Ground-State Entanglement in Interacting Bosonic Graphs

Abstract

We consider a collection of bosonic modes corresponding to the vertices of a graph $\Gamma .$ Quantum tunneling can occur only along the edges of $\Gamma$ and a local self-interaction term is present. Quantum entanglement of one vertex with respect the rest of the graph is analyzed in the ground-state of the system as a function of the tunneling amplitude $\tau .$ The topology of $\Gamma$ plays a major role in determining the tunneling amplitude ${\tau }^{\ast }$ which leads to the maximum ground-state entanglement. Whereas in most of the cases one finds the intuitively expected result ${\tau }^{\ast }=\infty$ we show that it there exists a family of graphs for which the optimal value of$\tau$ is pushed down to a finite value. We also show that, for complete graphs, our bi-partite entanglement provides useful insights in the analysis of the cross-over between insulating and superfluid ground states

5 pages (LaTeX) 5 eps figures included

References in corpus (5)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Entanglement in quantum critical phenomena
• The entanglement of indistinguishable particles shared between two parties
• Entanglement of two-mode Bose-Einstein condensates
• Bi-partite mode entanglement of bosonic condensates on tunneling graph

Cited by in corpus (9)

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• Coherent cavity networks with complete connectivity
• Bipartite quantum states and random complex networks
• Properties of the single-site reduced density matrix in the Bose-Bose resonance model in the ground state and in quantum quenches
• Entanglement in the Bogoliubov vacuum
• Cluster Mean-Field Signature of Entanglement Entropy in Bosonic Superfluid-Insulator Transitions