Measurement of many-body chaos using a quantum clock

Abstract

There has been recent progress in understanding chaotic features in many-body quantum systems. Motivated by the scrambling of information in black holes, it has been suggested that the time dependence of out-of-time-ordered (OTO) correlation functions such as $⟨O_2(t)O_1(0)O_2(t)O_1(0)⟩$ is a faithful measure of quantum chaos. Experimentally, these correlators are challenging to access since they apparently require access to both forward and backward time evolution with the system Hamiltonian. Here, we propose a protocol to measure such OTO correlators using an ancilla which controls the direction of time. Specifically, by coupling the state of ancilla to the system Hamiltonian of interest, we can emulate the forward and backward time propagation, where the ancilla plays the role of a 'quantum clock'. Within this scheme, the continuous evolution of the entire system (the system of interest and the ancilla) is governed by a time-independent Hamiltonian. Our protocol is immune to errors that could occur when the direction of time evolution is externally controlled by a classical switch.

11 pages + Appendices, 9 figures

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Cited by in corpus (21)

• Hydrodynamics of electrons in graphene
• Slow scrambling in disordered quantum systems
• Jarzynski-like equality for the out-of-time-ordered correlator
• Relating out-of-time-order correlations to entanglement via multiple-quantum coherences
• Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation
• Minimal Model for Fast Scrambling
• Non-ergodicity in the Anisotropic Dicke model
• Out-of-time-order correlations and Floquet dynamical quantum phase transition
• Spectral Form Factor as an OTOC Averaged over the Heisenberg Group
• Thermalization and chaos in QED${}_3$
• Circuit QED with qutrit: coupling three or more atoms via virtual photon exchange
• Out-of-Time-Order Correlation as a Witness for Topological Phase Transitions
• Constraints on hydrodynamics from many-body quantum chaos
• Scaling laws of the out-of-time-order correlators at the transition to the spontaneous $\mathcal{P}\mathcal{T}$-symmetry breaking in a Floquet system
• Measuring operator size growth in quantum quench experiments
• Characteristic, dynamic, and near saturation regions of Out-of-time-order correlation in Floquet Ising models
• Chaos in a quantum rotor model
• Unambiguous measurement of information scrambling in a hierarchical star-topology system
• Directional scrambling of quantum information in helical multiferroics
• Efficient implementation of unitary transformations
• False signals of chaos from quantum probes