Evidence of a Critical Phase Transition in Purely Temporal Dynamics with Long-Delayed Feedback

Experimental evidence of an absorbing phase transition, so far associated with spatio-temporal dynamics is provided in a purely temporal optical system. A bistable semiconductor laser, with long-delayed opto-electronic feedback and multiplicative noise shows the peculiar features of a critical phenomenon belonging to the directed percolation universality class. The numerical study of a simple, effective model provides accurate estimates of the transition critical exponents, in agreement with both theory and our experiment. This result pushes forward an hard equivalence of non-trivial stochastic, long-delayed systems with spatio-temporal ones and opens a new avenue for studying out-of-equilibrium universality classes in purely temporal dynamics.