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



R. J. Lewis-Swan, Arghavan Safavi-Naini, John Bollinger, Ana Maria Rey


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 considered key concepts that reconcile seemingly unrelated behaviors including thermalization of isolated quantum systems and information loss in black holes. Moreover, these two concepts have revolutionized our understanding of nonequilibrium phenomena. Here, we demonstrate 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. 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. This model describes the coupling of a large spin to an oscillator and features rich behaviors, including a quantum phase transition and chaos. Here, we show that FOTOCs provide a direct measure of the spin- phonon Renyi entropy and quantum thermalization. Moreover, we connect the FOTOCs to the variance of simple operators. This allows us to observe fast scrambling in the parameter regime where the system's classical trajectories are chaotic, and to explicitly relate the quantum and classical Lyapunov exponents in a truly quantum many-body system in the absence of finite-size effects. Our results open a path for the experimental use of FOTOCs to quantify fast scrambling, to determine bounds on quantum information processing and to identify possible candidates of black hole analogs in contr
Nature Communications


Dicke model, ergodicity, out-of-time-order correlation, quantum chaos, scrambling, trapped-ion quantum simulator, volume law entanglement


Lewis-Swan, R. , Safavi-Naini, A. , Bollinger, J. and Rey, A. (2019), Unifying fast scrambling, thermalization and entanglement through the measurement of FOTOCs in the Dicke model, Nature Communications (Accessed October 1, 2022)
Created April 4, 2019, Updated October 12, 2021