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arXiv:2506.10151 · Physical Review X

Lieb-Mattis States for Robust Entangled Differential Phase Sensing

Raphael Kaubruegger, Diego Fallas Padilla, Athreya Shankar, Christoph Hotter, Sean R. Muleady, Jacob Bringewatt, Youcef Baamara, Erfan Abbasgholinejad, Alexey Vyacheslavovich Gorshkov, Klaus Mølmer, James K. Thompson, Ana María Rey

Published Apr 16, 2026• 2 citations
arXivHTMLPDF

Abstract

We explore a two-node, entanglement-enhanced sensor network for differential phase sensing that exploits decoherence-free subspaces to suppress common-mode noise, a primary limitation of many state-of-the-art quantum sensors. We identify a class of entangled states that, while not strictly optimal, achieve the same asymptotic sensitivity scaling as optimal states and can be prepared efficiently from initially unentangled atomic ensembles. Importantly, the preparation time decreases with increasing system size, which makes the states compatible with realistic noise processes in present-day quantum sensors that operate with large particle numbers but lack full error correction. We illustrate these ideas using two cavity-mediated preparation protocols: (i) coherent, unitary entanglement generation analogous to bosonic two-mode squeezing, yielding Heisenberg scaling, and (ii) dissipative preparation through collective emission into a shared cavity mode, providing a square-root improvement beyond the standard quantum limit. Numerical simulations show that both approaches remain effective at experimentally realistic cavity cooperativities, establishing a practical path toward scalable, quantum-enhanced differential phase sensing.

DOI
10.1103/ksyh-mb4s

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Abstract Atom interferometers are reaching sensitivities fundamentally constrained by quantum fluctuations. A main challenge is to integrate entanglement into quantum sensing protocols to enhance precision while ensuring robustness against noise and systematics. Here, we theoretically investigate differential phase measurements with two atom interferometers using spin-squeezed states of N atoms, accounting for common-mode phase noise spanning the full 2 π range. We estimate the differential signal using model-free ellipse fitting, a robust method requiring no device calibration and resilient to additional noise sources. Our results show that spin-squeezing enables sensitivities below the standard quantum limit (SQL). Specifically, we identify optimal squeezed states that minimize the differential phase uncertainty, scaling as N − 2 / 3 , thus overcoming the SQL by a factor N 1 / 6 , while eliminating the bias inherent in ellipse fitting methods. We benchmark our protocol against the Cramér–Rao bound and compare it with hybrid methods that incorporate auxiliary classical sensors. Our findings provide a pathway to robust and high-precision atom interferometry, in realistic noisy environments and using readily available states and estimation methods.
Distributed quantum sensing exploits entanglement to enhance the estimation of multiple parameters across a network of spatially-separated sensors, achieving sensitivities beyond the classical limit. Potential applications cover a plethora of technologies, from precision navigation to biomedical imaging and environmental monitoring. However, practical implementations are challenged by the complex optimal distribution of entanglement throughout the sensing nodes, which affects scalability and robustness. Here we demonstrate a reconfigurable network of Mach-Zehnder interferometers entangled via a single shared squeezed-vacuum resource. We achieve joint noise suppression of 4.36±0.354.36 \pm 0.354.36±0.35 dB below the standard quantum limit at the phase-uncertainty level of 10−910^{-9}10−9 . Furthermore, after full optimization in the low-intensity regime, we demonstrate a crossover from the standard quantum limit to the Heisenberg limit. The network estimates arbitrary linear combinations of phases, saturates the quantum Cramer-Rao bound in the ideal case, remains robust under realistic photon losses, and scales favorably with the number of sensors.
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Quantum metrology protocols using entangled states of large spin ensembles attempt to achieve measurement sensitivities surpassing the standard quantum limit (SQL), but in many cases they are severely limited by even small amounts of technical noise associated with imperfect sensor readout. Amplification strategies based on time-reversed coherent spin-squeezing dynamics have been devised to mitigate this issue, but are unfortunately very sensitive to dissipation, requiring a large single-spin cooperativity to be effective. Here, we propose a new dissipative protocol that combines amplification and squeezed fluctuations. It enables the use of entangled spin states for sensing well beyond the SQL even in the presence of significant readout noise. Further, it has a strong resilience against undesired single-spin dissipation, requiring only a large collective cooperativity to be effective.
We propose to simulate bosonic pair creation using large arrays of long-lived dipoles with multilevel internal structure coupled to an undriven optical cavity. Entanglement between the atoms, generated by the exchange of virtual photons through a common cavity mode, grows exponentially fast and is described by two-mode squeezing of effective bosonic quadratures. The mapping between an effective bosonic model and the natural spin description of the dipoles allows us to realize the analog of optical homodyne measurements via straightforward global rotations and population measurements of the electronic states, and we propose to exploit this for quantum-enhanced sensing of an optical phase (common and differential between two ensembles). We discuss a specific implementation based on Sr atoms and show that our sensing protocol is robust to sources of decoherence intrinsic to cavity platforms. Our proposal can open unique opportunities for next-generation optical atomic clocks.