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Bauer M, Rostagni G. Fifth Forces from QCD Axions Scale Differently. PHYSICAL REVIEW LETTERS 2024; 132:101802. [PMID: 38518308 DOI: 10.1103/physrevlett.132.101802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 01/29/2024] [Indexed: 03/24/2024]
Abstract
We reexamine the low-energy potential for a macroscopic fifth force generated from the exchange of two axions. The shift symmetry of the linear axion interactions leads to a potential falling off as V(r)∼1/r^{5}. We find that in the case of the QCD axion higher-order terms in the Lagrangian break the shift symmetry and lead to the dominant contribution to the potential scaling as V(r)∼1/r^{3}. These terms are generated by the same physics responsible for the axion mass, and therefore the new contributions to the potential induce a different force for external nucleons and leptons. We demonstrate how this result affects the sensitivity of searches for new long-range forces.
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Affiliation(s)
- Martin Bauer
- Department of Physics, Institute for Particle Physics Phenomenology, Durham University, Durham DH1 3LE, United Kingdom
| | - Guillaume Rostagni
- Department of Physics, Institute for Particle Physics Phenomenology, Durham University, Durham DH1 3LE, United Kingdom
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2
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Killian C, Burkley Z, Blumer P, Crivelli P, Gustafsson FP, Hanski O, Nanda A, Nez F, Nesvizhevsky V, Reynaud S, Schreiner K, Simon M, Vasiliev S, Widmann E, Yzombard P. GRASIAN: towards the first demonstration of gravitational quantum states of atoms with a cryogenic hydrogen beam. THE EUROPEAN PHYSICAL JOURNAL. D, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 2023; 77:50. [PMID: 37007801 PMCID: PMC10060317 DOI: 10.1140/epjd/s10053-023-00634-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Accepted: 03/12/2023] [Indexed: 06/19/2023]
Abstract
At very low energies, a light neutral particle above a horizontal surface can experience quantum reflection. The quantum reflection holds the particle against gravity and leads to gravitational quantum states (gqs). So far, gqs were only observed with neutrons as pioneered by Nesvizhevsky and his collaborators at ill. However, the existence of gqs is predicted also for atoms. The Grasian collaboration pursues the first observation and studies of gqs of atomic hydrogen. We propose to use atoms in order to exploit the fact that orders of magnitude larger fluxes compared to those of neutrons are available. Moreover, recently the q-Bounce collaboration, performing gqs spectroscopy with neutrons, reported a discrepancy between theoretical calculations and experiment which deserves further investigations. For this purpose, we set up a cryogenic hydrogen beam at 6 K . We report on our preliminary results, characterizing the hydrogen beam with pulsed laser ionization diagnostics at 243 nm .
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Affiliation(s)
- Carina Killian
- Stefan Meyer Institute for Subatomic Physics, Austrian Academy of Sciences, Kegelgasse 27, 1030 Vienna, Austria
| | - Zakary Burkley
- Institute for Particle Physics and Astrophysics, ETH, Zurich, 8093 Zurich, Switzerland
| | - Philipp Blumer
- Institute for Particle Physics and Astrophysics, ETH, Zurich, 8093 Zurich, Switzerland
| | - Paolo Crivelli
- Institute for Particle Physics and Astrophysics, ETH, Zurich, 8093 Zurich, Switzerland
| | - Fredrik P. Gustafsson
- Stefan Meyer Institute for Subatomic Physics, Austrian Academy of Sciences, Kegelgasse 27, 1030 Vienna, Austria
| | - Otto Hanski
- Department of Physics and Astronomy, University of Turku, 20014 Turku, Finland
| | - Amit Nanda
- Stefan Meyer Institute for Subatomic Physics, Austrian Academy of Sciences, Kegelgasse 27, 1030 Vienna, Austria
| | - François Nez
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Université, Collège de France, 75252 Paris, France
| | - Valery Nesvizhevsky
- Institut Max von Laue - Paul Langevin, 71 avenue des Martyrs, 38042 Grenoble, France
| | - Serge Reynaud
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Université, Collège de France, 75252 Paris, France
| | - Katharina Schreiner
- Institute for Particle Physics and Astrophysics, ETH, Zurich, 8093 Zurich, Switzerland
- Institut Max von Laue - Paul Langevin, 71 avenue des Martyrs, 38042 Grenoble, France
| | - Martin Simon
