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

TL;DR

This paper investigates ground state correlations of few-body bosonic systems in a harmonic trap, revealing finite particle number effects beyond the local density approximation across different interaction regimes.

Contribution

It provides a detailed analysis of correlation functions in few-particle bosonic systems, highlighting limitations of the local density approximation beyond the Gross-Pitaevskii regime.

Findings

Finite particle number effects are observed in the second order correlation function.

The local density approximation has limitations in strongly correlated regimes.

Exact numerical solutions complement analytical models for inhomogeneous systems.

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 Schroedinger equation are available employing the Multi-Configuration 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.