Defect Formation in Quench-Cooled Superfluid Phase Transition

We use neutron absorption in rotating ${}^{3}\mathrm{He}\ensuremath{-}B$ to heat locally a $\ensuremath{\sim}100\ensuremath{-}\ensuremath{\mu}\mathrm{m}\ensuremath{-}\mathrm{size}$ volume into normal phase. When the heated region cools back in microseconds, vortex lines are formed. We record with NMR the number of lines vs the applied superflow velocity and compare to the Kibble-Zurek theory of vortex-loop freeze-out from a random network of defects. The measurements confirm the calculated loop-size distribution and indicate that the superfluid state itself forms as a patchwork of competing $A\ensuremath{-}$ and $B\ensuremath{-}\mathrm{phase}$ blobs. The consequences to the $A\ensuremath{\rightarrow}B$ transition in supercooled ${}^{3}\mathrm{He}\ensuremath{-}A$ are discussed.