Unifying fast scrambling, thermalization and entanglement through the measurement of FOTOCs in the Dicke model

Understand

Scrambling of quantum information is the process by which 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 key concepts reconciling seemingly unrelated behaviors including thermalization of isolated quantum systems and information loss in black holes, and have revolutionized our understanding of non-equilibrium phenomena.
• Here, we demonstrate that a 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.
• We demonstrate the utility of FOTOCs by computing them in the Dicke model, an iconic model in quantum optics, recently implemented in atomic and trapped-ion setups.