  Controlled quantum systems such as ultracold atoms can provide powerful
platforms to study non-equilibrium dynamics of closed many-body quantum
systems, especially since a complete theoretical description is generally
challenging. In this Letter, we present a detailed study of the rich
out-of-equilibrium dynamics of an adjustable number $N$ of uncorrelated
condensates after connecting them in a ring-shaped optical trap. We observe the
formation of long-lived supercurrents and confirm the scaling of their winding
number with $N$ in agreement with the geodesic rule. Moreover, we provide
insight into the microscopic mechanism that underlies the smoothening of the
phase profile.
