Atom Interferometry as a Probe of the Terrestrial GMWT Geometric Amplitude Matter-Wave Phase Shifts, Dual-Species Tests, Gradiometry, Source-Mass Measurements, Aharonov–Bohm Phase, Frequency-Shift Outlook, and the Canonical 10−12 Contractive Scale
This article investigates atom interferometry, precision clocks, resonant cavities, and selected geometry-sensitive anomalies as experimental consistency tests for the Gravitation Matter–Wave Theory (GMWT). The central quantity is the terrestrial geometric amplitude εgeo⊕ =6πCGMWTNp,⊕ ≃2.3×10−12,derived from the geometric projection of the Earth’s protonic wave field, distinct from the energetic projection that reconstructs the gravitational acceleration g. Applied to the Earth radius, this amplitude gives a micrometric contraction scale∆Lgeo⊕ ≃ 14.5µm,which lies in the same domain as the effective phase-distance gT2 measured in millisecond light-pulse atom interferometry.The article then organizes a sequence of experimental comparisons into three levels.First-level established cases include atom-interferometric phase shifts, dual-species tests, gravity gradiometry, source-mass measurements, the gravitational Aharonov–Bohm phase, atomic clocks, blackbody-radiation shifts, and residual caesium fountain shifts. In these cases, the terrestrial GMWT amplitude enters explicitly as a normalized geometric factor.Exploratory first-level cases are then considered separately: the Tajmar superconducting ring anomaly and LIGO blip glitches, where the same terrestrial amplitude appears in geometry-sensitive but unresolved phenomena. Finally, second-level wave-geometric cases, including Hong–Ou–Mandel interference, Haroche-type cavities, high-finesse optical cavities, optomechanics, circuit-QED, and cesium anomalous phases, are used to test the broader GMWT idea that waves carry both energetic and geometric components. The aim is not to claim experimental confirmation of GMWT, nor to treat all cases as having the same evidential status. Rather, the article proposes a structured experimental roadmap showing that a single normalized GMWT architecture yields recurrent order-of magnitude correspondences across matter-wave phase, frequency shifts, effective wave-space dilations, inertial anomalies, and interferometric transients.
This article investigates atom interferometry, precision clocks, resonant cavities, and selected geometry-sensitive anomalies as experimental consistency tests for the Gravitation Matter–Wave Theory (GMWT). The central quantity is the terrestrial geometric amplitude εgeo⊕ =6πCGMWTNp,⊕ ≃2.3×10−12,derived from the geometric projection of the Earth’s protonic wave field, distinct from the energetic projection that reconstructs the gravitational acceleration g. Applied to the Earth radius, this amplitude gives a micrometric contraction scale∆Lgeo⊕ ≃ 14.5µm,which lies in the same domain as the effective phase-distance gT2 measured in millisecond light-pulse atom interferometry.The article then organizes a sequence of experimental comparisons into three levels.First-level established cases include atom-interferometric phase shifts, dual-species tests, gravity gradiometry, source-mass measurements, the gravitational Aharonov–Bohm phase, atomic clocks, blackbody-radiation shifts, and residual caesium fountain shifts. In these cases, the terrestrial GMWT amplitude enters explicitly as a normalized geometric factor.Exploratory first-level cases are then considered separately: the Tajmar superconducting ring anomaly and LIGO blip glitches, where the same terrestrial amplitude appears in geometry-sensitive but unresolved phenomena. Finally, second-level wave-geometric cases, including Hong–Ou–Mandel interference, Haroche-type cavities, high-finesse optical cavities, optomechanics, circuit-QED, and cesium anomalous phases, are used to test the broader GMWT idea that waves carry both energetic and geometric components. The aim is not to claim experimental confirmation of GMWT, nor to treat all cases as having the same evidential status. Rather, the article proposes a structured experimental roadmap showing that a single normalized GMWT architecture yields recurrent order-of magnitude correspondences across matter-wave phase, frequency shifts, effective wave-space dilations, inertial anomalies, and interferometric transients.
