Noninvasive Measurement of Dynamic Correlation Functions

TL;DR

This paper introduces a minimally invasive protocol using weak couplings to measure dynamic correlation functions in quantum systems, applicable to various initial states and platforms, with potential for ancilla-free implementations.

Contribution

It presents a novel weak coupling measurement protocol for dynamic correlations that minimizes backaction and is adaptable to different quantum systems and states.

Findings

Protocol reduces measurement disturbance significantly.

Implementation discussed for trapped ions and other platforms.

Backaction can be eliminated for spin-1/2 models and single-site observables.

Abstract

The measurement of dynamic correlation functions of quantum systems is complicated by measurement backaction. To facilitate such measurements we introduce a protocol, based on weak ancilla--system couplings, that is applicable to arbitrary (pseudo)spin systems and arbitrary equilibrium or nonequilibrium initial states. Different choices of the coupling operator give access to the real and imaginary parts of the dynamic correlation function. This protocol reduces disturbances due to the early time measurements to a minimum, and we quantify the deviation of the measured correlation functions from the theoretical, unitarily-evolved ones. Implementations of the protocol in trapped ions and other experimental platforms are discussed. For spin-$1/2$ models and single-site observables we prove that measurement backaction can be avoided altogether, allowing for the use of ancilla-free protocols.