Fisher information and entanglement of non-Gaussian spin states

Subtle entanglement in an atomic cloud In the quantum world, atoms can be correlated with each other—“entangled”—which reduces the uncertainty in the knowledge of some of their properties. Physicists then use this reduced uncertainty to perform precision measurements. Strobel et al. made an unusual type of entangled state consisting of hundreds of ultracold Rb atoms. These methods may in the future be able to generate states that will be more useful in precision measurement. Science, this issue p. 424 An unconventional entangled state is created out of a mesoscopic number of ultracold rubidium atoms. 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.