Weak-link to tunneling regime in a 3D atomic Josephson junction

We investigate the transition from weak-link transport to the tunneling Josephson regime in a three-dimensional (3D) Bose-Einstein condensate confined in a cylindrical, tube-like trap. By varying the height of a localized barrier, we map out the smooth crossover between these regimes through measurements of the critical current and Josephson oscillations. In the weak-link regime of the Josephson junction, dissipative transport is mediated by solitonic excitations in the form of vortex rings, which drive phase slips and generate a finite chemical potential difference across the junction. Increasing the barrier height suppresses these hydrodynamics excitations, yielding a tunneling-dominated Josephson regime characterized by phononic excitations. These findings elucidate the interplay between geometry, excitations, and dissipation in atomtronic weak links, and provide a quantitative framework for engineering coherent matter-wave circuits. Our results show excellent agreement with numerical simulations and analytical models.