  We investigate, experimentally and theoretically, the dynamic optical
hysteresis of a coherently driven cavity with non-instantaneous photon-photon
interactions. By scanning the frequency detuning between the driving laser and
the cavity resonance at different speeds across an optical bistability, we find
a hysteresis area that is a non-monotonic function of the scanning speed. As
the scanning speed increases and approaches the memory time of the
photon-photon interactions, the hysteresis area decays following a power law
with exponent -1. The exponent of this power law is independent of the system
parameters. To reveal this universal scaling behavior theoretically, we
introduce a memory kernel for the interaction term in the standard
driven-dissipative Kerr model. Our results offer new perspectives for exploring
non-Markovian dynamics of light using arrays of bistable cavities with low
quality factors, driven by low laser powers, and at room temperature.
