Recently, hysteresis has been observed experimentally in a quantized superfluid circuit [S. Eckel, J. G. Lee, F. Jendrzejewski, N. Murray, C. W. Clark, C. J. Lobb, W. D. Phillips, M. Edwards, and G. K. Campbell, Nature (London) 506, 200 (2014)], which is a very important step for developing atomtronic devices. Here we find that quantized phase slips occur as the angular velocity rises, and the average angular momenta are quantized at special angular velocities, immune to the nonlinear interactions. When the spin and orbital angular momentum coupling is introduced, we find that two hysteresis loops could arise for each spin, and there exists a phase slip for spin up in one loop and spin down in the other loop. At the special angular velocities, a phase slip emerges for spin down in the lower state of the loop. Especially, multistability appears if the angular velocity is located in the hysteretic region. These results can promote experimental verification and pave the way for atomtronic devices.

• Received 21 December 2016

DOI:https://doi.org/10.1103/PhysRevA.95.033612