  We present a scanning probe technique for measuring the dynamics of
individual fluxoid transitions in multiply connected superconducting
structures. In these measurements, a small magnetic particle attached to the
tip of a silicon cantilever is scanned over a micron-size superconducting ring
fabricated from a thin aluminum film. We find that near the superconducting
transition temperature of the aluminum, the dissipation and frequency of the
cantilever changes significantly at particular locations where the tip-induced
magnetic flux penetrating the ring causes the two lowest-energy fluxoid states
to become nearly degenerate. In this regime, we show that changes in the
cantilever frequency and dissipation are well-described by a stochastic
resonance (SR) process, wherein small oscillations of the cantilever in the
presence of thermally activated phase slips (TAPS) in the ring give rise to a
dynamical force that modifies the mechanical properties of the cantilever.
Using the SR model, we calculate the average fluctuation rate of the TAPS as a
function of temperature over a 32-dB range in frequency, and we compare it to
the Langer-Ambegaokar-McCumber-Halperin theory for TAPS in one-dimensional
superconducting structures.
