  Phase transitions and the associated symmetry breaking are at the heart of
many physical phenomena. Coupled systems with multiple interacting degrees of
freedom provide a fertile ground for emergent dynamics that is otherwise
inaccessible in their solitary counterparts. Here we show that coupled
nonlinear optical resonators can undergo self-organization in their spectrum
leading to a first-order phase transition. We experimentally demonstrate such a
spectral phase transition in time-multiplexed coupled optical parametric
oscillators. We switch the nature of mutual coupling from dispersive to
dissipative and access distinct spectral regimes of the parametric oscillator
dimer. We observe abrupt spectral discontinuity at the first-order transition
point which can pave the way for the realization of novel transition-edge
sensors. Furthermore, we show how non-equilibrium phase transitions can lead to
enhanced sensing, where the applied perturbation is not resolvable by the
underlying linear system. Our results can pave the way for sensing using
nonlinear driven-dissipative systems leading to performance enhancements
without sacrificing sensitivity.
