Experimental determination of correlations between spontaneously formed vortices in a superconductor

We have imaged spontaneously created arrays of vortices (magnetic flux quanta), generated in a superconducting film quenched through its transition temperature at rates around ${10}^{9}K\mathrm{/}s$. From these images, we calculated the positional correlation functions for two vortices and for 3 vortices. We compared our results with simulations of the time dependent Ginzburg Landau equation in 2D. The results are in agreement with the Kibble-Zurek scenario of spontaneous vortex creation. In addition, the correlation functions are insensitive to the presence of a gauge field.