# Dynamical Exploration of Amplitude Bistability in Engineered Quantum Systems

## TL;DR

This paper demonstrates amplitude bistability in a hybrid quantum system with long-lived nitrogen-vacancy centers coupled to a superconducting resonator, revealing critical slowing down over unprecedented timescales, and lays groundwork for future quantum technologies.

## Contribution

It introduces the experimental observation of amplitude bistability in a hybrid quantum system with long coherence times, highlighting a new regime of nonlinear quantum dynamics.

## Key findings

- Observation of amplitude bistability in a hybrid quantum system.
- Demonstration of critical slowing down over tens of thousands of seconds.
- Long spin lifetime enables exploration of nonlinear quantum phenomena.

## Abstract

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.