- Stefan Meyer Institute for Subatomic Physics, Austrian Academy of Sciences, Kegelgasse 27, 1030 Vienna, Austria
| | - Sergey Vasiliev
- Department of Physics and Astronomy, University of Turku, 20014 Turku, Finland
| | - Eberhard Widmann
- Stefan Meyer Institute for Subatomic Physics, Austrian Academy of Sciences, Kegelgasse 27, 1030 Vienna, Austria
| | - Pauline Yzombard
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Université, Collège de France, 75252 Paris, France
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3
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Tutunnikov I, Rajitha KV, Voronin AY, Nesvizhevsky VV, Averbukh IS. Impulsively Excited Gravitational Quantum States: Echoes and Time-Resolved Spectroscopy. PHYSICAL REVIEW LETTERS 2021; 126:170403. [PMID: 33988422 DOI: 10.1103/physrevlett.126.170403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2020] [Revised: 12/18/2020] [Accepted: 03/29/2021] [Indexed: 06/12/2023]
Abstract
We theoretically study an impulsively excited quantum bouncer (QB)-a particle bouncing off a surface in the presence of gravity. A pair of time-delayed pulsed excitations is shown to induce a wave-packet echo effect-a partial rephasing of the QB wave function appearing at twice the delay between pulses. In addition, an appropriately chosen observable [here, the population of the ground gravitational quantum state (GQS)] recorded as a function of the delay is shown to contain the transition frequencies between the GQSs, their populations, and partial phase information about the wave-packet quantum amplitudes. The wave-packet echo effect is a promising candidate method for precision studies of GQSs of ultracold neutrons, atoms, and antiatoms confined in closed gravitational traps.
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Affiliation(s)
- I Tutunnikov
- AMOS and Department of Chemical and Biological Physics, The Weizmann Institute of Science, Rehovot 7610001, Israel
| | - K V Rajitha
- AMOS and Department of Chemical and Biological Physics, The Weizmann Institute of Science, Rehovot 7610001, Israel
| | - A Yu Voronin
- P. N. Lebedev Physical Institute, 53 Leninsky Prospect, Moscow Ru-119333, Russia
| | - V V Nesvizhevsky
- Institut Max von Laue-Paul Langevin (ILL), 71 avenue des Martyrs, F-38042 Grenoble, France
| | - I Sh Averbukh
- AMOS and Department of Chemical and Biological Physics, The Weizmann Institute of Science, Rehovot 7610001, Israel
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4
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Abstract
In the Einstein–Cartan gravitational theory with the chameleon field, while changing its mass independently of the density of its environment, we analyze the Friedmann–Einstein equations for the Universe’s evolution with the expansion parameter a being dependent on time only. We analyze the problem of an identification of the chameleon field with quintessence, i.e., a canonical scalar field responsible for dark energy dynamics, and for the acceleration of the Universe’s expansion. We show that since the cosmological constant related to the relic dark energy density is induced by torsion (Astrophys. J.2016, 829, 47), the chameleon field may, in principle, possess some properties of quintessence, such as an influence on the dark energy dynamics and the acceleration of the Universe’s expansion, even in the late-time acceleration, but it cannot be identified with quintessence to the full extent in the classical Einstein–Cartan gravitational theory.
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5
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Llinares C, Brax P. Detecting Coupled Domain Walls in Laboratory Experiments. PHYSICAL REVIEW LETTERS 2019; 122:091102. [PMID: 30932538 DOI: 10.1103/physrevlett.122.091102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2018] [Revised: 12/03/2018] [Indexed: 06/09/2023]
Abstract
The inherently unstable nature of domain walls makes their detection in laboratory experiments extremely challenging. We propose a method to stabilize domain walls inside a cavity. The method requires domain walls coupled to matter, a condition that is fulfilled by the symmetron model. We suggest two ways in which the walls could be detected once stabilized: studying the trajectories of ultracold neutrons either via the deflection angle of a neutron beam induced by the attraction towards the wall or through the time difference of these particles passing through the wall. We give realistic estimates for these effects and expect that they should be detectable experimentally.
