Current–phase relations of a ring-trapped Bose–Einstein condensate with a weak link**Project supported by the National Natural Science Foundation of China (Grant No. 11874247), the National Key Research and Development Program of China (Grant Nos. 2017YFA0304500 and 2017YFA0304203), PCSIRT, China (Grant No. IRT-17R70), and the Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices, China (Grant No. KF201703).

Abstract

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.