Abstract:
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, M\"uller, Peters and Chu [Nature {\bf 463}, 926-929 (2010)] argued that atom interferometers also provide a very accurate test of the gravitational redshift (or universality of clock rates). Considering the atom as a clock operating at the Compton frequency associated with the rest mass, they claimed that the interferometer measures the gravitational redshift between the atom-clocks in the two paths of the interferometer at different values of gravitational potentials. In the present paper we analyze this claim in the frame of general relativity and of different alternative theories, and conclude that the interpretation of atom interferometers as testing the gravitational redshift at the Compton frequency is unsound. The present work is a summary of our extensive paper [Wolf et al., arXiv:1012.1194, Class. Quant. Grav. 28, 145017, (2011)], to which the reader is referred for more details.

Abstract:
In a recent paper, H. Mueller, A. Peters and S. Chu [A precision measurement of the gravitational redshift by the interference of matter waves, Nature 463, 926-929 (2010)] argued that atom interferometry experiments published a decade ago did in fact measure the gravitational redshift on the quantum clock operating at the very high Compton frequency associated with the rest mass of the Caesium atom. In the present Communication we show that this interpretation is incorrect.

Abstract:
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".

Abstract:
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.

Abstract:
We analyze the nature and performance of clocks formed by stabilizing an oscillator to the phase difference between two paths of an atom interferometer. The phase evolution has been modeled as being driven by the proper-time difference between the two paths, although it has an ambiguous origin in the non-relativistic limit and it requires a full quantum-field-theory treatment in the general case. We present conditions for identifying deviations from the non-relativistic limit as a way of testing the proper-time driven phase evolution model. We show that the system performance belies the premise that an atom-interferometer clock is referenced to a divided-down Compton oscillation, and we suggest that this implies there is no physical oscillation at the Compton frequency.

Abstract:
We review matter wave and clock comparison tests of the gravitational redshift. To elucidate their relationship to tests of the universality of free fall (UFF), we define scenarios wherein redshift violations are coupled to violations of UFF ("type II"), or independent of UFF violations ("type III"), respectively. Clock comparisons and atom interferometers are sensitive to similar effects in type II and precisely the same effects in type III scenarios, although type III violations remain poorly constrained. Finally, we describe the "Geodesic Explorer," a conceptual spaceborne atom interferometer that will test the gravitational redshift with an accuracy 5 orders of magnitude better than current terrestrial redshift experiments for type II scenarios and 12 orders of magnitude better for type III.

Abstract:
The recent realization that atom interferometers (AIs) can be used to test the gravitational redshift tests has proven to be controversial in some quarters. Here, we address the issues raised against the interpretation of AIs as redshift tests, reaffirming the fact that Mueller et al. [Nature 463, 926 (2010)] indeed report a gravitational redshift test.

Abstract:
We describe a collective state atomic interferometer (COSAIN) with the signal fringe as a function of phase-difference or rotation narrowed by $\sqrt{N}$ compared to a conventional interferometer - $N$ being the number of atoms - without entanglement. This effect arises from the interferences among collective states, and is a manifestation of interference at a Compton frequency of ten nonillion Hz, or a de Broglie wavelength of ten attometer, for $N=10^6$ and $v = 300 m/s$. The population of the collective state of interest is detected by a null measurement scheme, in which an event corresponding to detection of zero photons corresponds to the system being in that particular collective state. The signal is detected by collecting fluorescence through stimulated Raman scattering of Stokes photons, which are emitted predominantly against the direction of the probe beam, for a high enough resonant optical density. The sensitivity of the ideal COSAIN is found to be given by the standard quantum limit. However, when detection efficiency and collection efficiency are taken into account, the detection scheme of the COSAIN increases the quantum efficiency of detection significantly in comparison to a typical conventional Raman atomic interferometer employing fluorescence detection, yielding a net improvement in stability by as much as a factor of $10$. We discuss how the inhomogeneities arising from the non-uniformity in experimental parameters affect the COSAIN signal. We also describe an alternate experimental scheme to enhance resonant optical density in a COSAIN by using cross-linearly polarized counter-propagating Raman beams.

Abstract:
We propose a feasible laboratory interferometry experiment with matter waves in a gravitational potential caused by a pair of artificial field-generating masses. It will demonstrate that the presence of these masses (and, for moving atoms, time dilation) induces a phase shift, even if it does not cause any classical force. The phase shift is identical to that produced by the gravitational redshift (or time dilation) of clocks ticking at the atom's Compton frequency. In analogy to the Aharonov-Bohm effect in electromagnetism, the quantum mechanical phase is a function of the gravitational potential and not the classical forces.

Abstract:
The study of the gravitational redshift\,---\,a relative wavelength increase of $\approx 2 \times 10^{-6}$ was predicted for solar radiation by Einstein in 1908\,---\,is still an important subject in modern physics. In a dispute whether or not atom interferometry experiments can be employed for gravitational redshift measurements, two research teams have recently disagreed on the physical cause of the shift. Regardless of any discussion on the interferometer aspect\,---\,we find that both groups of authors miss the important point that the ratio of gravitational to the electrostatic forces is generally very small. For instance, the gravitational force acting on an electron in a hydrogen atom situated in the Sun's photosphere to the electrostatic force between the proton and the electron is approximately $3 \times 10^{-21}$. A comparison of this ratio with the predicted and observed solar redshift indicates a discrepancy of many orders of magnitude. Here we show, with Einstein's early assumption of the frequency of spectral lines depending only on the generating ion itself as starting point, that a solution can be formulated based on a two-step process in analogy with Fermi's treatment of the Doppler effect. It provides a sequence of physical processes in line with the conservation of energy and momentum resulting in the observed shift and does not employ a geometric description. The gravitational field affects the release of the photon and not the atomic transition. The control parameter is the speed of light. The atomic emission is then contrasted with the gravitational redshift of matter-antimatter annihilation events.