  Formation and evolution of topological defects in course of non-equilibrium
symmetry breaking phase transitions is of wide interest in many areas of
physics, from cosmology through condensed matter to low temperature physics.
Its study in strongly coupled systems, in absence of quasiparticles, is
especially challenging. We investigate breaking of U(1) symmetry and the
resulting spontaneous formation of vortices in a $(2+1)$-dimensional
holographic superconductor employing gauge/gravity duality, a
`first-principles' approach to study strongly coupled systems. Magnetic fluxons
with quantized fluxes are seen emerging in the post-transition superconducting
phase. As expected in type II superconductors, they are trapped in the cores of
the order parameter vortices. The dependence of the density of these
topological defects on the quench time, the dispersion of the typical winding
numbers in the superconductor, and the vortex-vortex correlations are
consistent with predictions of the Kibble-Zurek mechanism.
