  While renormalization group theory is a fully established method to capture
equilibrium phase transitions, the applicability of RG theory to universal
non-equilibrium behavior remains elusive. Here we address this question by
measuring the non-equilibrium dynamics triggered by a quench from superfluid to
thermal phase across the Berezinskii-Kosterlitz-Thouless transition in a 2D
Bose gas. We quench the system by splitting the 2D gas in two and probe the
relaxation dynamics by measuring the phase correlation function and vortex
density via matter-wave interferometry. The dynamics occur via a two-step
process of rapid phonon thermalization followed by slow dynamic vortex
unbinding. We demonstrate universal scaling laws for the algebraic exponents
and vortex density, supported by classical-field simulations, and show their
agreement with the real-time RG theory.
