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Measuring gravitational attraction with a lattice atom interferometer

Nature (2024)Cite this article

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Abstract

Despite being the dominant force of nature on large scales, gravity remains relatively elusive to precision laboratory experiments. Atom interferometers are powerful tools for investigating, for example, Earth’s gravity1, the gravitational constant2, deviations from Newtonian gravity3,4,5,6 and general relativity7. However, using atoms in free fall limits measurement time to a few seconds8, and much less when measuring interactions with a small source mass2,5,6,9. Recently, interferometers with atoms suspended for 70 s in an optical-lattice mode filtered by an optical cavity have been demonstrated10,11,12,13,14. However, the optical lattice must balance Earth’s gravity by applying forces that are a billionfold stronger than the putative signals, so even tiny imperfections may generate complex systematic effects. Thus, lattice interferometers have yet to be used for precision tests of gravity. Here we optimize the gravitational sensitivity of a lattice interferometer and use a system of signal inversions to suppress and quantify systematic effects. We measure the attraction of a miniature source mass to be amass = 33.3 ± 5.6stat ± 2.7syst nm s−2, consistent with Newtonian gravity, ruling out ‘screened fifth force’ theories3,15,16 over their natural parameter space. The overall accuracy of 6.2 nm s−2 surpasses by more than a factor of four the best similar measurements with atoms in free fall5,6. Improved atom cooling and tilt-noise suppression may further increase sensitivity for investigating forces at sub-millimetre ranges17,18, compact gravimetry19,20,21,22, measuring the gravitational Aharonov–Bohm effect9,23 and the gravitational constant2, and testing whether the gravitational field has quantum properties24.

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Fig. 1: Experimental apparatus and lattice atom interferometer trajectories.
Fig. 2: Experiment timescales.
Fig. 3: Measurement dataset.
Fig. 4: Constraints on deviations from Newtonian gravity.

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Data availability

All data presented in this paper are deposited online63.

Code availability

Analysis code is available on request.

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Acknowledgements

We thank A. Reynoso and J. Egelhoff for experimental assistance; J. Lopez, T. Gutierrez and G. Long for technical support; G. Louie and P. Bhattacharyya for discussions and comments on the manuscript; J. Axelrod, B. Elder, M. Jaffe, P. Haslinger, Y. Murakami, A. Singh and V. Xu and the entire Müller group for valuable discussions. This material is based on work supported by: National Science Foundation grants 1708160 and 2208029 (H.M.); Department of Defense Office of Naval Research grant N00014-20-1-2656 (H.M.); and Jet Propulsion Laboratory (JPL) grants 1659506 and 1669913 (H.M.).

Author information

Authors and Affiliations

  1. Department of Physics, University of California, Berkeley, Berkeley, CA, USA

    Cristian D. Panda, Matthew J. Tao, Miguel Ceja & Holger Müller

  2. Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, USA

    Justin Khoury

  3. Dipartimento di Fisica e Astronomia, Università di Firenze, INFN, CNR-INO, Sesto Fiorentino, Italy

    Guglielmo M. Tino

  4. European Laboratory for Non-Linear Spectroscopy (LENS), Sesto Fiorentino, Italy

    Guglielmo M. Tino

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  1. Cristian D. Panda
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Contributions

C.D.P., M.J.T. and M.C. built the apparatus and implemented experimental upgrades. C.D.P. designed the data-acquisition sequence and analysed data. C.D.P. and M.J.T. collected data. H.M. conceptualized and supervised the experiment. C.D.P. and H.M. wrote the original draft. J.K. and G.M.T. participated in the writing of the introduction and conclusion, highlighting the implications of the results for the fields of fundamental physics and atom interferometry. All authors contributed to the review and editing of the manuscript.

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Correspondence to Cristian D. Panda or Holger Müller.

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Extended data figures and tables

Extended Data Fig. 1 Atom sample entering source mass.

Sequence of images showing the Cs atom sample at various positions along its atomic elevator trajectory. Acquiring this sequence from three different perspectives triangulates the position of the atom sample with respect to the source mass with an accuracy better than 1 mm.

Extended Data Fig. 2 Map of source-mass gravity.

A 2D slice of the z component of the gravitational field calculated using finite element analysis in COMSOL is shown. The black square shows the extent of the hollow cylinder. Gravity is stronger on the left side of the map because of the presence of the rectangular slot on the right side.

Extended Data Fig. 3 Acceleration shift owing to lattice divergence als.

In an auxiliary measurement, we observe a linear change in measured acceleration als as a function of vertical position z. This is because of the differential AC Stark shift from the changing trap potential, ΔU(z), as the atoms are held in various positions along the diverging lattice potential. We observe good agreement between the analytic equation derived above, simulation and experiment. The bands correspond to 95% (2σ) confidence intervals.

Extended Data Fig. 4 Atom interferometer decoherence rate as a function of scatter.

Projected lattice atom interferometer decoherence (contrast decay κ) versus level of scatter of the surface of the mirror. The atoms are held 100 μm from the mirror at three different offset distances between the atom cloud and scatterer positions: 0, 0.3 and 1.0 mm. We observe marked decoherence when the scattered intensity is more than 100 ppm of the incident laser power.

Extended Data Table 1 Parameters varied in the search for unexpected systematic errors
Full size table
Extended Data Table 2 Parameters varied in the search for unexpected systematic errors—continued
Full size table

Supplementary information

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Panda, C.D., Tao, M.J., Ceja, M. et al. Measuring gravitational attraction with a lattice atom interferometer. Nature (2024). https://doi.org/10.1038/s41586-024-07561-3

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