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Optical and Quantum Sensing and Precision Metrology II

Quantum enhanced sensing of a spatially extended field

Alice Sinatra

Published Mar 5, 2026• 0 citations
Publisher

Abstract

The nonlocal correlations that exist in quantum physics can be used in a sensor network to improve the sensitivity of the measurement of an extended field or some of its spatial features. Taking an atomic ensemble in a spin squeezed state distributed in different spatial modes (the sensors) as a resource, I will show what kind of gain can be obtained in two different cases. First, assuming that local manipulations can be made on the sensors but all measurements are collective [1], and second, including some experimental results [2], assuming that both local manipulations and local measurements are possible on each sensor. Generalising to the case of a large number of sensors, we show applications to imaging and compressed sensing. --- References : [1] "Quantum-enhanced multiparameter estimation and compressed sensing of a field" Y. Baamara, M. Gessner, A. Sinatra, SciPost Physics 14, 050 (2023) https://scipost.org/SciPostPhys.14.3.050 ; [2] "Multiparameter estimation with an array of entangled atomic sensors" Yifan Li, Lex Joosten, Youcef Baamara, Paolo Colciaghi, Alice Sinatra, Philipp Treutlein, Tilman Zibold, https://arxiv.org/abs/2504.08677.

DOI
10.1117/12.3089858

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The nonlocal correlations that exist in quantum physics can be used in a sensor network to improve the sensitivity of the measurement of an extended field or some of its spatial features. Taking an atomic ensemble in a spin squeezed state distributed in different spatial modes (the sensors) as a resource, I will show what kind of gain can be obtained in two different cases. First, assuming that local manipulations can be made on the sensors but all measurements are collective [1], and second, including some experimental results [2], assuming that both local manipulations and local measurements are possible on each sensor. Generalising to the case of a large number of sensors, we show applications to imaging and compressed sensing. --- References : [1] "Quantum-enhanced multiparameter estimation and compressed sensing of a field" Y. Baamara, M. Gessner, A. Sinatra, SciPost Physics 14, 050 (2023) https://scipost.org/SciPostPhys.14.3.050 ; [2] "Multiparameter estimation with an array of entangled atomic sensors" Yifan Li, Lex Joosten, Youcef Baamara, Paolo Colciaghi, Alice Sinatra, Philipp Treutlein, Tilman Zibold, https://arxiv.org/abs/2504.08677.
We show that a significant quantum gain corresponding to squeezed or over-squeezed spin states can be obtained in multiparameter estimation by measuring the Hadamard coefficients of a 1D or 2D signal. The physical platform we consider consists of two-level atoms in an optical lattice in a squeezed-Mott configuration, or more generally by correlated spins distributed in spatially separated modes. Our protocol requires the possibility to locally flip the spins, but relies on collective measurements. We give examples of applications to scalar or vector field mapping and compressed sensing.
We show that a significant quantum gain corresponding to squeezed or over-squeezed spin states can be obtained in multiparameter estimation by measuring the Hadamard coefficients of a 1D or 2D signal. The physical platform we consider consists of twolevel atoms in an optical lattice in a squeezed-Mott configuration, or more generally by correlated spins distributed in spatially separated modes. Our protocol requires the possibility to locally flip the spins, but relies on collective measurements. We give examples of applications to scalar or vector field mapping and compressed sensing.
Quantum sensor networks promise precision advantages over classical and single-sensor strategies, in particular when the estimator is non-local. We address the problem of finding such estimators through a framework we connote spatial quantum sensing: given an underlying field interrogated by a network of quantum sensors at fixed positions, construct an estimator for a property of the field, for example, distinguishing a source of signal, or evaluating the field or its derivatives at an arbitrary point. We first treat polynomial fields, casting the task as an interpolation problem, and then generalize to fields modeled by analytic functions, which yields general least-squares estimators. A central and largely unaddressed question is under what conditions on sensor placement these estimators are well-defined and error-free. For mmm-dimensional arrays we give explicit constructions and proofs in the interpolation setting using algebraic geometry, and establish necessary and sufficient conditions in the general case. Comparing a non-local entangled protocol with the best local strategy, we show that entanglement yields maximal precision in distributed sensing under global resource constraints. Finally, we introduce error-free subspaces, a technique that translates prior knowledge of the field into a reduction in the number of required sensors. We expect these techniques to be broadly useful in sensing problems across scales, ranging from earth-scale experiments to local applications such as biological imaging.
Quantum enhanced multiparameter sensing is receiving great attention for its applications to vector sensing, imaging, sensor arrays, and clock networks. While for single parameter sensing, a clear theoretical framework has been developed, multiparameter sensing is surprisingly complex from a conceptual point of view. In this talk I will present our proof-of-principle experiment in multiparameter quantum enhanced sensing with a spatially separated array of entangled 87Rb atomic sensors. The production of these entangled sensors and flexible manipulation of the entanglement to optimize the sensor’s sensitivity will be described. Some of the conceptual questions regarding multiparameter sensing will also be addressed.
Quantum metrology takes advantage of quantum correlations to enhance the sensitivity of sensors and measurement techniques beyond their fundamental classical limit, given by the shot-noise limit. The use of both temporal and spatial correlations present in quantum states of light can extend quantum-enhanced sensing to a parallel configuration that can simultaneously probe an array of sensors or independently measure multiple parameters. To this end, we use multispatial-mode bright twin beams of light, which are characterized by independent quantum-correlated spatial subregions in addition to quantum temporal correlations, to probe a four-sensor quadrant plasmonic array. We show that it is possible to independently and simultaneously measure local changes in refractive index for all four sensors with a quantum enhancement in sensitivity in the range of 22% to 24% over the corresponding classical configuration. These results provide a first step toward highly parallel spatially resolved quantum-enhanced sensing techniques and pave the way toward more complex quantum sensing and quantum imaging platforms.
In quantum metrology, entangled states of many-particle systems are investigated to enhance measurement precision of the most precise clocks and field sensors. Whereas single-parameter quantum metrology is well established, joint multiparameter estimation poses conceptual challenges and has been explored only theoretically. We experimentally demonstrated multiparameter quantum metrology with an array of entangled atomic ensembles. By splitting a spin-squeezed ensemble, we created an atomic sensor array featuring intersensor entanglement that can be flexibly configured to enhance measurement precision of multiple parameters jointly. Using an optimal estimation protocol, we achieved substantial gains over the standard quantum limit in key multiparameter estimation tasks, thus grounding the concept of quantum enhancement of field sensor arrays and imaging devices.