  Phase transitions not allowed in equilibrium steady states may happen however
at the fluctuating level. We observe for the first time this striking and
general phenomenon measuring current fluctuations in an isolated diffusive
system. While small fluctuations result from the sum of weakly-correlated local
events, for currents above a critical threshold the system self-organizes into
a coherent traveling wave which facilitates the current deviation by gathering
energy in a localized packet, thus breaking translation invariance. This
results in Gaussian statistics for small fluctuations but non-Gaussian tails
above the critical current. Our observations, which agree with predictions
derived from hydrodynamic fluctuation theory, strongly suggest that rare events
are generically associated with coherent, self-organized patterns which enhance
their probability.
