Phase-Slip Statistics of a Single Isolated Flux-Biased Superconducting Ring

We describe measurements of the thermally activated transitions between fluxoid states of a single isolated superconducting ring. We compare these measurements with theoretical predictions in which all of the relevant parameters are determined via independent characterization of the same ring. This no-free-parameters comparison shows qualitative agreement over a wide range of temperatures. We discuss possible origins for the remaining discrepancies between the data and theory, in particular the choice of model for the superconducting order parameter’s damping.

Figure 1

$I(B)$ measured for increasing $B$ (black) and fit (red) for a ring with $R=546.8\mathrm{nm}$ and $T=900$, 1010, and 1060 mK top to bottom. The purple arrow denotes the phase slip between winding numbers 12 and 13, on which the thermal activation is subsequently measured.

Figure 2

(a) Measurement of $df(B)$ over the two phase slips that were repeatedly swept in order to collect the histograms, with blue arrows as sweep directions. The sweep-down traces are shifted vertically for clarity. The location of the up or down jump is denoted with a full or empty black dot. The distance between the up and down jump is denoted as $2⟨B⟩$ (green arrow). The absence of a jump around 310 G for sweep down is due to the size of the histogram loop. (b),(c) Histograms for sweep down/up (empty/full dots, respectively). (d) The sweep-down histogram is flipped around the mean and superimposed on the sweep-up histogram. Both histograms are shown around zero mean. These measurements were performed at 700 mK.

Figure 3

(a) Histograms as a function of temperature. Circles are data, full symbols denote sweep up and empty sweep down. Temperature is marked above each histogram. Histograms are shifted horizontally for clarity. (b) Escape rates obtained from the histograms in (a). Both panels: colored regions are the LAMH prediction for histograms/escape rate respectively in the two regimes, no finite-width correction (FWC) (blue) and FWC (red).

Figure 4

(a) Mean switching value $⟨B(T)⟩$, data are shown as circles. (b) Histogram width $\sigma (T)$, where full or empty dots are data for sweep-up or down histograms. Dotted lines in (b) are a prediction for $B_c$. Both panels: colored regions are the LAMH prediction for mean/width respectively in the two regimes, no FWC (blue) and FWC (red), corresponding to cases with or without the finite-width correction, respectively.

Figure 5

The factor $\eta$ in the escape rate exponent [see Eq. (1)] extracted as detailed in the text.