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.
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.
We propose an experimental setup to probe the interplay between the quantum superposition principle and gravitational time dilation arising from the mass-energy equivalence. It capitalizes on state-of-the-art atom interferometers that can keep atoms trapped in a superposition of heights in Earth's gravitational field for exceedingly long times, reaching the minute scale. Our proposal consists of adding two additional laser pulses to the existing experiments that would set up a clock trapped at a superposition of heights, reading a quantum superposition of relativistic proper times. We develop a method to include relativistic corrections to Bloch oscillations, which describe the trapped part of the interferometer. We derive the trajectories and corresponding phases acquired in each arm of the interferometer. We then show that a superposition of proper times manifests in the interference pattern in two ways: visibility modulations and a shift of the atom's resonant frequency. We argue that the latter might be observable with current technology.
The creation of delocalized coherent superpositions of quantum systems experiencing different relativistic effects is an important milestone in future research at the interface of gravity and quantum mechanics.This milestone could be achieved by generating a superposition of quantum clocks that follow paths with different gravitational time dilation and investigating the consequences on the interference signal when they are eventually recombined.Light-pulse atom interferometry with elements employed in optical atomic clocks is a promising candidate for that purpose, but it suffers from major challenges including its insensitivity to the gravitational redshift in a uniform field.All of these difficulties can be overcome with the novel scheme presented here, which is based on initializing the clock when the spatially separate superposition has already been generated and performing a doubly differential measurement where the differential phase shift between the two internal states is compared for different initialization times.This scheme can be exploited to test the universality of the gravitational redshift with delocalized coherent superpositions of quantum clocks, and it is argued that its experimental implementation should be feasible with a new generation of 10-meter atomic fountains that will soon become available.Interestingly, the approach also offers significant advantages for more compact setups based on guided interferometry or hybrid configurations.Furthermore, in order to provide a solid foundation for the analysis of the various interferometry schemes and the effects that can be measured with them, a general formalism for a relativistic description of atom interferometry in curved spacetime is developed.It can describe freely falling atoms as well as the effects of external forces and guiding potentials, and it can be applied to a very wide range of situations.As an important ingredient for quantum-clock interferometry, suitable diffraction mechanisms for atoms in internal-state superpositions are investigated too.Finally, the relation of the proposed doubly differential measurement scheme to other experimental approaches and to tests of the universality of free fall is discussed in detail.
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.
The creation of delocalized coherent superpositions of quantum systems experiencing di erent relativistic e ects is an important milestone in future research at the interface of gravity and quantum mechanics. This could be achieved by generating a superposition of quantum clocks that follow paths with di erent gravitational time dilation and investigating the consequences on the interference signal when they are eventually recombined. Light-pulse atom interferometry with elements employed in optical atomic clocks is a promising candidate for that purpose, but su ers from major challenges including its insensitivity to the gravitational redshift in a uniform eld. All these di- culties can be overcome with a novel scheme presented here which is based on initializing the clock when the spatially separate superposition has already been generated and performing a doubly differential measurement where the di erential phase shift between the two internal states is compared for di erent initialization times. This can be exploited to test the universality of the gravitational redshift (UGR) with delocalized coherent superpositions of quantum clocks and it is argued that its experimental implementation should be feasible with a new generation of 10-meter atomic fountains that will soon become available. Interestingly, the approach also o ers signi cant advantages for more compact set-ups based on guided interferometry or hybrid con gurations. Furthermore, in order to provide a solid foundation for the analysis of the various interferometry schemes and the e ects that can be measured with them, a general formalism for a relativistic description of atom interferometry in curved spacetime is developed. It can deal with freely falling atoms, but also include the e ects of external forces and guiding potentials, and can be applied to a very wide range of situations. As an important ingredient for quantum-clock interferometry, suitable difraction mechanisms for atoms in internal-state superpositions are investigated too. Finally, the relation of the proposed doubly-di erential measurement scheme to other experimental approaches and to tests of the universality of free fall (UFF) is discussed in detail.
Optical clocks based on atoms and ions probe relativistic effects with unprecedented sensitivity. They resolve time dilation due to atom motion or different positions in the gravitational potential through frequency shifts. However, all measurements of time dilation so far can be explained effectively as the result of dynamics with respect to a classical proper time parameter. Here we show that atomic clocks can probe effects where a classical description of the proper time dynamics is insufficient as superpositions of proper time emerge. We apply a Hamiltonian formalism to derive time dilation effects in harmonically trapped clock atoms and show how second-order Doppler shifts due to the vacuum energy, squeezing, and quantum corrections to the dynamics arise. We also demonstrate that time-dilation-induced entanglement between motion and clock evolution can become observable in state-of-the-art clocks when the motion of the atoms is strongly squeezed, realizing proper time interferometry. Our results show that experiments with trapped ion clocks are within reach of probing relativistic evolution of clocks for which a quantum description of proper time becomes necessary.