This thesis examines how atomic quantum systems can be utilized to probe spacetime effects in regimes where quantum mechanics and general relativity intersect, and how gravitational phenomena imprint on experimentally accessible observables. The work is based on two complementary studies. In Article I, we propose an experimental scheme that combines trapped-atom interferometry with Ramsey interrogation to realize a clock held in a spatial superposition at two heights in Earth’s gravitational field. Using a path-integral treatment of interferometric phases and incorporating the internal-energy contribution to mass, we derive leading relativistic corrections and identify two signatures of proper-time superposition: (i) oscillations of interferometric visibility and (ii) an effective shift of the clock transition frequency. We argue that this frequency-shift signature may be within reach of current or near-term technology, even when visibility changes are too small to resolve. In Article II, we develop a general framework for spontaneous emission in curved spacetime and apply it to a gravitational-wave background. We demonstrate that gravitational waves can induce spectral sidebands and directional modulations in the emitted radiation, and formulate parameter estimation via Fisher-information-based sensitivity bounds, yielding order-of-magnitude requirements for detectability under idealized measurement conditions.
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 present cumulative thesis (Publications (I)–(III) [1– 3]) explores three complementary directions: (i) tunneling-based gravimetry, (ii) phase contributions of tunneled Ramsey clocks, and (iii) resource optimization for very-long-baseline atom interferometers designed for the detection of gravitational waves and dark matter. The development of atom interferometers and atomic clocks seeks to steadily increase the measurement sensitivity, with the ultimate bound set by the Heisenberg limit. Enhancements can be achieved by exploiting quantum phenomena such as entanglement and squeezing, which allow sensitivities below the shot-noise limit. Another fundamental quantum effect, tunneling, remains less explored in the context of metrology, despite its inherent quantum nature. While entanglement and squeezing have already been demonstrated in atom interferometers, tunneling has not yet been widely investigated for gravimetric sensing applications. Publication (I) explores two configurations of tunneling-based gravimeters using a matter-wave Fabry–Pérot interferometer. (i) In the transmission setup, the wave packet is prepared in front of the cavity generated by optical potentials and transmitted. (ii) In the tunneling setup, the wave packet is prepared inside the cavity, representing a configuration without a classical analogue. Through our numerical simulations of the wave packet dynamics, including gravitational effects, we find that gravity primarily alters the motion of the packet by accelerating, decelerating, and deforming it, which modifies in particular its width at impact. While a single Gaussian barrier shows no resonances, the Fabry–Pérot configuration supports multiple resonances, defining tunable working points and acting as a velocity filter. In Publication (II), we turn to the phase accumulated during tunneling, investigated via a Ramsey clock. The Ramsey clock consists of a superposition of two internal states, accumulating a phase that is read out via a Ramsey sequence. Adopting an operational definition where time is what you read off a clock, we identify a tunneling time associated with the tunneling phase, alongside relativistic contributions accumulated by the tunneled clock. This approach naturally unifies several conventional definitions of tunneling time. Furthermore, the tunneling phase can be amplified experimentally by introducing state-dependent barrier heights through differential light shifts. In Publication (III), we study differential geometries of terrestrial very-long baseline atom interferometers, currently in development for gravitational-wave and dark-matter detection. We analyze three strategies for signal enhancement: (i) large-momentum-transfer pulses to increase atom–light interaction points, (ii) resonant-mode enhancement by matching the interrogation time to the target frequency, and (iii) extending baseline lengths. The achievable number of pulses is limited by atomic losses, distributed between large-momentum-transfer sequences and number of diamonds. Additionally, more diamonds require taller atomic fountains, constrained by the finite baseline. Thus, a trade-off emerges between the number of large-momentum-transfer pulses, the number of diamonds, and the baseline length. Considering this interplay, we derive an analytical relation for the optimal number of pulses under given loss rates. We explicitly optimize the allocation of the available resources and account for the finite spatial extent of individual interferometers, baseline constraints, and atom loss from imperfect pulses.