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Affiliation(s)
- Claudio Llinares
- Institute for Computational Cosmology, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom and Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Portsmouth PO1 3FX, United Kingdom
| | - Philippe Brax
- Institut de Physique Théorique, Université Paris-Saclay, CEA, CNRS, F-91191 Gif-sur-Yvette Cedex, France
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6
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Jenke T, Bosina J, Cronenberg G, Filter H, Geltenbort P, Ivanov AN, Micko J, Pitschmann M, Rechberger T, Sedmik RI, Thalhammer M, Abele H. Testing gravity at short distances: Gravity Resonance Spectroscopy with qBounce. EPJ WEB OF CONFERENCES 2019. [DOI: 10.1051/epjconf/201921905003] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Neutrons are the ideal probes to test gravity at short distances – electrically neutral and only hardly polarizable. Furthermore, very slow, so-called ultracold neutrons form bound quantum states in the gravity potential of the Earth. This allows combining gravity experiments at short distances with powerful resonance spectroscopy techniques, as well as tests of the interplay between gravity and quantum mechanics. In the last decade, the qBounce collaboration has been performing several measurement campaigns at the ultracold and very cold neutron facility PF2 at the Institut Laue-Langevin. A new spectroscopy technique, Gravity Resonance Spectroscopy, was developed. The results were applied to test various Dark Energy and Dark Matter scenarios in the lab, like Axions, Chameleons and Symmetrons. This article reviews Gravity Resonance Spectroscopy, explains its key technology and summarizes the results obtained during the past decade.
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Burrage C. What laboratory experiments can teach us about cosmology: A chameleon example. EPJ WEB OF CONFERENCES 2019. [DOI: 10.1051/epjconf/201921905001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Laboratory experiments can shed light on theories of new physics introduced in order to explain cosmological mysteries, including the nature of dark energy and dark matter. In this article I will focus on one particular example of this, the chameleon model. The chameleon is an example of a theory which could modify gravity on cosmological distance scales, but its non-linear behavior means that it can also be tested with suitably designed laboratory experiments. The aim of this overview is to present recent theoretical developments to the experimental community.
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Burrage C, Sakstein J. Tests of chameleon gravity. LIVING REVIEWS IN RELATIVITY 2018; 21:1. [PMID: 29576739 PMCID: PMC5856913 DOI: 10.1007/s41114-018-0011-x] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/26/2017] [Accepted: 02/06/2018] [Indexed: 06/08/2023]
Abstract
Theories of modified gravity, where light scalars with non-trivial self-interactions and non-minimal couplings to matter-chameleon and symmetron theories-dynamically suppress deviations from general relativity in the solar system. On other scales, the environmental nature of the screening means that such scalars may be relevant. The highly-nonlinear nature of screening mechanisms means that they evade classical fifth-force searches, and there has been an intense effort towards designing new and novel tests to probe them, both in the laboratory and using astrophysical objects, and by reinterpreting existing datasets. The results of these searches are often presented using different parametrizations, which can make it difficult to compare constraints coming from different probes. The purpose of this review is to summarize the present state-of-the-art searches for screened scalars coupled to matter, and to translate the current bounds into a single parametrization to survey the state of the models. Presently, commonly studied chameleon models are well-constrained but less commonly studied models have large regions of parameter space that are still viable. Symmetron models are constrained well by astrophysical and laboratory tests, but there is a desert separating the two scales where the model is unconstrained. The coupling of chameleons to photons is tightly constrained but the symmetron coupling has yet to be explored. We also summarize the current bounds on f(R) models that exhibit the chameleon mechanism (Hu and Sawicki models). The simplest of these are well constrained by astrophysical probes, but there are currently few reported bounds for theories with higher powers of R. The review ends by discussing the future prospects for constraining screened modified gravity models further using upcoming and planned experiments.
