  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. With the
recent observation of quantum oscillations in superfluid 4He near 2K, we can
now envision analogous practical superfluid helium devices. The characteristic
function which determines the dynamics of such systems is the current-phase
relation Is(phi), which gives the relationship between the superfluid current
Is 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
4He weak link formed by an array of nano-apertures separating two reservoirs of
superfluid 4He. As we vary the coupling strength between the two reservoirs, we
observe a transition from a strongly coupled regime in which Is(phi) is linear
and flow is limited by 2pi phase slips, to a weak coupling regime where Is(phi)
becomes the sinusoidal signature of a Josephson weak link.
