  Vorticity in closed quantum fluid circuits is known to arise in the form of
persistent currents. In this work, we develop a method to engineer transport of
the quantized vorticity between density-coupled ring-shaped atomic
Bose-Einstein condensates in experimentally accessible regimes. Introducing a
tunable weak link between the rings, we observe and characterize the
controllable periodic transfer of the current and investigate the role of
temperature on suppressing these oscillations via a range of complementary
state-of-the-art numerical methods. Our setup paves the way for precision
measurements of local acceleration and rotation.
