  Understanding and characterizing phase transitions in driven-dissipative
systems constitutes a new frontier for many-body physics. A generic feature of
dissipative phase transitions is a vanishing gap in the Liouvillian spectrum,
which leads to long-lived deviations from the steady-state as the system is
driven towards the transition. Here, we show that photon correlation
measurements can be used to characterize the corresponding critical slowing
down of nonequilibrium dynamics. We focus on the extensively studied phenomenon
of optical bistability in GaAs cavity-polaritons, which can be described as a
first-order dissipative phase transition. Increasing the excitation strength
towards the bistable range results in an increasing photon-bunching signal
along with a decay time that is prolonged by more than nine orders of magnitude
as compared to that of low density polaritons. In the limit of strong polariton
interactions leading to pronounced quantum fluctuations, the mean-field
bistability threshold is washed out. Nevertheless, the scaling of the
Liouvillian gap closing as thermodynamic limit is approached provides a
signature of the emerging dissipative phase transition. Our results establish
photon correlation measurements as an invaluable tool for studying dynamical
properties of dissipative phase transitions without requiring phase-sensitive
interferometric measurements.
