Current-phase relations of a ring-trapped Bose-Einstein condensate with a weak link

The current-phase relations of a ring-trapped Bose-Einstein condensate interrupted by a rotating rectangular barrier are extensively investigated with an analytical solution. A current-phase diagram, single and multi-valued relation, is presented with a rescaled barrier height and width. Our results show that the finite size makes the current-phase relation deviate a little bit from the cosine form for the soliton solution in the limit of a vanishing barrier, and the periodic boundary condition selects only the plane wave solution in the case of high barrier. The reason for multi-valued current-phase relation is given by investigating the behavior of soliton solution.