Abstract Tensor measurements play a vital role in both fundamental sciences and interdisciplinary applications such as navigation and remote sensing which require sensitive perception of the gradient of vector fields. Fundamentally, these measurements rely on the estimation of multiple parameters, which is a key focus in metrology. Quantum metrology has achieved remarkable success in surpassing the standard quantum limit for single-parameter estimation, offering extraordinary sensitivity. Quantum multiparameter estimation has also been demonstrated recently with few-particle quantum systems. Here, we develop tensor quantum metrology by advancing multiparameter quantum sensing to an unprecedented level with both high scalability and multidimensional performance, fulfilling the essential demands on sensitivity for tensor measurements. We generate a bright, multidimensional polarization-entangled light source from an atomic ensemble, with three simultaneously squeezed Stokes operators, enabling superior performance in multiparameter quantum sensing compared to conventional polarization-entangled light. By employing such a quantum light in a tensor magnetometry, we achieve a 6 dB quantum enhancement in both direction and amplitude measurements of magnetic field gradient, with a directional gradient sensitivity of 21μrad/cm/√Hz and an amplitude gradient sensitivity of 6 fT/cm/√Hz. As the first realization of high-sensitivity quantum-enhanced sensing of a tensor field, this work marks a milestone in the advancement of quantum metrology.
Abstract Tensor measurements play a vital role in both fundamental sciences and interdisciplinary applications such as navigation and remote sensing which require sensitive perception of the gradient of vector fields. Fundamentally, these measurements rely on the estimation of multiple parameters, which is a key focus in metrology. Quantum metrology has achieved remarkable success in surpassing the standard quantum limit for single-parameter estimation, offering extraordinary sensitivity. Quantum multiparameter estimation has also been demonstrated recently with few-particle quantum systems. Here, we develop tensor quantum metrology by advancing multiparameter quantum sensing to an unprecedented level with both high scalability and multidimensional performance, fulfilling the essential demands on sensitivity for tensor measurements. We generate a bright, multidimensional polarization-entangled light source from an atomic ensemble, with three simultaneously squeezed Stokes operators, enabling superior performance in multiparameter quantum sensing compared to conventional polarization-entangled light. By employing such a quantum light in a tensor magnetometry, we achieve a 6 dB quantum enhancement in both direction and amplitude measurements of magnetic field gradient, with a directional gradient sensitivity of 21μrad/cm/√Hz and an amplitude gradient sensitivity of 6 fT/cm/√Hz. As the first realization of high-sensitivity quantum-enhanced sensing of a tensor field, this work marks a milestone in the advancement of quantum metrology.
Abstract In the last few decades, the atomic magnetometry [1–7] has experienced remarkable development and reached to an outstanding sensitivity. This exciting technology is finding applications in various of fields [8–18]. The last two obstacles to further improve the sensitivity of magnetometry are quantum fluctuations and ambient magnetic field. For magnetometry based on optical readout of atomic ensemble’s spin precession, the fundamental limitation of sensitivity is restricted by spin projection noise (SPN) and photon shot noise (PSN). Meanwhile, in practical applications, ambient magnetic field noise which is regarded as a common-mode magnetic-field (CMM) noise is also limiting the sensitivity. Several techniques for reducing PSN [19–25], SPN [26, 27], and CMM noise [7, 28–31] have been proposed, respectively. To achieve the best sensitivity, it is essential to find an efficacious way to eliminate the noises from different sources, simultaneously. For this purpose, here we demonstrate a sub-shot-noise magnetic gradiometer utilizing entangled optical detection with quantum-correlated twin beams. This leads to the simultaneous suppression of PSN and CMM noise. The quantum enhancement spans a frequency range from 7 Hz to 6 MHz with maximum squeezing of 5.5 dB below the standard quantum limit (SQL). The sensitivity of gradient magnetic field reaches 18 fT/cm√Hz at 20 Hz with these sophisticated techniques. Our study opens up new possibilities to use quantum-enhanced technology in developing sensitive magnetometry for practical applications with noisy and physically demanding environments.
