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Entanglement dynamics and scrambling in a trapped-ion quantum simulator of the Dicke model


When quantum information "scrambles", information initially stored in the local degrees of freedom of a quantum many-body system spreads over its many-body degrees of freedom, becoming inaccessible to local probes and thus apparently lost. Scrambling and entanglement are considered key concepts that reconcile seemingly antithetical behaviors including thermalization of isolated quantum systems and information loss in black holes. Moreover, these two concepts have revolutionized our understanding of non-equilibrium phenomena. I will show that a specific family of fidelity out-of-time-order correlators (FOTOCs), recently measured in a trapped-ion  quantum simulator via time reversal of the many-body dynamics followed by a fidelity measurement, can serve as a unifying diagnostic tool that elucidates the intrinsic connection between fast scrambling, volume law entanglement, ergodicity, quantum chaos, and the associated butterfly effect in the semiclassical dynamics of the system. I will demonstrate the utility of the FOTOCs using the Dicke model which has been recently benchmarked in a 2d trapped-ion quantum simulator.