The computation of the phase shift in a symmetric atom interferometer in the presence of a gravitational field is reviewed. The difference of action-phase integrals between the two paths of the interferometer is zero for any Lagrangian which is at most quadratic in position and velocity. We emphasize that in a large class of theories of gravity the atom interferometer permits a test of the weak version of the equivalence principle (or universality of free fall) by comparing the acceleration of atoms with that of ordinary bodies, but is insensitive to that aspect of the equivalence principle known as the gravitational redshift or universality of clock rates.
The computation of the phase shift in a symmetric atom interferometer in the presence of a gravitational field is reviewed. The difference of action-phase integrals between the two paths of the interferometer is zero for any Lagrangian which is at most quadratic in position and velocity. We emphasize that in a large class of theories of gravity the atom interferometer permits a test of the weak version of the equivalence principle (or universality of free fall) by comparing the acceleration of atoms with that of ordinary bodies, but is insensitive to that aspect of the equivalence principle known as the gravitational redshift or universality of clock rates.
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.
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".
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.
The search for a fundamental, self-consistent theoretical framework to cover phenomena over all energy scales is possibly the most challenging quest of contemporary physics. Approaches to reconcile quantum mechanics and general relativity entail the modification of their foundations such as the equivalence principle. This corner stone of general relativity is suspected to be violated in various scenarios and is therefore under close scrutiny. Experiments based on the manipulation of cold atoms are excellently suited to challenge its different facets. Freely falling atoms constitute ideal test masses for tests of the universality of free fall in interferometric setups. Moreover, the superposition of internal energy eigenstates provides the notion of a clock, which allows to perform tests of the gravitational redshift. Furthermore, as atom interferometers constitute outstanding phasemeters, they hold the promise to detect gravitational waves, another integral aspect of general relativity. In recent years, atom interferometers have developed into versatile sensors with excellent accuracy and stability, and allow to probe physics at the interface of quantum mechanics and general relativity without classical analog. In this thesis, various aspects regarding tests of general relativity with atom interferometry have been theoretically investigated. This includes the analysis of fundamental effects as well as feasibility studies of experimental configurations. The work is partially focussed on a space-borne mission scenario for a dedicated quantum test of the universality of free fall beyond state-of-the-art by dropping matter waves of different elements. To enable the target accuracy at the level of 10^(−17), a compensation scheme has been developed and discussed, mitigating the detrimental effects of imperfect test mass co-location upon release and relaxing the requirements on the source preparation by several orders of magnitude. In addition, it was demonstrated that the careful design of quantum degenerate sources is indispensable for these experiments, requiring tailored schemes to prepare miscible binary sources. The possibility to test the gravitational redshift with atom interferometers has also been examined in this thesis and connected to the ideas of clock interferometry. With the proof that closed light pulse atom interferometers without transitions between internal internal states are not sensitive to gravitational time dilation, an ongoing scientific debate has been resolved. Instead, certain configurations were shown to implement a quantum version of the special-relativistic twin paradox, for which an experiment has been proposed. Finally, requirements on atomic sources and atom optics for scenarios of gravitational wave detection on ground and in space have been investigated.
The weak equivalence principle (WEP), that is, the universality of free fall, states that all point-like neutral particles in a gravitational field fall in the same way. This is the basis of the geometrization of the gravitational interaction. Together with further requirements on the behavior of point particles, light propagation and clocks one can show that gravity is modeled by a Riemannian geometry. Since in the quantum domain all objects are extended, it is not clear whether the notion of a WEP in the quantum domain makes sense at all. We show that for matter wave interferometry the notion of WEP still can be given a meaning. We give a short overview over schemes which allows a violation of the WEP and emphasize that there are also schemes which show that there might be violations of the WEP in the quantum regime which are not present classically. This makes a test of the WEP with quantum matter necessary. We also give a brief outline of the efforts made for testing the WEP with interferometry with cold atoms in the Bremen drop tower carried out by the QUANTUS and PRIMUS collaboration.
We describe a test of the equivalence principle with quantum probe particles based on atom interferometry. For the measurement, a light pulse atom interferometer based on the diffraction of atoms from effective absorption gratings of light has been developed. A differential measurement of the Earth’s gravitational acceleration g for the two rubidium isotopes 85 Rb and 87 Rb has been performed, yielding a difference Δ g / g =(1.2±1.7)×10 −7 . In addition, the dependence of the free fall on the relative orientation of the electron to the nuclear spin was studied by using atoms in two different hyperfine states. The determined difference in the gravitational acceleration is Δ g / g =(0.4±1.2)×10 −7 . Within their experimental accuracy, both measurements are consistent with a free atomic fall that is independent from internal composition and spin orientation.