R\'enyi Entropies from Random Quenches in Atomic Hubbard and Spin Models

TL;DR

This paper introduces a practical method to measure R'enyi entropies in atomic Hubbard and spin models using random quenches and projective measurements, enabling exploration of entanglement properties in complex quantum systems.

Contribution

The authors propose a novel protocol utilizing engineered disorder and random unitaries for measuring R'enyi entropies in arbitrary dimensions with existing quantum gas microscopes.

Findings

Protocol feasible with current AMO quantum simulators.

Can measure area law scaling of entanglement in 2D spin models.

Allows study of entanglement growth in many-body localized systems.

Abstract

We present a scheme for measuring R\'enyi entropies in generic atomic Hubbard and spin models using single copies of a quantum state and for partitions in arbitrary spatial dimension. Our approach is based on the generation of random unitaries from random quenches, implemented using engineered time-dependent disorder potentials, and standard projective measurements, as realized by quantum gas microscopes. By analyzing the properties of the generated unitaries and the role of statistical errors, with respect to the size of the partition, we show that the protocol can be realized in exisiting AMO quantum simulators, and used to measure for instance area law scaling of entanglement in two-dimensional spin models or the entanglement growth in many-body localized systems.