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

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.

15+3 pages, 8+3 figures; close to published version; Editors' Suggestion

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Cited by in corpus (10)

• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Entangled time-crystal phase in an open quantum light-matter system
• Chaos and Thermalization in the Spin-Boson Dicke Model
• Macroscopic quantum synchronization effects
• Realizing limit cycles in dissipative bosonic systems
• Far from equilibrium field theory for strongly coupled light and matter: dynamics of frustrated multi-mode cavity QED
• Tricritical Dicke model with and without dissipation
• Dynamics of spin-momentum entanglement from superradiant phase transitions
• Local vs non-local dynamics in cavity-coupled Rydberg atom arrays
• Synchronization of Quasi-Particle Excitations in a Quantum Gas with Cavity-Mediated Interactions