Analytical Results on Quantum Correlations of Few Bosons in a Double-Well Trap

Romanian Reports in Physics Volume 67, Issue 1, 2015, Pages 273-294 Analytical Results on Quantum Correlations of Few Bosons in a Double-Well Trap (Article) Galante, M.a, Mazzarella, G.ab , Salasnich, L.abc a Dipartimento di Fisica e Astronomia “Galileo Galilei”, Via Marzolo 8, Padova, Italy b CNISM, Consorzio Interuniversitario per le Scienze Fisiche della Materia, Via Marzolo 8, Padova, Italy c Istituto Nazionale di Ottica (INO) del Consiglio Nazionale delle Ricerche (CNR) Sezione di Sesto Fiorentino, Via Nello Carrara 1, Sesto Fiorentino, Italy View additional affiliations View references (39) Abstract We consider a finite number N of interacting bosonic atoms at zero temperature confined in a one-dimensional double-well trap and study this system by using the two-site Bose-Hubbard (BH) Hamiltonian. For systems with N = 2, N = 3, and N = 4 bosons we analytically solve the eigenproblem associated to this Hamiltonian and find its lowest energetic state. We investigate the structure of the ground state by varying the strength of the boson-boson interaction from the strongly attractive regime to the deep repulsive one. We characterize the ground state of the two-site BH Hamiltonian by calculating the Fisher information F, the coherence visibility _, and the entanglement entropy S. For these quantities we provide analytical formulas that we use to study F, _, and S as functions of the interaction between the particles. We discuss the difference existing, in the deep repulsive regime, between the case with an even number of bosons and that with an odd number of particles, both in the structure of the lowest energetic state and in the behavior of the three above ground-state characterizing parameters.