Thermal vs. Entanglement Entropy: A Measurement Protocol for Fermionic Atoms with a Quantum Gas Microscope

TL;DR

This paper proposes a protocol to measure the second Renyi entropy of fermionic atoms in optical lattices using quantum gas microscopes, enabling experimental tests of entanglement properties and theoretical predictions like area laws.

Contribution

It introduces a novel measurement scheme for entanglement entropy in fermionic systems using state coupling and site-resolved detection, applicable to equilibrium and non-equilibrium states.

Findings

Protocol allows measurement of entanglement entropy with existing technology

Demonstrates the interplay between thermal and entanglement entropy in Fermi-Hubbard models

Enables testing of theoretical entanglement area laws experimentally

Abstract

We show how to measure the order-two Renyi entropy of many-body states of spinful fermionic atoms in an optical lattice in equilibrium and non-equilibrium situations. The proposed scheme relies on the possibility to produce and couple two copies of the state under investigation, and to measure the occupation number in a site- and spin-resolved manner, e.g. with a quantum gas microscope. Such a protocol opens the possibility to measure entanglement and test a number of theoretical predictions, such as area laws and their corrections. As an illustration we discuss the interplay between thermal and entanglement entropy for a one dimensional Fermi-Hubbard model at finite temperature, and its possible measurement in an experiment using the present scheme.