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arXiv:2507.11395 · Physical Review A

Metrology using atoms in an array of double-well potentials

Danish Ali Hamza, Jan Chwedeńczuk

Published Jan 8, 2026• 1 citation
arXivHTMLPDF

Abstract

Quantum effects, such as entanglement, Einstein-Podolsky-Rosen steering, and Bell correlations, can enhance metrological sensitivity beyond the standard quantum limit. These correlations are typically generated through interactions between atoms or molecules, or during the passage of a laser pulse through a birefringent crystal. Here, we consider an alternative method of generating scalable, many-body entangled states, and demonstrate their usability for quantum-enhanced metrology. Our setup is a one-dimensional (1D) array of double-well potentials holding independent and uncorrelated Bose-Einstein condensates. The beam-splitting transformation mixes the signal between adjacent wells and yields a strongly entangled state through a many-body equivalent of the Hong-Ou-Mandel effect. We demonstrate this entanglement can improve the sensitivity of quantum sensors. In our analysis, we account for the effects of atomic fluctuations and identify the optimal measurement that saturates the quantum Cramer-Rao bound.

DOI
10.1103/m3hx-1t2q

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Quantum effects, such as entanglement, Einstein-Podolsky-Rosen steering, and Bell correlations, can enhance metrological sensitivity beyond the standard quantum limit. These correlations are typically generated through interactions between atoms or molecules, or during the passage of a laser pulse through a birefringent crystal. Here, we consider an alternative method of generating scalable, many-body entangled states, and demonstrate their usability for quantum-enhanced metrology. Our setup is a one-dimensional (1D) array of double-well potentials holding independent and uncorrelated Bose-Einstein condensates. The beam-splitting transformation mixes the signal between adjacent wells and yields a strongly entangled state through a many-body equivalent of the Hong-Ou-Mandel effect. We demonstrate this entanglement can improve the sensitivity of quantum sensors. In our analysis, we account for the effects of atomic fluctuations and identify the optimal measurement that saturates the quantum Cramer-Rao bound.
Atom interferometers are among the most sensitive tools in quantum metrology but are typically limited by the standard quantum limit (SQL). Entangled input states can surpass this bound and approach Heisenberg scaling. We present a metrology-ready 87Rb platform that combines sub-500 ms Bose-Einstein condensate (BEC) production in time-averaged optical potentials with state-resolved, single-atom-resolved detection. We create high-fidelity Twin-Fock states via spin-changing collisions and observe Hong-Ou-Mandel-type atomic interference of up to 10 atoms. Using these states' near-perfect number correlations for heralding, interferometry can be perfomed with large Dicke states for sub-SQL metrology at total atom numbers of 1000 and beyond.
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Quantum-enhanced sensing typically relies on preparing specific entangled states. However, engineering these states in scalable many-body systems remains challenging due to the difficulty of designing robust preparation protocols and accounting for realistic noise. We show that evolving a simple product state under native time-independent Hamiltonian dynamics in Rydberg atom arrays generates complex many-body correlations that can potentially enable quantum-enhanced parameter estimation reaching the Heisenberg limit (HL). The key challenge is then shifted to extracting the metrological information encoded in spatial correlations of measurement patterns. We introduce a neural correlation learning framework that combines Bayesian inference with neural networks trained on calibration data. Operating in a two-stage calibration-and-sensing protocol, we numerically demonstrate that this framework effectively extracts many-body correlations to saturate the Cramér--Rao bound dictated by the classical Fisher information. Consequently, it achieves quantum-enhanced sensitivity surpassing the standard quantum limit (SQL). Furthermore, the learned estimator is robust to realistic noise, and remains accurate in the absence of rare measurement patterns. Our results establish a hardware-efficient and scalable paradigm for quantum sensing in interacting many-body systems without requiring engineered entangled states.
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Quantum-enhanced metrology can be achieved by entangling a probe with an auxiliary system, passing the probe through an interferometer, and subsequently making measurements on both the probe and auxiliary system. Conceptually, this corresponds to performing metrology with the purification of a (mixed) probe state. We demonstrate via the quantum Fisher information how to design mixed states whose purifications are an excellent metrological resource. In particular, we give examples of mixed states with purifications that allow (near) Heisenberg-limited metrology and provide examples of entangling Hamiltonians that can generate these states. Finally, we present the optimal measurement and parameter-estimation procedure required to realize these sensitivities (i.e., that saturate the quantum Cram\'er-Rao bound). Since pure states of comparable metrological usefulness are typically challenging to generate, it may prove easier to use this approach of entanglement and measurement of an auxiliary system. An example where this may be the case is atom interferometry, where entanglement with optical systems is potentially easier to engineer than the atomic interactions required to produce nonclassical atomic states.
Many-particle entanglement is a fundamental concept of quantum physics that still presents conceptual challenges. Although nonclassical states of atomic ensembles were used to enhance measurement precision in quantum metrology, the notion of entanglement in these systems was debated because the correlations among the indistinguishable atoms were witnessed by collective measurements only. Here, we use high-resolution imaging to directly measure the spin correlations between spatially separated parts of a spin-squeezed Bose-Einstein condensate. We observe entanglement that is strong enough for Einstein-Podolsky-Rosen steering: We can predict measurement outcomes for noncommuting observables in one spatial region on the basis of corresponding measurements in another region with an inferred uncertainty product below the Heisenberg uncertainty bound. This method could be exploited for entanglement-enhanced imaging of electromagnetic field distributions and quantum information tasks.