Close to the demixing transition, the degree of freedom associated with relative density fluctuations of a two-component Bose-Einstein condensate is described by a nondissipative Landau-Lifshitz equation. In the quasi-one-dimensional weakly immiscible case, this mapping surprisingly predicts that a dark-bright soliton should oscillate when subject to a constant force favoring separation of the two components. We propose a realistic experimental implementation of this phenomenon which we interpret as a spin-Josephson effect in the presence of a movable barrier.

• Received 28 September 2022
• Revised 18 April 2023
• Accepted 10 May 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.220403