Measurement of linear response functions in Nuclear Magnetic Resonance

TL;DR

This paper demonstrates how to measure multi-time correlation functions in a nuclear magnetic resonance system to determine linear response functions and physical properties like magnetic susceptibility, utilizing quantum information techniques.

Contribution

It introduces a method to measure multi-time correlation functions in NMR systems using quantum information techniques, enabling the computation of higher-order response functions.

Findings

Successfully measured three-time correlation functions at arbitrary times.

Measured time correlation functions up to tenth order at fixed times.

Demonstrated the ability to compute physical response functions like magnetic susceptibility.

Abstract

We measure multi-time correlation functions of a set of Pauli operators on a two-level system, which can be used to retrieve its associated linear response functions. The two-level system is an effective spin constructed from the nuclear spins of $^{1}$H atoms in a solution of $^{13}$C-labeled chloroform. Response functions characterize the linear response of the system to a family of perturbations, allowing us to compute physical quantities such as the magnetic susceptibility of the effective spin. We use techniques exported from quantum information to measure time correlations on the two-level system. This approach requires the use of an ancillary qubit encoded in the nuclear spins of the $^{13}$C atoms and a sequence of controlled operations. Moreover, we demonstrate the ability of such a quantum platform to compute time-correlation functions of arbitrary order, which relate to higher-order corrections of perturbative methods. Particularly, we show three-time correlation functions for arbitrary times, and we also measure time correlation functions at fixed times up to tenth order.