Low-density, one-dimensional quantum gases in a split trap

We investigate degenerate quantum gases in one dimension, trapped in a harmonic potential which is split centrally by a point-like potential. Since the single-particle eigenfunctions of such a system are known for all strengths of the central potential, the dynamics for non-interacting fermionic gases and low-density, strongly interacting bosonic gases can be investigated exactly using the Fermi-Bose mapping theorem. We calculate the exact many-particle ground state wavefunctions for both particle species, investigate soliton-like solutions, and compare the bosonic system to the well known physics of Bose gases described by the Gross-Pitaevskii equation. We also address the experimentally important questions of the creation and detection of such states.