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Nonlinear systems, whose outputs are not directly proportional to theirinputs, are well known to exhibit many interesting and important phenomenawhich have profoundly changed our technological landscape over the last 50years. Recently the ability to engineer quantum metamaterials throughhybridisation has allowed to explore these nonlinear effects in systems with nonatural analogue. Here we investigate amplitude bistability, which is one ofthe most fundamental nonlinear phenomena, in a hybrid system composed of asuperconducting resonator inductively coupled to an ensemble ofnitrogen-vacancy centres. One of the exciting properties of this spin system isits extremely long spin life-time, more than ten orders of magnitude longerthan other relevant timescales of the hybrid system. This allows us todynamically explore this nonlinear regime of cavity quantum electrodynamics(cQED) and demonstrate a critical slowing down of the cavity population on theorder of several tens of thousands of seconds - a timescale much longer thanobserved so far for this effect. Our results provide the foundation for futurequantum technologies based on nonlinear phenomena.

Dynamical Exploration of Amplitude Bistability in Engineered Quantum Systems