  Nonlinear systems, whose outputs are not directly proportional to their
inputs, are well known to exhibit many interesting and important phenomena
which have profoundly changed our technological landscape over the last 50
years. Recently the ability to engineer quantum metamaterials through
hybridisation has allowed to explore these nonlinear effects in systems with no
natural analogue. Here we investigate amplitude bistability, which is one of
the most fundamental nonlinear phenomena, in a hybrid system composed of a
superconducting resonator inductively coupled to an ensemble of
nitrogen-vacancy centres. One of the exciting properties of this spin system is
its extremely long spin life-time, more than ten orders of magnitude longer
than other relevant timescales of the hybrid system. This allows us to
dynamically explore this nonlinear regime of cavity quantum electrodynamics
(cQED) and demonstrate a critical slowing down of the cavity population on the
order of several tens of thousands of seconds - a timescale much longer than
observed so far for this effect. Our results provide the foundation for future
quantum technologies based on nonlinear phenomena.
