correlations of the mixed steady state, in particular, exhibiting a peak in the logarithmic entanglement negativity.

DOI
10.1103/physreva.95.013812

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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 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.
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