Ground-state properties of few dipolar bosons in a quasi-one-dimensional harmonic trap

We study the ground state of few bosons with repulsive dipole-dipoleinteraction in a quasi-one-dimensional harmonic trap by means of the exactdiagonalization method. Up to three interaction regimes are found depending onthe strength of the dipolar interaction and the ratio of transverse to axialoscillator lengths: a regime where the dipolar Bose gas resembles a system ofweakly delta-interacting bosons, a second regime where the bosons arefermionized, and a third regime where the bosons form a Wigner crystal. In thefirst two regimes, the dipole-dipole potential can be replaced by a deltapotential. In the crystalline state, the overlap between the localized wavepackets is strongly reduced and all the properties of the boson system equalthose of its fermionic counterpart. The transition from the Tonks-Girardeau gasto the solidlike state is accompanied by a rapid increase of the interactionenergy and a considerable change of the momentum distribution, which we traceback to the different short-range correlations in the two interaction regimes.Comment: This arXiv version contains at the end the Erratum to the published versio