Measurement of many-body chaos using a quantum clock

TL;DR

This paper introduces a quantum clock protocol using an ancilla to measure out-of-time-ordered correlators, providing a new way to experimentally probe many-body quantum chaos without classical time control.

Contribution

A novel protocol employing an ancilla as a quantum clock to measure OTO correlators, enabling chaos detection with a time-independent Hamiltonian.

Findings

Protocol successfully emulates forward and backward time evolution.

Method is robust against errors from classical time control.

Enables experimental access to quantum chaos measures.

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 $\langle O_2(t) O_1(0) O_2(t) O_1(0) \rangle $ 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.