Josephson Dynamics in 2D Ring-shaped Condensates

We investigate Josephson transport in a fully closed, two-dimensional superfluid circuit formed by a ring-shaped 87Rb Bose-Einstein condensate that contains two optical barriers acting as movable weak links. Translating these barriers at controlled speeds imposes a steady bias current, enabling direct mapping of the current-chemical-potential (I-{\Delta}{\mu}) characteristics. For narrow junctions (w \approx 1{\mu}m) the circuit exhibits a pronounced dc branch that terminates at a critical current I_c = 9(1) x 10^3 s^{-1}; above this threshold the system switches to an ac, resistive regime. Classical-field simulations that include the moving barriers quantitatively reproduce both the nonlinear I-{\Delta}{\mu} curve and the measured I_c, validating the underlying microscopic picture. Analysis of the ensuing phase dynamics shows that dissipation is mediated by the nucleation and traversal of vortex-antivortex pairs through the junctions, while the bulk condensate remains globally phase-locked \textemdash direct evidence of the ring's topological constraint enforcing quantized circulation. These results establish a cold-atom analogue of a SQUID in which Josephson dynamics can be resolved at the single-vortex level, providing a versatile platform for atomtronic circuit elements, non-reciprocal Josephson devices, and on-chip Sagnac interferometers for multi-axis rotation sensing.