Imaging phase slip dynamics in micron-size superconducting rings

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.