Measurement Protocol for the Entanglement Spectrum of Cold Atoms

TL;DR

This paper proposes a practical experimental protocol for measuring the entanglement spectrum in cold atom systems, enabling the exploration of quantum many-body properties and topological phases.

Contribution

It introduces a novel measurement scheme using Ramsey spectroscopy and conditional swap gates, feasible with cold atoms, to access the entanglement spectrum experimentally.

Findings

Protocol can reveal topological features of the Haldane phase

Implementation via Rydberg interactions or cavity coupling is feasible

Enables experimental access to entanglement spectrum in cold atoms

Abstract

Entanglement, and, in particular the entanglement spectrum, plays a major role in characterizing many-body quantum systems. While there has been a surge of theoretical works on the subject, no experimental measurement has been performed to date because of the lack of an implementable measurement scheme. Here, we propose a measurement protocol to access the entanglement spectrum of many-body states in experiments with cold atoms in optical lattices. Our scheme effectively performs a Ramsey spectroscopy of the entanglement Hamiltonian and is based on the ability to produce several copies of the state under investigation together with the possibility to perform a global swap gate between two copies conditioned on the state of an auxiliary qubit. We show how the required conditional swap gate can be implemented with cold atoms, either by using Rydberg interactions or coupling the atoms to a cavity mode. We illustrate these ideas on a simple (extended) Bose-Hubbard model where such a measurement protocol reveals topological features of the Haldane phase.