Observation of the diffusive Nambu-Goldstone mode of a non-equilibrium phase transition

Second-order phase transitions are governed by spontaneous symmetry break-ing, which yield collective excitations with a gapless spectrum called Nambu-Goldstone (NG) modes. While NG modes in conservative systems are propa-gating excitations, non-equilibrium phase transitions have been predicted tofeature a diffusive NG mode. We present the first experimental evidence of adiffusive NG mode in a non-equilibrium Bose-Einstein condensate of micro-cavity polaritons. The NG mode is observed as a spectral narrowing in thespectroscopic response of the condensate. Additionally, explicitly breaking thesymmetry causes the opening of a gap in the spectrum and the disappearanceof the NG mode. Our observations confirm the diffusive dynamics of the NGmode of non-equilibrium phase transitions and establish a promising frame-work to investigate fundamental questions in statistical mechanics.