Boson Pairs in a One-dimensional Split Trap

Department of Physics, National University of Ireland, UCC, Cork, Republic of Ireland(Dated: February 1, 2008)We describe the properties of a pair of ultracold bosonic atoms in a one-dimensional harmonictrapping potential with a tunable zero-ranged barrier at the trap centre. The full characterisationof the ground state is done by calculating the reduced single-particle density, the momentum dis-tribution and the two-particle entanglement. We derive several analytical expressions in the limitof infinite repulsion (Tonks-Girardeau limit) and extend the treatment to finite interparticle inter-actions by numerical solution. As pair interactions in double wells form a fundamental buildingblock for many-body systems in periodic potentials, our results have implications for a wide rangeof problems.