Interaction-based quantum metrology showing scaling beyond the Heisenberg limit
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Quantum metrology aims to use entanglement and other quantum resources to improve precision measurement. An interferometer using N independent particles to measure a parameter χ can achieve at best the standard quantum limit of sensitivity, δχ ∝ N(-1/2). However, using N entangled particles and exotic states, such an interferometer can in principle achieve the Heisenberg limit, δχ ∝ N(-1). Recent theoretical work has argued that interactions among particles may be a valuable resource for quantum metrology, allowing scaling beyond the Heisenberg limit. Specifically, a k-particle interaction will produce sensitivity δχ ∝ N(-k) with appropriate entangled states and δχ ∝ N(-(k-1/2)) even without entanglement. Here we demonstrate 'super-Heisenberg' scaling of δχ ∝ N(-3/2) in a nonlinear, non-destructive measurement of the magnetization of an atomic ensemble. We use fast optical nonlinearities to generate a pairwise photon-photon interaction (corresponding to k = 2) while preserving quantum-noise-limited performance. We observe super-Heisenberg scaling over two orders of magnitude in N, limited at large numbers by higher-order nonlinear effects, in good agreement with theory. For a measurement of limited duration, super-Heisenberg scaling allows the nonlinear measurement to overtake in sensitivity a comparable linear measurement with the same number of photons. In other situations, however, higher-order nonlinearities prevent this crossover from occurring, reflecting the subtle relationship between scaling and sensitivity in nonlinear systems. Our work shows that interparticle interactions can improve sensitivity in a quantum-limited measurement, and experimentally demonstrates a new resource for quantum metrology.
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Exceptions to the limitation of m include the Dicke model, the Lipkin-Meshkov-Glick model, and the Mølmer-Sørensen interaction.
“Exceptions to this include the Dicke model [40] where collective coherence leads to superradiance, the Lipkin-Meshkov-Glick model [41], where all particles interact with each other, and the Mølmer-Sørensen interaction [42], in which an ensemble of ions are effectively coupled by a spatially uniform electromagnetic field.”
From Enhancing the Charging Power of Quantum Batteries (2017) · cites this paper as [41]
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- Authors
- Napolitano, M., Koschorreck, M., Dubost, B., Behbood, N., Sewell, R. J., & Mitchell, M. W.
- Affiliations
- Institute of Photonic Sciences (ES)
- Centre National de la Recherche Scientifique (FR)
- Corresponding author
- Napolitano, M.
- Venue
- Nature
- Published
- 2011-03
- Volume
- 471
- Issue
- 7339
- Pages
- 486-489
- ISSN
- 0028-0836 (ISSN-L)
- 1476-4687
- OpenAlex
- W2122138985
- Cited by
- 245
- References
- 28
- Citations by year
- 2026: 11 · 2025: 18 · 2024: 16 · 2023: 12 · 2022: 18 · 2021: 19 · 2020: 14 · 2019: 14 · 2018: 11 · 2017: 14 · 2016: 13 · 2015: 13 · 2014: 26 · 2013: 23 · 2012: 18
- FWCI
- 21.22
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Nature (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Keywords
- quantum metrology, Heisenberg limit, interparticle interactions, nonlinear measurements, non-destructive measurement, atomic magnetization, atomic ensembles, photon-photon interaction, precision measurement, quantum noise, higher-order nonlinearities, entanglement, standard quantum limit, quantum Fisher information, quantum Fisher information matrix
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