Article
of data points during the second sequence, that is, the mean value of
m 2. As illustrated in Extended Data Fig. 4a, the linearity of the mean
value versus the RF peak amplitude is good, indicating the validity of
the linearity of the RF signal generator’s output reading Uset and the
response of atomic spins, further enabling the extrapolation that we
use, BRF ∝ Uapp ∝ Uset.
Based on the aforementioned observation, we can obtain the rela-
tion between the applied magnetic field and the output of the signal
generator as
BT 0 ()=9.6 86 ×10×−8 10 Pset/2^0 (14)where Pset (in units of dB m) is the set output power reading of the RF
signal generator. Through this calibration, we get the peak amplitude
of the applied RF magnetic field in the magnetic field detection experi-
ment, which is about 1.00 pT (Pset = −97 dB m on our signal generator).
Data availability
The datasets generated and analysed during this study are available
from the corresponding authors upon reasonable request.
- Bell, W. E. & Bloom, A. L. Optically driven spin precession. Phys. Rev. Lett. 6 , 280–281 (1961).
- Shen, H. Spin Squeezing and Entanglement with Room Temperature Atoms for Quantum
Sensing and Communication. PhD thesis, Univ. of Copenhagen (2015). - Julsgaard, B., Sherson, J., Sørensen, J. L. & Polzik, E. S. Characterizing the spin state of an
atomic ensemble using the magneto-optical resonance method. J. Opt. B 6 , 5–14 (2004). - Yonezawa, H. et al. Quantum-enhanced optical-phase tracking. Science 337 , 1514–1517
(2012).
38. Huelga, S. F. et al. Improvement of frequency standards with quantum entanglement.
Phys. Rev. Lett. 79 , 3865–3868 (1997).
39. André, A., Sørensen, A. S. & Lukin, M. D. Stability of atomic clocks based on entangled
atoms. Phys. Rev. Lett. 92 , 230801 (2004).
40. Auzinsh, M. et al. Can a quantum nondemolition measurement improve the sensitivity of
an atomic magnetometer? Phys. Rev. Lett. 93 , 173002 (2004).
41. Braverman, B., Kawasaki, A. & Vuletić, V. Impact of non-unitary spin squeezing on atomic
clock performance. New J. Phys. 20 , 103019 (2018).
42. Budker, D. & Kimball, D. F. J. Optical Magnetometry (Cambridge Univ. Press, 2013).
43. Kominis, I. K., Kornack, T. W., Allred, J. C. & Romalis, M. V. A subfemtotesla multichannel
atomic magnetometer. Nature 422 , 596 (2003).
44. Jensen, K. Quantum Information, Entanglement and Magnetometry with Macroscopic Gas
Samples and Non-Classical Light. PhD thesis, Univ. of Copenhagen (2011).
Acknowledgements We thank M. Balabas for assistance in the vapour cell fabrication and
V. Vuletić for discussions. This work is supported by the National Key Research Program of
China under grants 2016YFA0302000 and 2017YFA0304204, and the NNSFC under grants
61675047 and 91636107. K.M. acknowledges support from the Villum Foundation. H.S.
acknowledges financial support from a UK Royal Society Newton International Fellowship
(NF170876).
Author contributions K.M., H.S. and Y.X. conceived the idea. H.B., J.D., S.J., X.L., P.L., I.N.,
E.E.M., H.S. and Y.X. designed the experiment, performed the measurements and analysed the
data together with all other authors. K.-F.Z. helped with the fabrication and characterization of
vapour cells. H.B., M.W. and H.S. carried out the theoretical analysis under K.M.’s supervision.
H.B., H.S., K.M. and Y.X. wrote the manuscript with contributions from all other authors. H.S.
and Y.X. supervised the project.
Competing interests The authors declare no competing interests.Additional information
Supplementary information is available for this paper at https://doi.org/10.1038/s41586-020-
2243-7.
Correspondence and requests for materials should be addressed to K.M., H.S. or Y.X.
Peer review information Nature thanks Julian Martinez-Rincon and the other, anonymous,
reviewer(s) for their contribution to the peer review of this work.
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