A transportable atom interferometer-based gravity gradiometer has been developed at JPL to carry out measurements of Earth's gravity field at ever finer spatial resolutions, and to facilitate high-resolution monitoring of temporal variations in the gravity field from ground- and flight-based platforms. Existing satellite-based gravity missions such as CHAMP and GRACE measure the gravity field via precise monitoring of the motion of the satellites; i.e. the satellites themselves function as test masses. JPL's quantum gravity gradiometer employs a quantum phase measurement technique, similar to that employed in atomic clocks, made possible by recent advances in laser cooling and manipulation of atoms. This measurement technique is based on atomwave interferometry, and individual laser-cooled atoms are used as drag-free test masses. The quantum gravity gradiometer employs two identical atom interferometers as precision accelerometers to measure the difference in gravitational acceleration between two points (Figure 1). By using the same lasers for the manipulation of atoms in both interferometers, the accelerometers have a common reference frame and non-inertial accelerations are effectively rejected as common mode noise in the differential measurement of the gravity gradient. As a result, the dual atom interferometer-based gravity gradiometer allows gravity measurements on a moving platform, while achieving the same long-term stability of the best atomic clocks. In the laboratory-based prototype (Figure 2), the cesium atoms used in each atom interferometer are initially collected and cooled in two separate magneto-optic traps (MOTs). Each MOT, consisting of three orthogonal pairs of counter-propagating laser beams centered on a quadrupole magnetic field, collects up to 10(exp 9) atoms. These atoms are then launched vertically as in an atom fountain by switching off the magnetic field and introducing a slight frequency shift between pairs of lasers to create a moving rest frame for the trapped atoms. While still in this moving-frame molasses, the laser frequencies are further detuned from the atomic resonance (while maintaining this relative frequency shift) to cool the atom cloud's temperature to 2 K or below, corresponding to an rms velocity of less than 2 cm/s. After launch, the cold atoms undergo further state and velocity selection to prepare for atom interferometry. The atom interferometers are then realized using laser-induced stimulated Raman transitions to perform the necessary manipulations of each atom, and the resulting interferometer phase is measured using laser-induced fluorescence for state-normalized detection. More than 20 laser beams with independent controls of frequency, phase, and intensity are required for this measurement sequence. This instrument can facilitate the study of Earth's gravitational field from surface and air vehicles, as well as from space by allowing gravity mapping from a low-cost, single spacecraft mission. In addition, the operation of atom interferometer-based instruments in space offers greater sensitivity than is possible in terrestrial instruments due to the much longer interrogation times available in the microgravity environment. A space-based quantum gravity gradiometer has the potential to achieve sensitivities similar to the GRACE mission at long spatial wavelengths, and will also have resolution similar to GOCE for measurement at shorter length scales.
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 AharonovBohm effect in electromagnetism, the quantum mechanical phase is a function of the gravitational potential and not the classical forces.
Very Long Baseline Atom Interferometry (VLBAI) corresponds to ground-based atomic matter-wave interferometry on large scales in space and time, letting the atomic wave functions interfere after free evolution times of several seconds or wave packet separation at the scale of meters. As inertial sensors, e.g., accelerometers, these devices take advantage of the quadratic scaling of the leading order phase shift with the free evolution time to enhance their sensitivity, giving rise to compelling experiments. With shot noise-limited instabilities better than 10−9 m/s2 at 1 s at the horizon, VLBAI may compete with state-of-the-art superconducting gravimeters, while providing absolute instead of relative measurements. When operated with several atomic states, isotopes, or species simultaneously, tests of the universality of free fall at a level of parts in 1013 and beyond are in reach. Finally, the large spatial extent of the interferometer allows one to probe the limits of coherence at macroscopic scales as well as the interplay of quantum mechanics and gravity. We report on the status of the VLBAI facility, its key features, and future prospects in fundamental science.