Low-density, one-dimensional quantum gases in the presence of a localized attractive potential

We investigate low-density, quantum-degenerate gases in the presence of a localized attractive potential in the centre of a one-dimensional harmonic trap. The attractive potential is modelled using a parameterized d-function, allowing us to determine all single-particle eigenfunctions analytically. From these we calculate the ground-state many-body properties for a system of spin-polarized fermions and, using the Bose-Fermi mapping theorem, extend the results to strongly interacting bosonic systems. We discuss the single-particle densities, the pair-correlation functions, the reduced single-particle density matrices and the momentum distributions as a function of the particle number and strength of the attractive point potential. As an important experimental observable, we place special emphasis on spatial coherence properties of such samples.