The granularity of weakly occupied bosonic fields beyond the local density approximation

Abstract

We examine ground state correlations for repulsive, quasi one-dimensional bosons in a harmonic trap. In particular, we focus on the few particle limit N = 2, 3, 4, . . ., where exact numerical solutions of the many particle Schrödinger equation are available, by employing the multiconfiguration time-dependent Hartree method. Our numerical results for the inhomogeneous system are modeled with the analytical solution of the homogeneous problem using the Bethe ansatz and the local density approximation. Tuning the interaction strength from the weakly correlated Gross-Pitaevskii to the strongly correlated Tonks-Girardeau regime reveals finite particle number effects in the second-order correlation function beyond the local density approximation. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.