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
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.
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Supplementary Material
Summary
Materials and Methods
Figs. S1 to S5
Resources
File (strobel.sm.pdf)
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Information & Authors
Information
Published In
Science
Volume 345 | Issue 6195
25 July 2014
25 July 2014
Copyright
Copyright © 2014, American Association for the Advancement of Science.
Submission history
Received: 24 December 2013
Accepted: 3 June 2014
Published in print: 25 July 2014
Acknowledgments
We thank J. Tomkovič, E. Nicklas, and I. Stroescu for technical help and discussions. This work was supported by the Forschergruppe FOR760, the Deutsche Forschungsgemeinschaft, the Heidelberg Center for Quantum Dynamics, and the European Commission small or medium-scale focused research project QIBEC (Quantum Interferometry with Bose-Einstein condensates, contract no. 284584). W.M. acknowledges support by the Studienstiftung des deutschen Volkes. D.B.H. acknowledges support from the Alexander von Humboldt Foundation. L.P. acknowledges financial support by Ministero dell’Istruzione, dell’Universit e della Ricerca through Fondo per gli Investimenti della Ricerca di Base project no. RBFR08H058. QSTAR is the Max Planck Institute of Quantum Optics, LENS, Istituto Italiano di Tecnologia, Università degli Studi di Firenze Joint Center for Quantum Science and Technology in Arcetri.
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