Abstract
Spectroscopy is a method typically used to assess an unknown quantity of energy by means of a frequency measurement. In many problems, resonance techniques1,2 enable high-precision measurements, but the observables have generally been restricted to electromagnetic interactions. Here we report the application of resonance spectroscopy to gravity. In contrast to previous resonance methods, the quantum mechanical transition is driven by an oscillating field that does not directly couple an electromagnetic charge or moment to an electromagnetic field. Instead, we observe transitions between gravitational quantum states when the wave packet of an ultra-cold neutron couples to the modulation of a hard surface as the driving force. The experiments have the potential to test the equivalence principle3 and Newton’s gravity law at the micrometre scale4,5.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to the full article PDF.
USD 39.95
Prices may be subject to local taxes which are calculated during checkout



Similar content being viewed by others
References
Rabi, I. I., Millman, S., Kusch, P. & Zacharias, J. R. The molecular beam resonance method for measuring nuclear magnetic moments. The magnetic moments of 3Li6, 3Li7 and 9F19. Phys. Rev. 55, 526–535 (1939).
Ramsey, N. F. Molecular Beams 1985 edn (paperback edition) 124–134 (Clarendon Press, 1956).
Kajari, E., Harshman, N. L., Rasel, E. M., Stenholm, S., Süßmann, G. & Schleich, W. P. Inertial and gravitational mass in quantum mechanics. Appl. Phys. B 100, 43–60 (2010).
Arkani-Hamed, N., Dimopolos, S. & Dvali, G. Phenomenology, astrophysics and cosmology of theories with submillimetre dimensions and TeV scale quantum gravity. Phys. Rev. D 59, 086004 (1999).
Antoniadis, I. Physics with large extra dimensions and non-newtonian gravity at sub-mm distances. Lect. Notes Phys. 631, 337–354 (2003).
Ramsey, N. F. Experiments with separated oscillatory fields and hydrogen masers. Rev. Mod. Phys. 62, 541–552 (1990).
Cronin, A., Schmiedmayer, J. & Pritchard, D. Optics and interferometry with atoms and molecules. Rev. Mod. Phys. 81, 1051–1129 (2009).
Vandersypen, L. M. K. & Chuang, I. L. NMR techniques for quantum control and computation. Rev. Mod. Phys. 76, 1037–1069 (2005).
Roos, C. F., Chwalla, M., Kim, K., Riebe, M. & Blatt, R. Designer atoms’ for quantum metrology. Nature 443, 316–319 (2006).
De Kieviet, M., Dubbers, D., Schmidt, C., Scholz, D. & Spinola, U. 3He Spin Echo: New atomic beam technique for probing phenomena in the neV range. Phys. Rev. Lett 75, 1919–1922 (1995).
Baker, C. A. et al. An improved experimental limit on the electric dipole moment of the neutron. Phys. Rev. Lett 97, 131801 (2006).
Abele, H., Jenke, T., Stadler, D. & Geltenbort, P. QuBounce: The dynamics of ultra-cold neutrons falling in the gravity potential of the Earth. Nucl. Phys. A827, 593c–595c (2009).
Jenke, T., Stadler, D., Abele, H. & Geltenbort, P. Q-BOUNCE—experiments with quantum bouncing ultracold neutrons. Nucl. Instr. Meth. A 611, 318–323 (2009).
Nesvizhevsky, V. V. et al. Quantum states of neutrons in the Earth’s gravitational field. Nature 415, 297–299 (2002).
Nesvizhevsky, V. V. et al. Study of neutron quantum states in the gravity field. Eur. Phys. J. C40, 479–491 (2005).
Westphal, A. et al. A quantum mechanical description of the experiment on the observation of gravitationally bound states. Eur. Phys. J. C51, 367–375 (2007).
Kreuz, M. et al. A method to measure the resonance transitions between the gravitationally bound quantum states of neutrons in the GRANIT spectrometer. Nucl. Instr. Meth. Phys. Res. A 611, 326–330 (2009).
