Transition from phase slips to the Josephson effect in a superfluid He-4 weak link

The rich dynamics of flow between two weakly coupled macroscopic quantum reservoirs has led to a range of important technologies. Practical development has so far been limited to superconducting systems, for which the basic building block is the so-called superconducting Josephson weak link(1). With the observation of quantum oscillations' in superfluid He-4 near 2 K, we can now envision analogous practical superfluid helium devices. The characteristic function that determines the dynamics of such systems is the current-phase relation I-s(phi), which gives the relationship between the superfluid current I-s flowing through a weak link and the quantum phase difference phi across it. Here we report the measurement of the current-phase relation of a superfluid He-4 weak link formed by an array of nano-apertures separating two reservoirs of superfluid He-4. As we vary the coupling strength between the two reservoirs, we observe a transition from a strongly coupled regime in which I-s(phi) is linear and flow is limited by 2 pi phase slips, to a weak-coupling regime where I-s(phi) becomes the sinusoidal signature of a Josephson weak link.