Zurek-Kibble Domain Structures: The Dynamics of Spontaneous Vortex Formation in Annular Josephson Tunnel Junctions

Phase transitions create a domain structure with defects, which has been argued by Zurek and Kibble (ZK) to depend in a characteristic way on the quench rate. We present an experiment to measure the ZK scaling exponent $\sigma$. Using long symmetric Josephson tunnel junctions, for which the predicted index is $\sigma =0.25$, we find $\sigma =0.27\pm 0.05$. Further, we agree with the ZK prediction for the overall normalization.

Figure 1

Sketch (dimensions are not to scale) of the cryogenic insert developed to perform the junction thermal cycles with a time scale changing over a broad range.The JTJs are fabricated within the chip (shown endways), to which the surface mounted resistor (SMR) is attached. The whole is surrounded with liquid He.

Figure 2

Time dependence of the junction temperature during a ”slow” thermal cycle from 10 to 4.2 K, as inferred from the junction gap voltage. Only below the horizontal dashed line does the continuous curve describe the temperature. The thick dashed line is the best fitting curve to (2), to be extrapolated to $T_c$.

Figure 3

Log-log plot of the measured probability $P_1$ to trap one fluxon versus the quenching time ${\tau }_Q$. Each point corresponds to 300 thermal cycles. The solid line (slope $b=0.27$) is the best linear fit, in good agreement with the $0.25$ value expected for symmetric JTJs. Errors in ${\tau }_Q$ are a few percent, and systematic errors in $P_1$ due to the neglect of fluxon-antifluxon pairs are $O(P_1^2)$, again a few percent.