Ground-state entanglement in interacting bosonic graphsP. 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 . Quantum tunneling can occur only along the edges of 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 . The topology of plays a major role in determining the tunneling amplitude that leads to the maximum value of the mode entanglement. Whereas in most of the cases one finds the intuitively expected result , we show that there exists a family of graphs for which the optimal value of 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