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# Determination of the fine-structure constant with an accuracy of 81 parts per trillion

## Abstract

The standard model of particle physics is remarkably successful because it is consistent with (almost) all experimental results. However, it fails to explain dark matter, dark energy and the imbalance between matter and antimatter in the Universe. Because discrepancies between standard-model predictions and experimental observations may provide evidence of new physics, an accurate evaluation of these predictions requires highly precise values of the fundamental physical constants. Among them, the fine-structure constant α is of particular importance because it sets the strength of the electromagnetic interaction between light and charged elementary particles, such as the electron and the muon. Here we use matter-wave interferometry to measure the recoil velocity of a rubidium atom that absorbs a photon, and determine the fine-structure constant α−1 = 137.035999206(11) with a relative accuracy of 81 parts per trillion. The accuracy of eleven digits in α leads to an electron g factor1,2—the most precise prediction of the standard model—that has a greatly reduced uncertainty. Our value of the fine-structure constant differs by more than 5 standard deviations from the best available result from caesium recoil measurements3. Our result modifies the constraints on possible candidate dark-matter particles proposed to explain the anomalous decays of excited states of 8Be nuclei4 and paves the way for testing the discrepancy observed in the magnetic moment anomaly of the muon5 in the electron sector6.

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## Data availability

The datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request.

## Code availability

The experimental data were analysed using a self-written analysis script, which is available from the corresponding author on reasonable request.

## References

1. 1.

Aoyama, T., Hayakawa, M., Kinoshita, T. & Nio, M. Tenth-order QED contribution to the electron g − 2 and an improved value of the fine structure constant. Phys. Rev. Lett. 109, 111807 (2012).

2. 2.

Aoyama, T., Kinoshita, T. & Nio, M. Theory of the anomalous magnetic moment of the electron. Atoms 7, 28 (2019).

3. 3.

Parker, R. H., Yu, C., Zhong, W., Estey, B. & Müller, H. Measurement of the fine-structure constant as a test of the Standard Model. Science 360, 191–195 (2018).

4. 4.

Krasznahorkay, A. J. et al. Observation of anomalous internal pair creation in 8Be: a possible indication of a light, neutral boson. Phys. Rev. Lett. 116, 042501 (2016).

5. 5.

Bennett, G. W. et al. Final report of the E821 muon anomalous magnetic moment measurement at BNL. Phys. Rev. D 73, 072003 (2006).

6. 6.

Terranova, F. & Tino, G. M. Testing the aμ anomaly in the electron sector through a precise measurement of h/M. Phys. Rev. A 89, 052118 (2014).

7. 7.

Mohr, P. J., Newell, D. B. & Taylor, B. N. CODATA recommended values of the fundamental physical constants: 2014. Rev. Mod. Phys. 88, 035009 (2016).

8. 8.

Laporta, S. High-precision calculation of the 4-loop contribution to the electron g − 2 in QED. Phys. Lett. B 772, 232–238 (2017).

9. 9.

Hanneke, D., Fogwell, S. & Gabrielse, G. New measurement of the electron magnetic moment and the fine structure constant. Phys. Rev. Lett. 100, 120801 (2008).

10. 10.

Wicht, A., Hensley, J. M., Sarajlic, E. & Chu, S. A preliminary measurement of the fine structure constant based on atom interferometry. Phys. Scr. T102, 82 (2002).

11. 11.

Battesti, R. et al. Bloch oscillations of ultracold atoms: a tool for a metrological determination of h/mRb. Phys. Rev. Lett. 92, 253001 (2004).

12. 12.

Mount, B. J., Redshaw, M. & Myers, E. G. Atomic masses of 6Li, 23Na, 39,41K, 85,87Rb, and 133Cs. Phys. Rev. A 82, 042513 (2010).

13. 13.

Huang, W. et al. The AME2016 atomic mass evaluation (I). Evaluation of input data; and adjustment procedures. Chin. Phys. C 41, 030002 (2017).

14. 14.

Sturm, S. et al. High-precision measurement of the atomic mass of the electron. Nature 506, 467–470 (2014).

15. 15.

Cladé, P., Guellati-Khélifa, S., Nez, F. & Biraben, F. Large momentum beam splitter using Bloch oscillations. Phys. Rev. Lett. 102, 240402 (2009).

16. 16.

Müller, H., Chiow, S.-w., Long, Q., Herrmann, S. & Chu, S. Atom interferometry with up to 24-photon-momentum-transfer beam splitters. Phys. Rev. Lett. 100, 180405 (2008).

17. 17.

Cadoret, M. et al. Combination of Bloch oscillations with a Ramsey–Bordé interferometer: new determination of the fine structure constant. Phys. Rev. Lett. 101, 230801 (2008).

18. 18.

