Interplay of spin and mass superfluidity in antiferromagnetic spin-1 Bose-Einstein condensates and bicirculation vortices

This paper investigates the coexistence and interplay of spin and mass superfluidity in antiferromagnetic spin-1 Bose-Einstein condensates (BEC). The hydrodynamic theory describes the spin degree of freedom by equations similar to the Landau-Lifshitz-Gilbert theory for bipartite antiferromagnetic insulators. The variables in the spin space are two subspins with absolute value ℏ/2, which play the role of two sublattice spins in the antiferromagnetic insulators. As well as in bipartite antiferromagnetic insulators, in antiferromagnetic spin-1 BEC there are two spin-wave modes: One is a gapless Goldstone mode and the other is gapped. The Landau criterion shows that in limit of small total spin (two subspins are nearly antiparallel), the instability of supercurrents starts from the gapped mode. In the opposite limit of large total spin (two subspins are nearly parallel), the gapless modes become unstable earlier than the gapped one. Mass and spin supercurrents decay via phase slips, when vortices cross streamlines of the supercurrent. The vortices participating in phase slips are nonsingular bicirculation vortices. They are characterized by two topological charges, which are winding numbers describing circulations of two angles around the vortex axis. The winding numbers can be half-integers. A particular example of a half-integer vortex is a half-quantum vortex with the superfluid velocity circulation h/2m. However, the superfluid velocity circulation is not a topological charge, and in general the quantum of this circulation can be continuously tuned from 0 to h/2m.