Geometric phase driven Josephson junction: Possible experimental scheme for the search of spin superfluidity

We use the Gross-Pitaevskii equation to study Josephson tunneling between two weakly coupled Bose-Einstein condensates, which compose spin-1 bosons. We show that a rotating magnetic field on one side can produce a phase difference across the junction, resulting in an oscillatory tunneling spin current. Besides numerical calculation, we derive analytical results in two extreme cases, namely the low- and high-frequency limits: in the low-frequency limit (magnetic field rotates adiabatically), a non-Abelian geometric phase arises and leads to the oscillatory spin current. By sharp contrast, the physics is intrinsically different in the high-frequency limit, where an average Zeeman energy difference leads to an oscillatory spin current. This proposed apparatus should be promising for the future experimental search of spin superfluidity.