  Recently demonstrated superconducting atom-chips provide a platform for
trapping atoms and coupling them to solid-state quantum systems. Controlling
these devices requires a full understanding of the supercurrent distribution in
the trapping structures. For type-II superconductors, this distribution is
hysteretic in the critical state due to the partial penetration of the magnetic
field in the thin superconducting film through pinned vortices. We report here
an experimental observation of this memory effect. Our results are in good
agreement with the redictions of the Bean model of the critical state without
adjustable parameters. The memory effect allows to write and store permanent
currents in micron-sized superconducting structures and paves the way towards
new types of engineered trapping potentials.