Bouchendira, R., Cladé, P., Guellati-Khélifa, S., Nez, F. & Biraben, F. New determination of the fine structure constant and test of the quantum electrodynamics. Phys. Rev. Lett. 106, 080801 (2011).

19. 19.

Lan, S.-Y., Kuan, P.-C., Estey, B., Haslinger, P. & Müller, H. Influence of the Coriolis force in atom interferometry. Phys. Rev. Lett. 108, 090402 (2012).

20. 20.

Jannin, R., Cladé, P. & Guellati-Khélifa, S. Phase shift due to atom–atom interactions in a light-pulse atom interferometer. Phys. Rev. A 92, 013616 (2015).

21. 21.

Bade, S., Djadaojee, L., Andia, M., Cladé, P. & Guellati-Khelifa, S. Observation of extra photon recoil in a distorted optical field. Phys. Rev. Lett. 121, 073603 (2018).

22. 22.

Gillot, P., Cheng, B., Merlet, S. & Pereira Dos Santos, F. Limits to the symmetry of a Mach-Zehnder-type atom interferometer. Phys. Rev. A 93, 013609 (2016).

23. 23.

Morel, L., Yao, Z., Cladé, P. & Guellati-Khélifa, S. Velocity-dependent phase shift in a light-pulse atom interferometer. Preprint at https://arxiv.org/abs/2006.14354 (2020).

24. 24.

Yu, C. et al. Atom-interferometry measurement of the fine structure constant. Ann. Phys. 531, 1800346 (2019).

25. 25.

Brodsky, S. J. & Drell, S. D. Anomalous magnetic moment and limits on fermion substructure. Phys. Rev. D 22, 2236–2243 (1980).

26. 26.

Bourilkov, D. Hint for axial-vector contact interactions in the data on e+ee+e(γ) at center-of-mass energies 192–208 GeV. Phys. Rev. D 64, 071701 (2001).

27. 27.

Aoyama, T., Kinoshita, T. & Nio, M. Revised and improved value of the QED tenth-order electron anomalous magnetic moment. Phys. Rev. D 97, 036001 (2018).

28. 28.

Davoudiasl, H., Lee, H.-S. & Marciano, W. J. Muon g−2, rare kaon decays, and parity violation from dark bosons. Phys. Rev. D 89, 095006 (2014).

29. 29.

Gabrielse, G., Fayer, S. E., Myers, T. G. & Fan, X. Towards an improved test of the standard model’s most precise prediction. Atoms 7, 45 (2019).

30. 30.

Feng, J. L. et al. Protophobic fifth-force interpretation of the observed anomaly in 8Be nuclear transitions. Phys. Rev. Lett. 117, 071803 (2016).

31. 31.

Riordan E. M. et al. Search for short-lived axions in an electron-beam-dump experiment. Phys. Rev. Lett. 59, 755–758 (1987).

32. 32.

NA64 Collaboration. Search for a hypothetical 16.7 MeV gauge boson and dark photons in the NA64 experiment at CERN. Phys. Rev. Lett. 120, 231802 (2018).

33. 33.

Banerjee, D. et al. Improved limits on a hypothetical X(16.7) boson and a dark photon decaying into e+e pairs. Phys. Rev. D 101, 071101 (2020).

34. 34.

Van Dyck, R. S., Schwinberg, P. & Dehmelt, H. New high-precision comparison of electron and positron g factors. Phys. Rev. Lett. 59, 26–29 (1987).

35. 35.

BABAR Collaboration. Search for a dark photon in e+e collisions at BaBar. Phys. Rev. Lett. 113, 201801 (2014).

36. 36.

Andia, M., Wodey, É., Biraben, F., Cladé, P. & Guellati-Khélifa, S. Bloch oscillations in an optical lattice generated by a laser source based on a fiber amplifier: decoherence effects due to amplified spontaneous emission. J. Opt. Soc. Am. B 32, 1038–1042 (2015).

37. 37.

Wolf, P. & Tourrenc, P. Gravimetry using atom interferometers: some systematic effects. Phys. Lett. A 251, 241–246 (1999).

38. 38.

Storey, P. & Cohen-Tannoudji, C. The Feynman path integral approach to atomic interferometry. A tutorial. J. Phys. II France 4, 1999–2027 (1994).

39. 39.

Weiss, D. S., Young, B. C. & Chu, S. Precision measurement of ħ/mCs based on photon recoil using laser-cooled atoms and atomic interferometry. Appl. Phys. B 59, 217–256 (1994).

40. 40.

Glück, M., Kolovsky, A. R. & Korsch, H. J. Wannier–Stark resonances in optical and semiconductor superlattices. Phys. Rep. 366, 103–182 (2002).

41. 41.

Cladé, P., Andia, M. & Guellati-Khélifa, S. Improving efficiency of Bloch oscillations in the tight-binding limit. Phys. Rev. A 95, 063604 (2017).

