Abstract The gravitational redshift (GR), as predicted by Einstein’s general theory of relativity, posits that two identical clocks situated at different gravitational potentials will tick at different rates. In this study, we explore the impact of the GR on a single-photon-based atom interferometer and propose a corresponding testing scheme. Our approach conceptualizes the atom interferometer as two coherent atomic clocks positioned at distinct elevations, which is referred to as an atomic clock interferometer, allowing us to derive the GR-induced phase shift. This effect becomes significant due to the notable energy difference between the two atomic internal states, comparable to other relativistic effects in single-photon-based atomic clock interferometers. Furthermore, our proposed scheme incorporates the velocity of the laser device to effectively mitigate other relativistic effects. The ensuing analysis indicates an anticipated GR test precision at the 10−5 level for our proposed approach.
Abstract The gravitational redshift (GR), as predicted by Einstein’s general theory of relativity, posits that two identical clocks situated at different gravitational potentials will tick at different rates. In this study, we explore the impact of the GR on a single-photon-based atom interferometer and propose a corresponding testing scheme. Our approach conceptualizes the atom interferometer as two coherent atomic clocks positioned at distinct elevations, which is referred to as an atomic clock interferometer, allowing us to derive the GR-induced phase shift. This effect becomes significant due to the notable energy difference between the two atomic internal states, comparable to other relativistic effects in single-photon-based atomic clock interferometers. Furthermore, our proposed scheme incorporates the velocity of the laser device to effectively mitigate other relativistic effects. The ensuing analysis indicates an anticipated GR test precision at the 10−5 level for our proposed approach.
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.
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.
Atom interferometers are excellent tools for measuring inertial forces. Their high accuracy and sensitivity allow them to test fundamental physics, e.g., Einstein’s equivalence principle (EEP). One of the main assumptions of EEP is the universality of gravitational redshift (UGR), which states that the ticking rate measured by two idealised clocks at different points in a gravitational field is independent of their internal composition [1]. Although UGR has been successfully tested with two independent atomic clocks, the same effect on a single clock in a delocalised superposition of states has not been observed yet [2]. A promising approach for a delocalised test of UGR is quantum clock interferometry (QCI), which uses a sequence of light pulses to split, redirect, and recombine coherent wave packets and drive transitions between the internal states of the atoms to measure differences in proper time imprinted in the interferometer’s phase shift [3]. An experimental realisation of such schemes requires atomic species with large internal transitions. In this work, we propose an interferometry sensitive to gravitational redshift. By performing a double differential measurement in a single shot, this configuration benefits from a common-mode rejection of spurious effects in the interferometer’s phase. The feasibility of QCI experiments measuring gravitational redshift depends on the availability of long-lived internal states with large energy differences, making the ytterbium (Yb) optical transition an ideal candidate. The clock transition is excited through a two-photon Doppler-free E1-M1 mechanism [4]. This process requires a narrow linewidth, 1 kHz, and a high-power, 20 W, light source. We present our frequency stabilisation scheme and power amplification of an 1156 nm laser to drive the clock transition on a cold Yb cloud. [1] F. Di Pumpo et al., Phys. Rev. D 107, 064007 (2023). [2] A. Roura et al., Phys. Rev. D 104 084001 (2021). [3] C. Ufrecht et al., Phys. Rev. Research 2 043240 (2020). [4] E. A. Alden et al., Phys. Rev. A 90, 012523 (2014)
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.
Introducing internal-state transitions simultaneously on each branch of a light-pulse atom interferometer, we propose a scheme that is concurrently sensitive to both violations of the universality of free fall and gravitational redshift, two premises of general relativity.In contrast to redshift tests with quantum clocks, a superposition of internal states is not necessary but merely transitions between them, leading to a generalized concept of clocks in this context.The experimental realization seems feasible with already demonstrated techniques.
Introducing internal-state transitions simultaneously on each branch of a light-pulse atom interferometer, we propose a scheme that is concurrently sensitive to both violations of the universality of free fall and gravitational redshift, two premises of general relativity. In contrast to redshift tests with quantum clocks, a superposition of internal states is not necessary but merely transitions between them, leading to a generalized concept of clocks in this context. The experimental realization seems feasible with already demonstrated techniques.