Crafting the dynamical structure of synchronization by harnessing bosonic multilevel cavity QED

TL;DR

This paper develops a framework for controlling and predicting the dynamical phases of collective atomic responses in cavity QED systems, revealing new synchronized chaotic phases induced by quantum correlations.

Contribution

It introduces a method to engineer and analyze the full range of synchronization phenomena in bosonic multilevel cavity QED, including a universal dynamical reduction approach.

Findings

Prediction of various dynamical responses after a quench

Discovery of a synchronized chaotic phase linked to quantum correlations

Identification of a first order non-equilibrium transition in Lyapunov exponent

Abstract

Many-body cavity QED experiments are established platforms to tailor and control the collective responses of ensembles of atoms, interacting through one or more common photonic modes. The rich diversity of dynamical phases they can host, calls for a unified framework. Here we commence this program by showing that a cavity QED simulator assembled from $N$-levels bosonic atoms, can reproduce and extend the possible dynamical responses of collective observables occurring after a quench. Specifically, by initializing the atoms in classical or quantum states, or by leveraging intra-levels quantum correlations, we craft on demand the entire synchronization/desynchronization dynamical crossover of an exchange model for $SU(N)$ spins. We quantitatively predict the onset of different dynamical responses by combining the Liouville-Arnold theorem on classical integrability with an ansatz for reducing the collective evolution to an effective few-body dynamics. Among them, we discover a synchronized chaotic phase induced by quantum correlations and associated to a first order non-equilibrium transition in the Lyapunov exponent of collective atomic dynamics. Our outreach includes extensions to other spin-exchange quantum simulators and a universal conjecture for the dynamical reduction of non-integrable all-to-all interacting systems.