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arXiv:1201.1778 · Classical and Quantum Gravity

Reply to comment on: ‘Does an atom interferometer test the gravitational redshift at the Compton frequency?’

Peter Wolf, Luc Blanchet A, Christian Bordé, Serge Reynaud, Christophe Salomon, Claude N. Cohen-Tannoudji

Published Jan 26, 2012• 15 citations
arXivHTMLPDF

Abstract

We reply to a comment by Hohensee et al on: 'Does an atom interferometer test the gravitational redshift at the Compton frequency' and show that the main result of that paper, namely that atom interferometric gravimeters do not test the gravitational redshift at the Compton frequency, remains valid.
DOI
10.1088/0264-9381/29/4/048002

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PublicationsWolf P., Blanchet L., Bordé C.J., Reynaud S., Salomon C. et Cohen-Tannoudji C., « Reply to the comment on ‘Does an atom interferometer test the gravitational redshift at the Compton frequency?’« , Class. Quantum Grav., 29, 2012, 048002.Wassen W., Cohen-Tannoudji C., Leduc M., Boiron D., Westbrook C.I., Truscott A., Baldwin K., Birkl G., Cancio P., Trippenbach M., « Cold and trapped metastable noble gases », Rev. Mod. Phys., 84, 2012, 175.OuvragesCohen-Tannoudji C. et Guéry-Odelin...

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Atomic interference experiments can probe the gravitational redshift via the internal energy splitting of atoms and thus give direct access to test the universality of the coupling between matter-energy and gravity at different spacetime points. By including possible violations of the equivalence principle in a fully quantized treatment of all atomic degrees of freedom, we characterize how the sensitivity to gravitational redshift violations arises in atomic clocks and atom interferometers, as well as their underlying limitations. Specifically, we show that: (i) Contributions beyond linear order to trapping potentials lead to such a sensitivity of trapped atomic clocks. (ii) Bragg-type interferometers, even with a superposition of internal states, with state-independent, linear interaction potentials are at first insensitive to gravitational redshift tests. However, modified configurations, for example by relaunching the atoms, can mimic such tests under certain conditions and may constitute a competitive alternative. (iii) Guided atom interferometers are comparable to atomic clocks. (iv) Internal transitions lead to state-dependent interaction potentials through which light-pulse atom interferometers can become sensitive to gravitational redshift violations.

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PublicationsWolf P., Blanchet L., Bordé C.J., Reynaud S., Salomon C. et Cohen-Tannoudji C., « Reply to the comment on ‘Does an atom interferometer test the gravitational redshift at the Compton frequency?’« , Class. Quantum Grav., 29, 2012, 048002.Wassen W., Cohen-Tannoudji C., Leduc M., Boiron D., Westbrook C.I., Truscott A., Baldwin K., Birkl G., Cancio P., Trippenbach M., « Cold and trapped metastable noble gases », Rev. Mod. Phys., 84, 2012, 175.OuvragesCohen-Tannoudji C. et Guéry-Odelin...
From the principle of equivalence, Einstein predicted that clocks slow down in a gravitational field. Since the general theory of relativity is based on the principle of equivalence, it is essential to test this prediction accurately. Muller, Peters and Chu claim that a reinterpretation of decade old experiments with atom interferometers leads to a sensitive test of this gravitational redshift effect at the Compton frequency. Wolf et al dispute this claim and adduce arguments against it. In this article, we distill these arguments to a single fundamental objection: an atom is NOT a clock ticking at the Compton frequency. We conclude that atom interferometry experiments conducted to date do not yield such sensitive tests of the gravitational redshift. Finally, we suggest a new interferometric experiment to measure the gravitational redshift, which realises a quantum version of the classical clock "paradox".
Atom interferometers allow the measurement of the acceleration of freely falling atoms with respect to an experimental platform at rest on Earth's surface. Such experiments have been used to test the universality of free fall by comparing the acceleration of the atoms to that of a classical freely falling object. In a recent paper, Müller, Peters and Chu [Nature {\bf 463}, 926-929 (2010)] argued that atom interferometers also provide a very accurate test of the gravitational redshift when considering the atom as a clock operating at the Compton frequency associated with the rest mass. We analyze this claim in the frame of general relativity and of different alternative theories. We show that the difference of "Compton phases" between the two paths of the interferometer is actually zero in a large class of theories, including general relativity, all metric theories of gravity, most non-metric theories and most theoretical frameworks used to interpret the violations of the equivalence principle. Therefore, in most plausible theoretical frameworks, there is no redshift effect and atom interferometers only test the universality of free fall. We also show that frameworks in which atom interferometers would test the redshift pose serious problems, such as (i) violation of the Schiff conjecture, (ii) violation of the Feynman path integral formulation of quantum mechanics and of the principle of least action for matter waves, (iii) violation of energy conservation, and more generally (iv) violation of the particle-wave duality in quantum mechanics. Standard quantum mechanics is no longer valid in such frameworks, so that a consistent interpretation of the experiment would require an alternative formulation of quantum mechanics. As such an alternative has not been proposed to date, we conclude that the interpretation of atom interferometers as testing the gravitational redshift is unsound.
Atomic interference experiments can probe the gravitational redshift via the internal energy splitting of atoms and thus give direct access to test the universality of the coupling between matter-energy and gravity at different spacetime points. By including possible violations of the equivalence principle in a fully quantized treatment of all atomic degrees of freedom, we characterize how the sensitivity to gravitational redshift violations arises in atomic clocks and atom interferometers, as well as their underlying limitations. Specifically, we show that: (i) Contributions beyond linear order to trapping potentials lead to such a sensitivity of trapped atomic clocks. (ii) Bragg-type interferometers, even with a superposition of internal states, with state-independent, linear interaction potentials are at first insensitive to gravitational redshift tests. However, modified configurations, for example by relaunching the atoms, can mimic such tests under certain conditions and may constitute a competitive alternative. (iii) Guided atom interferometers are comparable to atomic clocks. (iv) Internal transitions lead to state-dependent interaction potentials through which light-pulse atom interferometers can become sensitive to gravitational redshift violations.