In the past few decades, optical magnetometry has experienced remarkable development and reached to an outstanding sensitivity. For magnetometry based on optical readout of atomic ensemble, the fundamental limitation of sensitivity is restricted by spin projection noise and photon shot noise. Meanwhile, in practical applications, ambient magnetic noise also greatly limits the sensitivity. To achieve the best sensitivity, it is essential to find an efficacious way to eliminate the noises from different sources, simultaneously. Here, we demonstrate a quantum magnetic gradiometer with sub-shot-noise sensitivity using entangled twin beams with differential detection. The quantum enhancement spans a frequency range from 7 Hz to 6 MHz with maximum squeezing of 5.5 dB below the quantum noise limit. The sensitivity of gradiometer reaches 18 fT/cm[Formula: see text] at 20 Hz. Our study inspires future possibilities to use quantum-enhanced technology in developing sensitive magnetometry for practical applications in noisy and physically demanding environments.
Quantum metrology employs entanglement to enhance measurement precision [V. Giovannetti et al., Quantum-enhanced measurements: Beating the standard quantum limit, Science 306, 1330 (2004)SCIEAS0036-807510.1126/science.1104149, V. Giovannetti et al., Advances in quantum metrology, Nat. Photonics 5, 222 (2011)NPAHBY1749-488510.1038/nphoton.2011.35, and L. Pezzè et al., Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys. 90, 035005 (2018)RMPHAT0034-686110.1103/RevModPhys.90.035005]. The focus and progress so far have primarily centered on estimating a single parameter. In diverse application scenarios, estimation of more than one single parameter is often required. Joint estimation of multiple parameters can benefit from additional advantages for further enhanced precision. Here we report quantum-enhanced estimation of simultaneous spin rotations around two orthogonal axes, making use of spin-nematic squeezing in an atomic Bose-Einstein condensate. Aided by the F=2 atomic ground hyperfine manifold coupled to the nematic-squeezed F=1 states as an auxiliary field through a sequence of microwave (MW) pulses, multiple spin-1 observables are simultaneously measured, reaching an enhancement factor 3.3 to 6.3 decibels (dB) beyond the classical limit over a wide range of rotation angles. Our work realizes the first quantum enhanced multiparameter estimation using entangled massive particles. The techniques developed and the protocols implemented also highlight the application of two-mode squeezed vacuum states in quantum-enhanced sensing of noncommuting spin rotations simultaneously.
We study multiparameter sensing of two-dimensional (2D) and three-dimensional (3D) vector fields within the Bayesian framework for SU(2) quantum interferometry.We establish a method to determine the optimal quantum sensor, which establishes the fundamental limit on the precision of simultaneously estimating multiple parameters with an N -atom sensor.Keeping current experimental platforms in mind, we present sensors that have limited entanglement capabilities and yet significantly outperform sensors that operate without entanglement and approach the optimal quantum sensor in terms of performance.Furthermore, we show how these sensors can be implemented on current programmable quantum sensors with variational quantum circuits by minimizing a metrological cost function.The resulting circuits prepare tailored entangled states and perform measurements in an appropriate entangled basis to realize the best-possible quantum sensor given the native entangling resources available on a given sensor platform.Notable examples include a 2D and 3D quantum "compass" and a 2D sensor that provides a scalable improvement over unentangled sensors.Our results on optimal and variational multiparameter quantum metrology are useful for advancing precision measurements in fundamental science and ensuring the stability of quantum computers, which can be achieved through the incorporation of optimal quantum sensors in a quantum feedback loop.
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.
Quantum metrology has emerged as a powerful tool for timekeeping, field sensing, and precision measurements in fundamental physics. With the advent of distributed quantum metrology, its capabilities have extended to probing spatially distributed parameters across networked quantum systems. However, scalable implementations of distributed quantum metrology with multiparameter estimation remain limited, particularly due to the challenges of generating and distributing entanglement across a quantum network and dealing with incompatibilities in multiparameter quantum metrology. Here we demonstrate distributed multiparameter quantum metrology on a modular superconducting quantum network with low-loss microwave interconnects, a platform that uniquely combines fast gate operations, adaptive control, and deterministic non-local entanglement generation. Using a control-enhanced sequential protocol, we estimate all three components of a remote vector field, achieving up to 13.72 dB improvement in precision over the individual strategy. We further perform direct estimation of vector field gradients along two directions across spatially separated nodes, realizing a 3.44 dB gain over local entanglement strategies. These results establish superconducting quantum networks as a competitive and reconfigurable platform for scalable multiparameter distributed quantum metrology.