  Arrays of Josephson junctions are at the forefront of research on quantum
circuitry for quantum computing, simulation and metrology. They provide a
testing bed for exploring a variety of fundamental physical effects where
macroscopic phase coherence, nonlinearities and dissipative mechanisms compete.
Here we realize finite-circulation states in an atomtronic Josephson junction
necklace, consisting of a tunable array of tunneling links in a ring-shaped
superfluid. We study the stability diagram of the atomic flow by tuning both
the circulation and the number of junctions. We predict theoretically and
demonstrate experimentally that the atomic circuit withstands higher
circulations (corresponding to higher critical currents) by increasing the
number of Josephson links. The increased stability contrasts with the trend of
the superfluid fraction -- quantified by Leggett's criterion -- which instead
decreases with the number of junctions and the corresponding density depletion.
Our results demonstrate atomic superfluids in mesoscopic structured ring
potentials as excellent candidates for atomtronics applications, with prospects
towards the observation of non-trivial macroscopic superpositions of current
states.