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Affiliation(s)
- Clare Burrage
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD UK
| | - Jeremy Sakstein
- Department of Physics and Astronomy, Center for Particle Cosmology, University of Pennsylvania, Philadelphia, PA 19104 USA
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Brax P. What makes the Universe accelerate? A review on what dark energy could be and how to test it. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:016902. [PMID: 28936984 DOI: 10.1088/1361-6633/aa8e64] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Explaining the origin of the acceleration of the expansion of the Universe remains as challenging as ever. In this review, we present different approaches from dark energy to modified gravity. We also emphasize the quantum nature of the problem and the need for an explanation which should violate Weinberg's no go theorem. This might involve a self-tuning mechanism or the acausal sequestering of the vacuum energy. Laboratory tests of the coupling to matter of nearly massless scalar fields, which could be one of the features required to explain the cosmic acceleration, are also reviewed.
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Affiliation(s)
- Philippe Brax
- Institut de Physique Théorique, Université Paris-Saclay, CEA, CNRS, F-91191 Gif/Yvette Cedex, France
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10
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Burrage C, Copeland EJ, Millington P. Radiative Screening of Fifth Forces. PHYSICAL REVIEW LETTERS 2016; 117:211102. [PMID: 27911565 DOI: 10.1103/physrevlett.117.211102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2016] [Indexed: 06/06/2023]
Abstract
We describe a symmetron model in which the screening of fifth forces arises at the one-loop level through the Coleman-Weinberg mechanism of spontaneous symmetry breaking. We show that such a theory can avoid current constraints on the existence of fifth forces but still has the potential to give rise to observable deviations from general relativity, which could be seen in cold atom experiments.
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Affiliation(s)
- Clare Burrage
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Edmund J Copeland
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Peter Millington
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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11
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Schlögel S, Clesse S, Füzfa A. Probing modified gravity with atom-interferometry: A numerical approach. Int J Clin Exp Med 2016. [DOI: 10.1103/physrevd.93.104036] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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12
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Li K, Arif M, Cory DG, Haun R, Heacock B, Huber MG, Nsofini J, Pushin DA, Saggu P, Sarenac D, Shahi CB, Skavysh V, Snow WM, Young AR. Neutron limit on the strongly-coupled chameleon field. PHYSICAL REVIEW. D. (2016) 2016; 93:10.1103/physrevd.93.062001. [PMID: 34859165 PMCID: PMC8634167 DOI: 10.1103/physrevd.93.062001] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
The physical origin of the dark energy that causes the accelerated expansion rate of the Universe is one of the major open questions of cosmology. One set of theories postulates the existence of a self-interacting scalar field for dark energy coupling to matter. In the chameleon dark energy theory, this coupling induces a screening mechanism such that the field amplitude is nonzero in empty space but is greatly suppressed in regions of terrestrial matter density. However measurements performed under appropriate vacuum conditions can enable the chameleon field to appear in the apparatus, where it can be subjected to laboratory experiments. Here we report the most stringent upper bound on the free neutron-chameleon coupling in the strongly coupled limit of the chameleon theory using neutron interferometric techniques. Our experiment sought the chameleon field through the relative phase shift it would induce along one of the neutron paths inside a perfect crystal neutron interferometer. The amplitude of the chameleon field was actively modulated by varying the millibar pressures inside a dual-chamber aluminum cell. We report a 95% confidence level upper bound on the neutron-chameleon coupling β ranging from β < 4.7 × 106 for a Ratra-Peebles index of n = 1 in the nonlinear scalar field potential to β < 2.4 × 107 for n = 6, one order of magnitude more sensitive than the most recent free neutron limit for intermediate n. Similar experiments can explore the full parameter range for chameleon dark energy in the foreseeable future.
