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We study the dynamics of the relative phase of a bilayer of two-dimensionalsuperfluids after the two superfluids have been decoupled. We find that onshort time scales the relative phase shows "light cone" like dynamics andcreates a metastable superfluid state, which can be supercritical. We alsodemonstrate similar light cone dynamics for the transverse field Ising model.On longer time scales the supercritical state relaxes to a disordered state dueto dynamical vortex unbinding. This scenario of dynamically suppressed vortexproliferation constitutes a reverse-Kibble-Zurek effect. We study this effectboth numerically using truncated Wigner approximation and analytically within anewly suggested time dependent renormalization group approach (RG). Inparticular, within RG we show that there are two possible fixed points for thereal time evolution corresponding to the superfluid and normal steady states.So depending on the initial conditions and the microscopic parameters of theHamiltonian the system undergoes a non-equilibrium phase transition of theKosterlitz-Thouless type. The time scales for the vortex unbinding near thecritical point are exponentially divergent, similar to the equilibrium case.

Light cone dynamics and reverse Kibble-Zurek mechanism in two-dimensional superfluids following a quantum quench