Measurement of many-body chaos using a quantum clock
arXiv:1607.00079 · doi:10.1103/PhysRevA.94.062329
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 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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- Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation
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- Non-ergodicity in the Anisotropic Dicke model
- Properties and Applications of the Kirkwood-Dirac Distribution
- Out-of-time-order correlations and Floquet dynamical quantum phase transition
- Semiclassical roots of universality in many-body quantum chaos
- From Dual Unitarity to Generic Quantum Operator Spreading
- Thermalization and chaos in QED
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- Characteristic, dynamic, and near saturation regions of Out-of-time-order correlation in Floquet Ising models
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- Effects of topological and non-topological edge states on information propagation and scrambling in a Floquet spin chain
- Quantum chaos in PT symmetric quantum systems
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- Directional scrambling of quantum information in helical multiferroics
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- False signals of chaos from quantum probes