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# Distributed quantum sensing with mode-entangled spin-squeezed atomic states

## Abstract

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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## Data availability

The datasets generated and analysed during this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

## Code availability

The code used for the analysis is available from the corresponding author upon reasonable request.

## References

1. Grotti, J. et al. Geodesy and metrology with a transportable optical clock. Nat. Phys. 14, 437–441 (2018).

2. McGrew, W. F. et al. Atomic clock performance enabling geodesy below the centimetre level. Nature 564, 87–90 (2018).

3. Guo, X. et al. Distributed quantum sensing in a continuous-variable entangled network. Nat. Phys. 16, 281–284 (2020).

4. Zhao, S.-R. et al. Field demonstration of distributed quantum sensing without post-selection. Phys. Rev. X 11, 031009 (2021).

5. Zhang, Z. & Zhuang, Q. Distributed quantum sensing. Quantum Sci. Tech. 6, 043001 (2021).

6. Giovannetti, V., Lloyd, S. & Maccone, L. Quantum-enhanced positioning and clock synchronization. Nature 412, 417–419 (2001).

7. Beloy, K. et al. Frequency ratio measurements at 18-digit accuracy using an optical clock network. Nature 591, 564–569 (2021).

8. Bothwell, T. et al. Resolving the gravitational redshift across a millimetre-scale atomic sample. Nature 602, 420–424 (2022).

9. Pedrozo-Peñafiel, E. et al. Entanglement on an optical atomic-clock transition. Nature 588, 414–418 (2020).

10. Zheng, X. et al. Differential clock comparisons with a multiplexed optical lattice clock. Nature 602, 425–430 (2022).

11. Overstreet, C., Asenbaum, P., Curti, J., Kim, M. & Kasevich, M. A. Observation of a gravitational Aharonov–Bohm effect. Science 375, 226–229 (2022).

12. Liu, L.-Z. et al. Distributed quantum phase estimation with entangled photons. Nat. Photonics 15, 137–142 (2021).

13. Xia, Y. et al. Demonstration of a reconfigurable entangled radio-frequency photonic sensor network. Phys. Rev. Lett. 124, 150502 (2020).

14. Lu, H. et al. Experimental quantum network coding. npj Quantum Inf. 5, 89 (2019).

15. Bodine, M. I. et al. Optical atomic clock comparison through turbulent air. Phys. Rev. Res. 2, 033395 (2020).

16. Matsukevich, D. N. et al. Entanglement of remote atomic qubits. Phys. Rev. Lett. 96, 030405 (2006).

17. Chou, C. W. et al. Measurement-induced entanglement for excitation stored in remote atomic ensembles. Nature 438, 828–832 (2005).

18. Simon, J., Tanji, H., Ghosh, S. & Vuletić, V. Single-photon bus connecting spin-wave quantum memories. Nat. Phys. 3, 765–769 (2007).

19. Muralidharan, S. et al. Optimal architectures for long distance quantum communication. Sci. Rep. 6, 20463 (2016).

20. Gündoğan, M.et al. Proposal for space-borne quantum memories for global quantum networking. npj Quantum Inf. 7, 128 (2021).

21. Kómár, P. et al. A quantum network of clocks. Nat. Phys. 10, 582–587 (2014).

22. Polzik, E. S. & Ye, J. Entanglement and spin squeezing in a network of distant optical lattice clocks. Phys. Rev. A 93, 021404 (2016).

23. Leroux, I. D., Schleier-Smith, M. H. & Vuletić, V. Orientation-dependent entanglement lifetime in a squeezed atomic clock. Phys. Rev. Lett. 104, 250801 (2010).

24. Gessner, M., Pezzè, L. & Smerzi, A. Sensitivity bounds for multiparameter quantum metrology. Phys. Rev. Lett. 121, 130503 (2018).

25. Zhuang, Q., Zhang, Z. & Shapiro, J. H. Distributed quantum sensing using continuous-variable multipartite entanglement. Phys. Rev. A 97, 032329 (2018).

26. Eckert, K. et al. Differential atom interferometry beyond the standard quantum limit. Phys. Rev. A 73, 013814 (2006).

27. Nichol, B. C. et al. An elementary quantum network of entangled optical atomic clocks. Nature 609, 689–694 (2022).

28. Julsgaard, B., Kozhekin, A. & Polzik, E. S. Experimental long-lived entanglement of two macroscopic objects. Nature 413, 400–403 (2001).

29. Fadel, M., Zibold, T., Décamps, B. & Treutlein, P. Spatial entanglement patterns and Einstein–Podolsky–Rosen steering in Bose–Einstein condensates. Science 360, 409–413 (2018).

