Fisher Information and entanglement of non-Gaussian spin states

TL;DR

This paper introduces a method to create and analyze non-Gaussian entangled states in atomic systems, demonstrating their usefulness for quantum metrology beyond traditional spin squeezing.

Contribution

It develops a general approach to extract Fisher information from non-Gaussian states, revealing entanglement useful for precision measurements beyond classical limits.

Findings

Quantum states created are entangled but not spin squeezed.

Fisher information confirms metrologically useful entanglement.

Bayesian phase estimation achieves sub shot-noise sensitivity.

Abstract

Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian statistics. Here we report on the creation and characterization of non-Gaussian many-body entangled states. We develop a general method to extract the Fisher information, which reveals that the quantum dynamics of a classically unstable system creates quantum states that are not spin squeezed but nevertheless entangled. The extracted Fisher information quantifies metrologically useful entanglement which we confirm by Bayesian phase estimation with sub shot-noise sensitivity. These methods are scalable to large particle numbers and applicable directly to other quantum systems.