  Weak connections between superconductors or superfluids can differ from
classical links due to quantum coherence, which allows flow without resistance.
Transport properties through such weak links can be described with a single
function, the current-phase relationship, which serves as the quantum analog of
the current-voltage relationship. Here, we present a technique for
inteferometrically measuring the current-phase relationship of superfluid weak
links. We interferometrically measure the phase gradient around a ring-shaped
superfluid Bose-Einstein condensate (BEC) containing a rotating weak link,
allowing us to identify the current flowing around the ring. While our BEC weak
link operates in the hydrodynamic regime, this technique can be extended to all
types of weak links (including tunnel junctions) in any phase-coherent quantum
gas. Moreover, it can also measure the current-phase relationships of
excitations. Such measurements may open new avenues of research in quantum
transport.

Quantum Gases