  We have observed well-defined phase slips between quantized persistent
current states around a toroidal atomic (23Na) Bose-Einstein condensate. These
phase slips are induced by a weak link (a localized region of reduced
superfluid density) rotated slowly around the ring. This is analogous to the
behavior of a superconducting loop with a weak link in the presence of an
external magnetic field. When the weak link is rotated more rapidly,
well-defined phase slips no longer occur, and vortices enter into the bulk of
the condensate. A noteworthy feature of this system is the ability to
dynamically vary the weak link and hence the critical current, a feature which
is difficult to implement in superconducting or superfluid helium circuits.