30. Lange, K. et al. Entanglement between two spatially separated atomic modes. Science 360, 416–418 (2018).

31. Kunkel, P. et al. Spatially distributed multipartite entanglement enables EPR steering of atomic clouds. Science 360, 413–416 (2018).

32. Anders, F. et al. Momentum entanglement for atom interferometry. Phys. Rev. Lett. 127, 140402 (2021).

33. Greve, G. P., Luo, C., Wu, B. & Thompson, J. K. Entanglement-enhanced matter-wave interferometry in a high-finesse cavity. Nature 610, 472–477 (2022).

34. Hosten, O., Engelsen, N. J., Krishnakumar, R. & Kasevich, M. A. Measurement noise 100 times lower than the quantum-projection limit using entangled atoms. Nature 529, 505–508 (2016).

35. Malia, B. K., Martínez-Rincón, J., Wu, Y., Hosten, O. & Kasevich, M. A. Free space Ramsey spectroscopy in rubidium with noise below the quantum projection limit. Phys. Rev. Lett. 125, 043202 (2020).

36. Fadel, M., Yadin, B., Mao, Y., Byrnes, T. & Gessner, M. Multiparameter quantum metrology and mode entanglement with spatially split nonclassical spin states. Preprint at https://arxiv.org/abs/2201.11081 (2022).

37. Gessner, M., Smerzi, A. & Pezzè, L. Multiparameter squeezing for optimal quantum enhancements in sensor networks. Nat. Commun. 11, 3817 (2020).

38. Wineland, D. J., Bollinger, J. J., Itano, W. M. & Heinzen, D. J. Squeezed atomic states and projection noise in spectroscopy. Phys. Rev. A 50, 67–88 (1994).

39. Chaudhary, M. et al. Stroboscopic quantum nondemolition measurements for enhanced entanglement generation between atomic ensembles. Phys. Rev. A 105, 022443 (2022).

40. Abe, M. et al. Matter-wave atomic gradiometer interferometric sensor (MAGIS-100). Quantum Sci. Tech. 6, 044003 (2021).

41. Zhan, M.-S. et al. ZAIGA: Zhaoshan long-baseline atom interferometer gravitation antenna. Int. J. Mod. Phys. D 29, 1940005 (2019).

42. Wcisło, P. et al. New bounds on dark matter coupling from a global network of optical atomic clocks. Sci. Adv. 4, 6501 (2018).

43. Safronova, M. S., Porsev, S. G., Sanner, C. & Ye, J. Two clock transitions in neutral Yb for the highest sensitivity to variations of the fine-structure constant. Phys. Rev. Lett. 120, 173001 (2018).

44. Tino, G. M. Testing gravity with cold atom interferometry: results and prospects. Quantum Sci. Tech. 6, 024014 (2021).

45. Jing, Y., Fadel, M., Ivannikov, V. & Byrnes, T. Split spin-squeezed Bose–Einstein condensates. New J. Phys. 21, 093038 (2019).

46. Parazzoli, L. P., Hankin, A. M. & Biedermann, G. W. Observation of free-space single-atom matter wave interference. Phys. Rev. Lett. 109, 230401 (2012).

47. Malitesta, M., Smerzi, A. & Pezzè, L. Distributed quantum sensing with squeezed-vacuum light in a configurable network of Mach–Zehnder interferometers Preprint at https://arxiv.org/abs/2109.09178 (2021).

48. Kasevich, M. & Chu, S. Atomic interferometry using stimulated Raman transitions. Phys. Rev. Lett. 67, 181–184 (1991).

49. Malia, B. K. Integration of Spin Squeezed States Into Free Space Atomic Sensors. PhD thesis, Stanford Univ. (2021).

## Acknowledgements

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.

## Author information

Authors

### Contributions

B.K.M., Y.W. and J.M.-R. designed, constructed and characterized the experiment. B.K.M. and Y.W. performed data collection and analysis. M.A.K. supervised the research. All authors contributed to the manuscript.

### Corresponding author

Correspondence to Mark A. Kasevich.

## Ethics declarations

### Competing interests

M.A.K. serves as Chief Scientist, Consulting and is a shareholder of AOSense, Inc. All other authors declare no competing interests.

## Peer review

### Peer review information

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

### Extended Data Fig. 1 Apparatus.

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.

### Extended Data Fig. 2 Mode separation.

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.

### Extended Data Fig. 3 Interferometer sequence timing.

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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Reprints and Permissions

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

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• DOI: https://doi.org/10.1038/s41586-022-05363-z