  Second-order phase transitions are governed by spontaneous symmetry breaking,
which yield collective excitations with a gapless spectrum called
Nambu-Goldstone (NG) modes. While NG modes in conservative systems are
propagating excitations, non-equilibrium phase transitions have been predicted
to feature a diffusive NG mode. We present the first experimental evidence of a
diffusive NG mode in a non-equilibrium Bose-Einstein condensate of microcavity
polaritons. The NG mode is observed as a spectral narrowing in the
spectroscopic response of the condensate. Additionally, explicitly breaking the
symmetry causes the opening of a gap in the spectrum and the disappearance of
the NG mode. Our observations confirm the diffusive dynamics of the NG mode of
non-equilibrium phase transitions and establish a promising framework to
investigate fundamental questions in statistical mechanics.