42. 42.

Touahri, D. et al. Frequency measurement of the two-photon transition in rubidium. Opt. Commun. 133, 471–478 (1997).

43. 43.

Louchet-Chauvet, A. et al. The influence of transverse motion within an atomic gravimeter. New J. Phys. 13, 065025 (2011).

44. 44.

Hogan, J. M., Johnson, D. M. S. & Kasevich, M. A. Light-pulse atom interferometry. In Proc. of the International School of Physics Enrico Fermi Course CLXVIII on Atom Optics and Space Physics (eds. Arimondo, E. et al.) 411 (IOS Press, 2008).

## Acknowledgements

This work was supported by the US National Institute of Standards and Technology (NIST) Precision Measurement Grant Program under award number 60NANB16D271 and by the LABEX Cluster of Excellence FIRST-TF (ANR-10-LABX-48-01), within the Programme investissements d’avenir operated by the French National Research Agency (ANR). We are particularly grateful to R. Jannin and C. Courvoisier, who participated actively to the construction of the experimental setup, which was initially funded by the ANR, INAQED Project number ANR-12-JS04-0009.

## Author information

Authors

### Contributions

The experiment was performed by L.M., Y.Z., P.C. and S.G.-K. The data were analysed by L.M., P.C. and S.G.-K. The main text was written by S.G.-K. and the Methods section by L.M. and P.C. All authors discussed and approved the data as well as the manuscript.

### Corresponding author

Correspondence to Saïda Guellati-Khélifa.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Gerald Gabrielse and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Laser beam setup and detection.

a, Vacuum cell and laser beams used for the Raman transition and Bloch oscillations. b, Detection setup consisting of three horizontal retro-reflected light sheets, through which the atoms fall successively. The thick red line represents the probe beams of circular polarization, which are resonant with the atoms in the state |F = 2. The black line represents the beam that repumps atoms from |F = 1 to |F = 2. c, Light pulse sequence implemented for the measurement protocol. Shown are the temporal variables used in Methods.

### Extended Data Fig. 2 Control of the laser beam alignment and the magnetic field.

a, Distributions of the shot-to-shot variations of the auto-alignment procedure for mirrors M1 and M2 (see Extended Data Fig. 1a). b, Scatter plot of the contrast with respect to the sweep rate of the piezoelectric transducer of the mirror mounts (M2) for a 700-ms-long interferometer. c, Raw determinations of integrated h/m with and without Earth rotation compensation. Each point correspond to 400 sets of four spectra. The total interrogation time is 60 h. d, Blue: measured magnetic field, obtained by measuring the resonance of the magnetically sensitive |F = 1, mF = 1 → |F = 2, mF = −1 transition. Orange: interpolation used for the modelling of the systematic effect. e, Allan deviation of the frequency measurement.

### Extended Data Fig. 3 Frequency control of Raman lasers.

a, Raman phase-lock system. Top left: laser arrangement used to extract a beat note between the two lasers. Bottom left: radio-frequency chain for the phase lock. Right: setup used for the measurement of the phase between the two lasers. NKT, fibre laser from NKT photonics; RIO, diode laser from RIO lasers; EDFA, erbium-doped fiber amplifier; SHG-PPLN, second-harmonic generation using a periodic crystal; AOM, acousto-optic modulator; PID, proportional-integral-derivative controller. b, Frequency of the radio-frequency generator of the PLL for each Raman direction (red and blue lines). ωC is changed with the Raman direction (right) to obtain symmetrized ramps. c, Average interferometric phase with respect to the average correction deduced from the phase of the beat note.

### Extended Data Fig. 4 Analysis of the effect of local fluctuations on laser intensity.

a, Typical intensity profile of the laser beam. b, Characterization of the short-scale noise on the beam intensity. The intensity of the laser used for Bloch oscillations is reduced, leading to losses of atoms in the experiment (bottom). This induces a systematic effect on the recoil measurement (upper). To match the experimental data with the Monte Carlo simulation results, we added a small noise (2% at a scale of 50 μm) to the pictures recorded with a camera. c, Correction from the intensity profile calculated for each configuration. Only independent uncertainties are displayed, obtained from the Monte Carlo simulation. d, Results of the Monte Carlo simulation for the estimation of the effect of the one-photon light shift for different initial velocity and Raman inversion compensation (orange points: perfect compensation; blue and green points: one-photon light shift is 20% greater for one or the other Raman direction). The simulation was performed for all interferometer configurations (top: Raman high power; bottom: Raman low power) and different (TR, NB, τB) values (from left to right).

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Morel, L., Yao, Z., Cladé, P. et al. Determination of the fine-structure constant with an accuracy of 81 parts per trillion. Nature 588, 61–65 (2020). https://doi.org/10.1038/s41586-020-2964-7

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