A supercritical superfluid Or: Seeing vortices unbind

We study the dynamics of the relative phase of a bilayer of two-dimensional superfluids after the two superfluids have been decoupled, using truncated Wigner approximation. We find that on short time scales the relative phase shows ``light cone'' like dynamics, and creates a metastable quasi-superfluid state. On longer time scales this state relaxes to a disordered state due to dynamical vortex unbinding. We note that these results are directly measurable in interference experiments.