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Atom-trap trace analysis of 41Ca/Ca down to the 10–17 level


The cosmogenic isotope 41Ca with a half-life of 99,000 years can, in principle, serve as a tracer for environmental processes at an age scale beyond the reach of 14C. With accelerator mass spectrometry, the ratio of 41Ca/Ca has been measured down to the 10−15 level in natural samples. A wide range of potential applications, such as the burial dating of bones and exposure dating of rocks, require measuring even smaller 41Ca/Ca ratios in the range of 10−16 to 10−15. Here we achieved this by employing the atom-trap trace analysis method in which individual 41Ca atoms are selectively captured in a magneto-optical trap and counted by detecting their fluorescence. We realized a precision of 12% on the 41Ca/Ca ratio at the level of 10−16 and achieved a detection limit at the level of 10−17, which is below the distribution of natural abundances. We verified the accuracy of the 41Ca/Ca results through a series of measurements of reference samples, and performed demonstration analyses on bone, rock and seawater samples. Our table-top method has the potential to explore the suitability of 41Ca as a tracer.

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Fig. 1: Single-atom detection.
Fig. 2: MOT fluorescence of Ca isotopes as a function of the trap laser frequency at 423 nm.
Fig. 3: Reference sample measurements.

Data availability

Source data are provided in Extended Data Tables 2 and 3 and available via Zenodo at (ref. 35).


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We thank D. Sheng, A.-W. Liu, Q.-X. Li and G. Jin for helpful discussions. We thank T.-F. Xu and Y. Yang for providing the seawater sample. This work is supported by the Innovation Program for Quantum Science and Technology through grant no. 2021ZD0303100 to T.-Y.X., W.-W.S., W.J., G.-M.Y., H.-M.Z., T.X. and Z.-T.L.; the National Natural Science Foundation of China through grant no. 41727901 to T.-Y.X., W.-W.S., S.E., W.J., G.-M.Y., H.-M.Z., T.X. and Z.-T.L.; the Strategic Priority Research Program of the Chinese Academy of Sciences through grant no. XDB21010200 to T.X. and Z.-T.L.; and Innovation Program for Quantum Science and Technology through grant no. 2021ZD0303101 to T.-Y.X., W.-W.S., S.E., W.J., G.-M.Y., H.-M.Z., T.X. and Z.-T.L.

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Authors and Affiliations



T.X. and Z.-T.L. conceived the research and supervised the project. T.-Y.X., W.-W.S., S.E., W.J., G.-M.Y., H.-M.Z., T.X. and Z.-T.L. developed the ATTA apparatus, W.-W.S. performed the ATTA measurements, T.-Y.X. developed the procedure for calcium extraction and preparation, G.-D.M. and T.-Y.X. developed the procedure for extracting calcium from granite, Y.-C.F. performed the AMS measurements, and G.-D.M. and F.H. collected the granite sample. W.-W.S., T.-Y.X., W.J., T.X. and Z.-T.L. analysed the data and discussed the results. T.-Y.X., W.-W.S., T.X. and Z.-T.L. wrote the paper. All the authors reviewed the paper.

Corresponding authors

Correspondence to T. Xia or Z.-T. Lu.

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Competing interests

T.-Y.X., T.X., W.-W.S., Z.-T.L. and W.J. have applied for a patent on the basis of this work (Chinese patent application no. CN115201172A, in substantive examination). The other authors declare no competing interests.

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Nature Physics thanks Marc Caffee, Stewart Freeman and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Schematic diagram of an ATTA apparatus for 41Ca/Ca analysis.

The oven, transverse cooling (TC), transverse focusing (TF), Zeeman slower (ZS), and magneto-optical trap (MOT) are aligned coaxially. The atom chopper rotates to block the atom beam while detecting 41Ca in the MOT. The purple arrows represent 423-nm laser beams that cool, load, and detect the Ca atoms. The blue arrows represent 453-nm repump laser beams.

Extended Data Fig. 2 Energy level diagram of the neutral Ca atom.

The purple and blue arrows represent the atomic transitions for cooling and trapping at 423 nm and for repump at 453 nm, respectively. The percentages are branching ratios of spontaneous decay channels. Dashed lines represent inter-combination transitions.

Extended Data Fig. 3 Time sequence of single-atom detection.

Status of atom beam, Zeeman slower (ZS) laser, magneto-optical trap (MOT) laser, and CCD camera are shown. The repump laser beam (453-nm) is kept on constantly. The atomic beam is switched by a mechanical chopper with 18-ms rising/falling edges. A 500-ms period is divided into three phases: loading, detection and releasing. Single 41Ca atoms are captured into the MOT in the loading phase, detected in the detection phase, and released from the MOT in the releasing phase.

Extended Data Table 1 Configurations of laser beams for cooling and trapping
Extended Data Table. 2 Reference samples calibrated by AMS
Extended Data Table 3 41Ca/Ca ratios of reference samples measured by ATTA
Extended Data Table 4 Relative uncertainties in 41Ca/Ca measurements

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Xia, TY., Sun, WW., Ebser, S. et al. Atom-trap trace analysis of 41Ca/Ca down to the 10–17 level. Nat. Phys. 19, 904–908 (2023).

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