Hamilton, W. A., Klein, A. G., Opat, G. I. & Timmins, P. A. Neutron diffraction by surface acoustic waves. Phys. Rev. Lett. 58, 2770–2773 (1987).
Felber, J., Gähler, R., Rausch, C. & Golub, R. Matter waves at a vibrating surface: Transition from quantum-mechanical to classical behaviour. Phys. Rev. A53, 319–328 (1996).
Steane, A., Szriftgiser, P., Desbiolles, P. & Dalibard, J. Phase modulation of atomic de Broglie waves. Phys. Rev. Lett. 74, 4972–4975 (1995).
Bernet, S., Oberthaler, M. K., Abfalterer, R., Schmiedmayer, J. & Zeilinger, A. Coherent frequency shift of atomic matter waves. Phys. Rev. Lett. 77, 5160–5163 (1996).
Grimm, R., Weidemüller, M. & Ovchinnikov, Y. B. Optical dipole traps for neutral atoms. Adv. Atomic Mol. Opt. Phys. 42, 95–170 (2000).
Callin, P. & Burgess, C. P. Deviations from Newton’s law in supersymmetric large extra dimensions. Nucl. Phys. B752, 60–79 (2006).
Sundrum, R. Towards an effective particle-string resolution of the cosmological constant problem. J. High Energy Phys. 07, 001 (1999).
Westphal, A., Abele, H. & Baeßler, S. Analytically derived limits on short-range fifth forces from quantum states of neutrons in the Earth’s gravitational field. Preprint at http://arxiv.org/abs/hep-ph/0703108.
Baeßler, S., Nesvizhevsky, V. V., Protasov, K. V. & Voronin, A. Y. Constraint on the coupling of axionlike particles to matter via an ultracold neutron gravitational experiment. Phys. Rev. D 75, 075006 (2007).
Abele, H., Baessler, S. & Westphal, A. in Quantum Gravity—from Theory to Experimental Search’ (ed. Lämmerzahl, C.) (Lect. Notes Phys., Vol. 631, Springer, 2003).
Nesvizhevsky, V. V. & Protasov, K. V. Constraints on non-Newtonian gravity from the experiment on neutron quantum states in the earth’s gravitational field. Classical Quant. Gravity 21, 4557–4566 (2004).
Abele, H. The neutron. Its properties and basic interactions. Prog. Part. Nucl. Phys. 60, 1–81 (2008).
Abele, H., Jenke, T., Leeb, H. & Schmiedmayer, J. Ramsey’s method of separated oscillating fields and its application to gravitationally induced quantum phaseshifts. Phys. Rev. D 81, 065019 (2010).
Acknowledgements
We gratefully acknowledge support from the Austrian Science Fund (FWF) under Contract No. I529-N20 and the German Research Foundation (DFG) as part of the Priority Programme (SPP) 1491 ‘Precision experiments in particle and astrophysics with cold and ultracold neutrons’, the DFG Excellence Initiative ‘Origin of the Universe’, and DFG support under Contract No. Ab128/2-1. The neutron mirrors were characterized by S-DH Sputterdünnschichttechnik, Heidelberg.
Author information
Authors and Affiliations
Contributions
All of the authors made a substantial contribution to this work.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Rights and permissions
About this article
Cite this article
Jenke, T., Geltenbort, P., Lemmel, H. et al. Realization of a gravity-resonance-spectroscopy technique. Nature Phys 7, 468–472 (2011). https://doi.org/10.1038/nphys1970
Received:
Accepted:
Published:
Issue date:
DOI: https://doi.org/10.1038/nphys1970
This article is cited by
-
Relaxation to Quantum Equilibrium and the Born Rule in Nelson’s Stochastic Dynamics
Foundations of Physics (2023)
-
Tests of fundamental quantum mechanics and dark interactions with low-energy neutrons
Nature Reviews Physics (2021)
-
Interference of several gravitational quantum states of antihydrogen in GBAR experiment
Hyperfine Interactions (2019)
-
Acoustic Rabi oscillations between gravitational quantum states and impact on symmetron dark energy
Nature Physics (2018)
-
The dark side of neutrons
Nature Physics (2018)


