Experimental verification of the area law of mutual information in a quantum field simulator

TL;DR

This paper experimentally verifies the area law of mutual information in a quantum field simulator using ultra-cold atoms, advancing the understanding of entanglement in quantum many-body systems.

Contribution

It provides the first experimental measurement of the von Neumann entropy and mutual information in a quantum field simulator, confirming fundamental theoretical predictions.

Findings

Verified the area law of mutual information in a quantum simulator

Studied the effects of temperature and separation on mutual information

Demonstrated the use of ultra-cold atoms to probe quantum entanglement

Abstract

Theoretical understanding of the scaling of entropies and the mutual information has led to significant advances in the research of correlated states of matter, quantum field theory, and gravity. Measuring von Neumann entropy in quantum many-body systems is challenging as it requires complete knowledge of the density matrix. In this work, we measure the von Neumann entropy of spatially extended subsystems in an ultra-cold atom simulator of one-dimensional quantum field theories. We experimentally verify one of the fundamental properties of equilibrium states of gapped quantum many-body systems, the area law of quantum mutual information. We also study the dependence of mutual information on temperature and the separation between the subsystems. Our work is a crucial step toward employing ultra-cold atom simulators to probe entanglement in quantum field theories.