  Strongly coupled dissipative optical cavities with nonlinear interactions
give new opportunities to explore symmetry breaking phenomena and phase
transitions, Josephson dynamics and quantum criticality. Among the different
experimental realizations, photonic crystal coupled nanocavities operating in
the laser regime are outstanding systems since nonlinearity, gain/dissipation
and intercavity coupling can be judiciously tailored. Yet, although most common
scenarios emerge from quasi-dynamical equilibrium where the gain nearly
compensates for losses, little is known about far out-of-equilibrium dynamics
resulting, for instance, from short pulsed pumping inducing a classical
"quench". Here we show that bimodal nanolasers generically display transient
dynamics after quench which, when projected onto the nonlasing mode, exhibit
superthermal light. Such a mechanism is akin to the fast cooling of a
suspension of Brownian particles under gravity, with the intracavity intensity
playing the role of the inverse temperature. We implement a simple experimental
technique to access the probability density functions, that enabled quantifying
the distance from thermal equilibrium --and hence the degree of residual
order-- via the Gibbs entropy. This allowed us to further detect mixing of
thermal states with coherent broken parity phases, thus paving the road for
investigating far nonequilibrium thermodynamics with multimode optical
oscillators.
