In recent years there has been enormous progress in matter wave interferometry. The Colella-Overhauser-Werner (COW) type of neutron interferometer and the Kasevich-Chu (K-C) atom interferometer are the prototypes of such devices and the issue of whether they are sensitive to relativistic effects has recently aroused much controversy. We examine the question as to what extent the gravitational redshift and the related twin paradox effect can be seen in both of these atom and neutron interferometers. We point out an asymmetry between the two types of devices. Because of this, the nonvanishing, nonrelativistic residue of both effects can be seen in the neutron interferometer, while in the K-C interferometer the effects cancel out, leaving no residue, although they could be present in other types of atom interferometers. Also, the necessary shifting of the laser frequency (chirping) in the atom interferometer effectively changes the laboratory into a free-fall system, which could be exploited for other experiments.
In recent years there has been enormous progress in matter wave interferometry. The Colella-Overhauser-Werner (COW) type of neutron interferometer and the Kasevich-Chu (K-C) atom interferometer are the prototypes of such devices and the issue of whether they are sensitive to relativistic effects has recently aroused much controversy. We examine the question as to what extent the gravitational redshift and the related twin paradox effect can be seen in both of these atom and neutron interferometers. We point out an asymmetry between the two types of devices. Because of this, the nonvanishing, nonrelativistic residue of both effects can be seen in the neutron interferometer, while in the K-C interferometer the effects cancel out, leaving no residue, although they could be present in other types of atom interferometers. Also, the necessary shifting of the laser frequency (chirping) in the atom interferometer effectively changes the laboratory into a free-fall system, which could be exploited for other experiments.
Motivated by the recent debate on whether the Kasevich-Chu atom interferometer can measure the gravitational redshift, we show that in different representations of quantum mechanics chosen for the calculation, the observed phase shift appears as though it originates from different physical phenomena. In particular, we demonstrate that the decomposition of the total phase shift into three dynamical phases, which emerges in a semiclassical approach and is at the very heart of the redshift controversy, does not appear in an exact treatment based on a representation-free analysis. Here only two phenomena determine the phase shift: the difference of the laser phases and the acceleration of the atom. Hence, the Kasevich-Chu interferometer is an accelerometer or gravimeter.
The phase shift in interferometry due to the space-time curvature is computed in nonrelativistic and relativistic physics. This treatment is applied to an interferometer analogous to the perfect crystal interferometer used in the Colella-Overhauser-Werner experiment with thermal neutrons, an interferometer consisting of only horizontal mirrors, suitable for ultracold neutrons, and optical interferometry. Experiments are proposed to detect the effect of the tidal forces of the Earth, Moon, and the Sun, for the first time in interferometry. The phase shift in neutron interferometry due to terrestrial objects is considered and an experiment is proposed with superfluid helium as the source of gravity. This would provide, for the first time, direct evidence concerning the gravitational interaction between two quantum-mechanical states. The possibility of detecting purely general-relativistic effects due to curvature, by means of neutron interferometry, is also explored.
The neutron interferometer is a unique instrument that allows one to construct a neutron wave packet of macroscopic size, divide it into two components separated by centimeters, and then coherently recombine them. A number of experiments clearly showing the difference between quantum and classical theory have been performed with it, which are suitable for presentation in elementary quantum courses. This article presents a simple mathematical model of the interferometer, which can be used to illustrate clearly many of the surprising features of quantum systems. For example, one can describe an experiment to determine which component beam the neutron takes (an analog of the two-slit electron experiment). One can then trace in detail the loss of coherence of the wave function, rather than merely invoke the usual "handwaving" uncertainty arguments. The author discusses the effect of gravity on the neutron beam [the classic COW (Colella, Overhauser, and Werner) experiment], including a simple analysis in an accelerated reference frame, and its relation to the equivalence principle, the red shift, and the twin paradox. Also described are the effect of rotation of the neutron by 360\ifmmode^\circ\else\textdegree\fi{} to change its phase, the effect on the wave function of measuring the absence of the particle from a beam ("Dicke's paradox"), and a realizable version of Wheeler's "delayed-choice" experiments, as well as their relation to the problem of "Schr\"odinger's cat." The treatment is suitable for bright undergraduates and first-year graduate students.
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.
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.
The authors discuss the coherence properties of neutron scattering from perfect crystals and apply them to the splitting and coherent recombination of a neutron beam in a Laue-type interferometer. They also point out the difference between neutron and x-ray scattering in such devices and discuss the effect of a relative displacement of the various interferometer slabs on the fringe pattern. All this can be done without using the detailed dynamical theory of x-ray scattering. Various experiments are discussed, especially the neutron-gravity experiment of Colella, Overhauser, and Werner, which is analyzed both in the laboratory frame and in a frame freely falling with the neutron beam. The older electron diffraction experiment of Marton et al., and its relevance to the Aharonov---Bohm effect, is also discussed and reinterpreted, because the standard interpretation is not consistent with the results of the neutron experiment. An Appendix presents a general discussion of the transformation to a uniformly accelerated reference frame, as a guide to help analyze future such experiments.