Acoustic Rabi oscillations between gravitational quantum states and impact on symmetron dark energy


The standard model of cosmology provides a robust description of the evolution of the Universe. Nevertheless, the small magnitude of the vacuum energy is troubling from a theoretical point of view9. An appealing resolution to this problem is to introduce additional scalar fields. However, these have so far escaped experimental detection, suggesting some kind of screening mechanism may be at play. Although extensive exclusion regions in parameter space have been established for one screening candidate—chameleon fields10,17—another natural screening mechanism based on spontaneous symmetry breaking has also been proposed, in the form of symmetrons11. Such fields would change the energy of quantum states of ultracold neutrons in the gravitational potential of the Earth. Here, we demonstrate a spectroscopic approach based on the Rabi resonance method that probes these quantum states with a resolution of ΔE =2 × 10−15 eV. This allows us to exclude the symmetron as the origin of dark energy for a large volume of the three-dimensional parameter space.

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Fig. 1: Schematic views of the experimental set-up.
Fig. 2: Observed transition rates for the local gravitational acceleration measurement.
Fig. 3: Qualitative sketch of the effective symmetron potential.
Fig. 4: Laboratory measurements constrain a large parameter range for the symmetron fields.


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H.A. thanks M. Faber and A. Ivanov for useful discussions. We gratefully acknowledge support from the Austrian Fonds zur Förderung der Wissenschaftlichen Forschung (FWF) under contract no. I529-N20, no. 531-N20 and no. I862-N20, and the German Research Foundation (DFG) as part of the Priority Programme (SPP) 1491 “Precision experiments in particle and astrophysics with cold and ultra-cold neutrons”. We also gratefully acknowledge support from the French L’Agence nationale de la recherche (ANR) under contract no. ANR-2011-ISO4-007-02, Programme Blanc International—SIMI4-Physique. This work is supported in part by the EU Horizon 2020 research and innovation programme under the Marie-Sklodowska grant no. 690575. This article is based upon work related to the COST Action CA15117 (CANTATA) supported by COST (European Cooperation in Science and Technology).

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G.C., H.F., P.G., M.T., T.J. and H.A. performed the experiment. G.C., T.J., M.P., H.F. and H.A. analysed the data. M.P., G.P. and P.B. provided the theoretical contributions. All authors contributed to the manuscript.

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Correspondence to Hartmut Abele.

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Supplementary Notes 1–2, Supplementary Figure 1, Supplementary Table 1, Supplementary References 1–2

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Cronenberg, G., Brax, P., Filter, H. et al. Acoustic Rabi oscillations between gravitational quantum states and impact on symmetron dark energy. Nature Phys 14, 1022–1026 (2018).

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