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arXiv:1912.00258 · Journal of Physics B Atomic Molecular and Optical Physics

Measuring out-of-time-ordered correlation functions with a single impurity qubit in a bosonic Josephson junction

J. Mumford, W. Kirkby, Duncan H J O’Dell

Published Apr 6, 2020• 9 citations
arXivHTMLPDF

Abstract

Abstract We calculate the out-of-time-ordered correlation function (OTOC) of a single impurity qubit coupled to a fully connected many-particle system, such as a bosonic Josephson junction, or spins with long-range interactions. In these systems, the qubit OTOC can be used to detect both ground state and excited state quantum phase transitions (QPTs), making it a robust order parameter that is considerably more sensitive than the standard one-body correlation function. Finite size scaling exponents for an N body system can also be accurately extracted from the long-time OTOC dynamics, however, for short times there is a discrepancy due to the fact that the qubit has not had enough time to couple to the larger system. Our results show that the OTOC of even the smallest probe is enough to diagnose a QPT in fully connected models but, like a continuous measurement, can still cause a backaction effect which leads to weakly chaotic dynamics and gradual information scrambling.

DOI
10.1088/1361-6455/ab8715

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arXiv:1906.00533•Physical review. B./Physical review. B•Nov 6, 2019•21 citations
Abstract We calculate the out-of-time-ordered correlation function (OTOC) of a single impurity qubit coupled to a fully connected many-particle system, such as a bosonic Josephson junction, or spins with long-range interactions. In these systems, the qubit OTOC can be used to detect both ground state and excited state quantum phase transitions (QPTs), making it a robust order parameter that is considerably more sensitive than the standard one-body correlation function. Finite size scaling exponents for an N body system can also be accurately extracted from the long-time OTOC dynamics, however, for short times there is a discrepancy due to the fact that the qubit has not had enough time to couple to the larger system. Our results show that the OTOC of even the smallest probe is enough to diagnose a QPT in fully connected models but, like a continuous measurement, can still cause a backaction effect which leads to weakly chaotic dynamics and gradual information scrambling.
Out-of-time-order correlators (OTOCs) play an increasingly important role in different fields of physics and in particular they provide a way of quantifying information scrambling in quantum many-body systems. We verify that an OTOC can be used to probe an excited-state quantum phase transition (ESQPT) in a quantum many-body system. We examine the dynamical properties of an OTOC in the Lipkin-Meshkov-Glick model, which undergoes an ESQPT, using the exact diagonalization method. We show that the long-time evolution of the proposed OTOC is remarkably different in the different phases of the ESQPT. In consequence, we put the long-time averaged value of the OTOC forward as a possible ESQPT order parameter. Our results highlight the connections between OTOCs and ESQPTs, opening the possibility of using OTOCs for accessing experimentally ESQPTs in quantum many-body systems.
Abstract Information scrambling, which is the spread of local information through a system’s many-body degrees of freedom, is an intrinsic feature of many-body dynamics. In quantum systems, the out-of-time-ordered correlator (OTOC) quantifies information scrambling. Motivated by experiments that have measured the OTOC at infinite temperature and a theory proposal to measure the OTOC at finite temperature using the thermofield double state, we describe a protocol to measure the OTOC in a finite temperature spin chain that is realized approximately as one half of the ground state of two moderately-sized coupled spin chains. We consider a spin Hamiltonian with particle–hole symmetry, for which we show that the OTOC can be measured without needing sign-reversal of the Hamiltonian. We describe a protocol to mitigate errors in the estimated OTOC, arising from the finite approximation of the system to the thermofield double state. We show that our protocol is also robust to main sources of decoherence in experiments.
Out-of-time-ordered correlators (OTOCs) have received considerable recent attention as qualitative witnesses of information scrambling in many-body quantum systems. Theoretical discussions of OTOCs typically focus on closed systems, raising the question of their suitability as scrambling witnesses in realistic open systems. We demonstrate empirically that the nonclassical negativity of the quasiprobability distribution (QPD) behind the OTOC is a more sensitive witness for scrambling than the OTOC itself. Nonclassical features of the QPD evolve with timescales that are robust with respect to decoherence and are immune to false positives caused by decoherence. To reach this conclusion, we numerically simulate spin-chain dynamics and three measurement protocols (the interferometric, quantum-clock, and weak-measurement schemes) for measuring OTOCs. We target experiments based on quantum-computing hardware such as superconducting qubits and trapped ions.
Out-of-Time-Order Correlator (OTOC) provides a way of quantifying information scrambling in quantum many-body systems and receives increasing attention from different fields. We extend the application of the OTOC to probe the excited-state quantum phase transitions (ESQPT) in spinor Bose–Einstein condensate in an external magnetic field. Using the quantum approach, mean-field theory, and numerical simulations, we have obtained the phase transition points and dynamical properties around them, and have demonstrated that these features can be detected by the OTOC. Our further investigations reveal that the detection efficiency is guaranteed under different magnetization conditions. Our results provide theoretical suggestions for using the OTOCs for experimentally accessing ESQPT in spinor quantum gases and other quantum many-body systems.
Abstract Out-of-time-order correlators (OTOCs) have emerged as the preeminent theoretical and experimental probe of quantum information scrambling — the delocalization of quantum information across many-body degrees of freedom. Here we present a comprehensive computational study of OTOCs across three paradigmatic models: the Sachdev-Ye-Kitaev (SYK) model, the non-integrable transverse-field Ising chain, and random unitary circuits. Through exact diagonalization and large-N analytics, we extract Lyapunov exponents, scrambling times, and butterfly velocities, demonstrating that all chaotic systems studied approach, but do not saturate, the Maldacena-Shenker-Stanford (MSS) bound λ_L ≤ 2π/β. Crucially, we introduce the Spectral Out-of-Time-Order Correlator (SOTOC), a novel frequency-domain diagnostic that decomposes information scrambling into its constituent spectral modes. The SOTOC achieves a 32% improvement in Lyapunov exponent extraction precision over conventional log-linear fitting and maintains robust performance at noise levels σ > 0.30, where traditional methods fail. Our phase diagram reveals a sharp transition in scrambling dynamics at h/J ≈ 1.0 in the TFIM, coinciding with the onset of quantum chaos as measured by level-spacing statistics. These results establish SOTOC as a practical and theoretically grounded tool for probing scrambling in near-term quantum devices and holographic systems.
The out-of-time-ordered correlator (OTOC) is central to the understanding of information scrambling in quantum many-body systems. In this work, we show that the OTOC in a quantum many-body system close to its critical point obeys dynamical scaling laws which are specified by a few universal critical exponents of the quantum critical point. Such scaling laws of the OTOC imply a universal form for the butterfly velocity of a chaotic system in the quantum critical region and allow one to locate the quantum critical point and extract all universal critical exponents of the quantum phase transitions. We numerically confirm the universality of the butterfly velocity in a chaotic model, namely, the transverse axial next-nearest-neighbor Ising model, and show the feasibility of extracting the critical properties of quantum phase transitions from OTOC using the Lipkin-Meshkov-Glick model.