Europhys. Lett.
Volume 68, Number 2, October 2004
Page(s) 163 - 169
Section General
Published online 01 October 2004
Europhys. Lett., 68 (2), pp. 163-169 (2004)
DOI: 10.1209/epl/i2004-10129-2

Ground-state entanglement in interacting bosonic graphs

P. Giorda1, 2 and P. Zanardi1, 3, 2

1  Institute for Scientific Interchange (ISI), Villa Gualino Viale Settimio Severo 65, I-10133 Torino, Italy
2  Istituto Nazionale per la Fisica della Materia (INFM), UdR Torino-Politecnico I-10129 Torino, Italy
3  Department of Mechanical Engineering, Massachusetts Institute of Technology Cambridge, MA 02139, USA

received 24 March 2004; accepted in final form 28 June 2004

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 to the rest of the graph (mode entanglement) 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 $\tau_{\rm max}$ that leads to the maximum value of the mode entanglement. Whereas in most of the cases one finds the intuitively expected result $\tau_{\rm max}=\infty$, we show that 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 crossover between insulating and superfluid ground states.

03.67.Mn - Entanglement production, characterization, and manipulation.
03.75.Gg - Entanglement and decoherence in Bose-Einstein condensates.
03.75.Lm - Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices and topological excitations.

© EDP Sciences 2004