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Affiliation(s)
- K. Li
- Department of Physics, Indiana University, Bloomington, Indiana 47408, USA
- Center for Exploration of Energy and Matter, Indiana University, Bloomington, Indiana 47408, USA
| | - M. Arif
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - D. G. Cory
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
| | - R. Haun
- Department of Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - B. Heacock
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
- Triangle Universities Nuclear Laboratory, Durham, North Carolina 27708, USA
| | - M. G. Huber
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - J. Nsofini
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - D. A. Pushin
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - P. Saggu
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - D. Sarenac
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - C. B. Shahi
- Department of Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - V. Skavysh
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - W. M. Snow
- Department of Physics, Indiana University, Bloomington, Indiana 47408, USA
- Center for Exploration of Energy and Matter, Indiana University, Bloomington, Indiana 47408, USA
| | - A. R. Young
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
- Triangle Universities Nuclear Laboratory, Durham, North Carolina 27708, USA
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13
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Abstract
Fundamental questions about dark matter and dark energy are probed in laboratory experiments
[Also see Reports by
Hamilton
et al.
and
XENON Collaboration
]
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Affiliation(s)
- Jörg Schmiedmayer
- Vienna Center for Quantum Science and Technology Atominstitut, TU-Wien Stadionallee 2 1020 Vienna, Austria.
| | - Hartmut Abele
- Vienna Center for Quantum Science and Technology Atominstitut, TU-Wien Stadionallee 2 1020 Vienna, Austria.
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Abele H, Jenke T, Konrad G. Spectroscopy with cold and ultra-cold neutrons. EPJ WEB OF CONFERENCES 2015. [DOI: 10.1051/epjconf/20159305002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Ivanov A, Pitschmann M. Nonrelativistic approximation of the Dirac equation for slow fermions in static metric spacetimes. Int J Clin Exp Med 2014. [DOI: 10.1103/physrevd.90.045040] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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17
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Jenke T, Cronenberg G, Burgdörfer J, Chizhova LA, Geltenbort P, Ivanov AN, Lauer T, Lins T, Rotter S, Saul H, Schmidt U, Abele H. Gravity resonance spectroscopy constrains dark energy and dark matter scenarios. PHYSICAL REVIEW LETTERS 2014; 112:151105. [PMID: 24785025 DOI: 10.1103/physrevlett.112.151105] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2013] [Indexed: 06/03/2023]
Abstract
We report on precision resonance spectroscopy measurements of quantum states of ultracold neutrons confined above the surface of a horizontal mirror by the gravity potential of Earth. Resonant transitions between several of the lowest quantum states are observed for the first time. These measurements demonstrate that Newton's inverse square law of gravity is understood at micron distances on an energy scale of 10-14 eV. At this level of precision, we are able to provide constraints on any possible gravitylike interaction. In particular, a dark energy chameleon field is excluded for values of the coupling constant β>5.8×108 at 95% confidence level (C.L.), and an attractive (repulsive) dark matter axionlike spin-mass coupling is excluded for the coupling strength gsgp>3.7×10-16 (5.3×10-16) at a Yukawa length of λ=20 μm (95% C.L.).
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Affiliation(s)
- T Jenke
- Atominstitut, Technische Universität Wien, Stadionallee 2, 1020 Wien, Austria
| | - G Cronenberg
- Atominstitut, Technische Universität Wien, Stadionallee 2, 1020 Wien, Austria
| | - J Burgdörfer
- Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria
| | - L A Chizhova
- Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria
| | - P Geltenbort
- Institut Laue-Langevin, BP 156, 6 Rue Jules Horowitz, 38042 Grenoble Cedex 9, France
| | - A N Ivanov
- Atominstitut, Technische Universität Wien, Stadionallee 2, 1020 Wien, Austria
| | - T Lauer
- FRM II, Technische Universität München, Lichtenbergstraße 1, 85748 Garching, Germany
| | - T Lins
- Atominstitut, Technische Universität Wien, Stadionallee 2, 1020 Wien, Austria
| | - S Rotter
- Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria
| | - H Saul
- Atominstitut, Technische Universität Wien, Stadionallee 2, 1020 Wien, Austria
| | - U Schmidt
- Physikalisches Institut, Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
| | - H Abele
- Atominstitut, Technische Universität Wien, Stadionallee 2, 1020 Wien, Austria
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