  The properties of one-dimensional superconductors are strongly influenced by
topological fluctuations of the order parameter, known as phase slips, which
cause the decay of persistent current in superconducting rings and the
appearance of resistance in superconducting wires. Despite extensive work,
quantitative studies of phase slips have been limited by uncertainty regarding
the order parameter's free energy landscape. Here we show detailed agreement
between measurements of the persistent current in isolated flux-biased rings
and Ginzburg-Landau theory over a wide range of temperature, magnetic field,
and ring size; this agreement provides a quantitative picture of the free
energy landscape. We also demonstrate that phase slips occur deterministically
as the barrier separating two competing order parameter configurations
vanishes. These results will enable studies of quantum and thermal phase slips
in a well-characterized system and will provide access to outstanding questions
regarding the nature of one-dimensional superconductivity.
