  Atomtronics is an emerging interdisciplinary field that seeks new
functionality by creating devices and circuits where ultra-cold atoms, often
superfluids, play a role analogous to the electrons in electronics. Hysteresis
is widely used in electronic circuits, e.g., it is routinely observed in
superconducting circuits and is essential in rf-superconducting quantum
interference devices [SQUIDs]. Furthermore, hysteresis is as fundamental to
superfluidity (and superconductivity) as quantized persistent currents,
critical velocity, and Josephson effects. Nevertheless, in spite of multiple
theoretical predictions, hysteresis has not been previously observed in any
superfluid, atomic-gas Bose-Einstein condensate (BEC). Here we demonstrate
hysteresis in a quantized atomtronic circuit: a ring of superfluid BEC
obstructed by a rotating weak link. We directly detect hysteresis between
quantized circulation states, in contrast to superfluid liquid helium
experiments that observed hysteresis directly in systems where the quantization
of flow could not be observed and indirectly in systems that showed quantized
flow. Our techniques allow us to tune the size of the hysteresis loop and to
consider the fundamental excitations that accompany hysteresis. The results
suggest that the relevant excitations involved in hysteresis are vortices and
indicate that dissipation plays an important role in the dynamics. Controlled
hysteresis in atomtronic circuits may prove to be a crucial feature for the
development of practical devices, just as it has in electronic circuits like
memory, digital noise filters (e.g., Schmitt triggers), and magnetometers
(e.g., SQUIDs).
