In my talk I will give an analytic expression for the eigenfunctions of ultracold quasi-one-dimensional atoms (bosons or fermions) with arbitrary spin in the regime of infinite repulsion. I will show that the energy levels of these systems are highly degenerate and calculate its magnetic properties, spin densities and momentum distributions. I will compare these results to numerical calculations in the regime of strong but finite repulsion.

The wave function of spinless one-dimensional bosons with infinite delta repulsion can be constructed (exactly) from the wave function of non-interacting fermions (Marvin Girardeau, 1960). The construction scheme is surprisingly easy and allows one to predict quickly many properties of these systems. However, it turned out to be rather complicated to include the spin of the particles and until now this problem was unsolved. We have found a generalization of Girardeau's method to particles with spin.