Controllable arrays of ions and ultra-cold atoms can simulate complex many-body phenomena and may provide insights into unsolved problems in modern science. To this end, experimentally feasible protocols for quantifying the buildup of quantum correlations and coherence are needed, as performing full state tomography does not scale favorably with the number of particles. Here we develop and experimentally demonstrate such a protocol, which uses time reversal of the manybody dynamics to measure out-of-time-order correlation functions (OTOCs) in a long-range Ising spin quantum simulator with more than 100 ions in a Penning trap. By measuring a family of OTOCs as a function of a tunable parameter we obtain fine-grained information about the state of the system encoded in the multiple quantum coherence spectrum, extract the quantum state purity, and demonstrate the buildup of up to 8-body correlations. Future applications of this protocol could enable studies of many-body localization, quantum phase transitions, and tests of the holographic duality between quantum and gravitational systems.Time-reversal has fascinated and puzzled physicists for centuries. In an iconic example, Josef Loschmidt argued that the second law of thermodynamics would be violated by time-reversing an entropy-increasing collision [1]. Ludwig Boltzmann responded by formulating the probabilistic definition of entropy, one of the cornerstones of statistical mechanics, and, now a fundamental concept in quantum information. Since the days of Boltzmann and Loschmidt, the notion of time-reversal has moved from the arena of thought experiments into the laboratory, with time-reversal of non-interacting quantum systems in the form of Hahn spin echoes [2] forming an essential part of nuclear magnetic resonance (NMR) [3] and magnetic resonance imaging.Recently, the experimental implementation of manybody time-reversal protocols [4,5] in atomic quantum systems have attracted attention [6][7][8][9] for their potential to quantify the flow of quantum information in time and set bounds on thermalization times [10][11][12][13], which might also enable experimental tests of the holographic duality between quantum and gravitational systems [6,[14][15][16][17]. The key quantities sought after are special types of outof-time-order correlation (OTOC) functions,whereŴ (τ ) = e iĤτŴ e −iĤτ , withĤ an interacting many-body Hamiltonian andŴ andV two commuting unitary operators. Physically, F (τ ) measures the "scrambling" of quantum information across the system's manybody degrees of freedom, for example, how fast an initial * These authors contributed equally.† john.bollinger@nist.gov ‡ arey@jila.colorado.edu local perturbation becomes inaccessible to local probesencapsulates the degree by which the initially commuting operatorsŴ andV fail to commute at later times due to the interactions generated byĤ, which we adopt as an operational definition of scrambling.Most theoretical studies of scrambling have focused on so-called fast scramblers in thermal states [10,11,16]...
Scrambling is the process by which information stored in local degrees of freedom spreads over the many-body degrees of freedom of a quantum system, becoming inaccessible to local probes and apparently lost. Scrambling and entanglement can reconcile seemingly unrelated behaviors including thermalization of isolated quantum systems and information loss in black holes. Here, we demonstrate that fidelity out-of-time-order correlators (FOTOCs) can elucidate connections between scrambling, entanglement, ergodicity and quantum chaos (butterfly effect). We compute FOTOCs for the paradigmatic Dicke model, and show they can measure subsystem Rényi entropies and inform about quantum thermalization. Moreover, we illustrate why FOTOCs give access to a simple relation between quantum and classical Lyapunov exponents in a chaotic system without finite-size effects. Our results open a path to experimental use FOTOCs to explore scrambling, bounds on quantum information processing and investigation of black hole analogs in controllable quantum systems.
Motional heating of ions in microfabricated traps is one of the open challenges hindering experimental realizations of large-scale quantum processing devices. Recently, a series of measurements of the heating rates in surface-electrode ion traps characterized their frequency, distance, and temperature dependencies, but our understanding of the microscopic origin of this noise remains incomplete. In this work we develop a theoretical model for the electric field noise which is associated with a random distribution of adsorbed atoms on the trap electrode surface. By using first-principles calculations of the fluctuating dipole moments of the adsorbed atoms we evaluate the distance, frequency, and temperature dependence of the resulting electric field fluctuation spectrum. Our theory reproduces correctly the d −4 dependence with distance of the ion from the electrode surface and calculates the noise spectrum beyond the standard scenario of two-level fluctuators by incorporating all the relevant vibrational states. Our model predicts a regime of 1/f noise which commences at roughly the frequency of the fundamental phonon transition rate and a thermally activated noise spectrum which for higher temperatures exhibits a crossover as a function of frequency.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.