Estimation of Coupling Constants of a Three-Spin Chain: Case Study of Hamiltonian Tomography with NMR

TL;DR

This paper demonstrates an experimental method using NMR to estimate coupling constants in a three-spin chain with Ising interactions, focusing on edge spin measurements for Hamiltonian tomography.

Contribution

It provides an experimental validation of Hamiltonian tomography for a three-spin chain using NMR, specifically estimating coupling constants from edge spin data.

Findings

Successful estimation of coupling constants in a three-spin chain

Experimental validation using alanine molecule with three $^{13}$C nuclei

Edge spin measurements suffice for Hamiltonian reconstruction

Abstract

It has been shown that inter-spin interaction strengths in a spins-1/2 chain can be evaluated by accessing one of the edge spins only. We demonstrate this experimentally for the simplest case, a three-spin chain, with nuclear magnetic resonance (NMR) technique. The three spins in the chain interact through nearest-neighbor Ising interactions under site-dependent transverse fields. The employed molecule is an alanine containing three $^{13}$C nuclei, each of which has spin-1/2.