Quantum sensors are used for precision timekeeping, field sensing and quantum communication1,2,3. Comparisons among a distributed network of these sensors are capable of, for example, synchronizing clocks at different locations4,5,6,7,8. The performance of a sensor network is limited by technical challenges as well as the inherent noise associated with the quantum states used to realize the network9. For networks with only spatially localized entanglement at each node, the noise performance of the network improves at best with the square root of the number of nodes10. Here we demonstrate that spatially distributed entanglement between network nodes offers better scaling with network size. A shared quantum nondemolition measurement entangles a clock network with up to four nodes. This network provides up to 4.5 decibels better precision than one without spatially distributed entanglement, and 11.6 decibels improvement as compared to a network of sensors operating at the quantum projection noise limit. We demonstrate the generality of the approach with atomic clock and atomic interferometer protocols, in scientific and technologically relevant configurations optimized for intrinsically differential comparisons of sensor outputs.
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The datasets generated and analysed during this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.
The code used for the analysis is available from the corresponding author upon reasonable request.
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We acknowledge support from Department of Energy award DE-SC0019174-0001, the Department of Energy Q-NEXT NQI, a Vannevar Bush Faculty Fellowship and NSF QLCI Award OMA – 2016244.
M.A.K. serves as Chief Scientist, Consulting and is a shareholder of AOSense, Inc. All other authors declare no competing interests.
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Nature thanks Augusto Smerzi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.
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Extended data figures and tables
The atoms (black circle) are localized near the centre of the cavity. The Raman lasers enter the vacuum chamber at a 45° angle to the cavity axis. The reflected light from the probe laser is used in the homodyne detection.
Contrast of the collective fluorescent measurement as a function of separation time between two 0.33 μs Raman π pulses. Solid curve is an exponential fit to the data with a decay rate of 0.46 μs. Note that T = 0 corresponds to a single pulse with a total time of 2π. Error bars represent a 95% confidence interval.
Space time diagram in the inertial frame of a single-mode interferometer. Solid (dashed) lines represent the trajectory of the spin down (up) state. White (grey) waves represent the finite time of the microwave (Raman) pulses.
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Malia, B.K., Wu, Y., Martínez-Rincón, J. et al. Distributed quantum sensing with mode-entangled spin-squeezed atomic states. Nature (2022). https://doi.org/10.1038/s41586-022-05363-z