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.
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.
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.
According to relativity, the reading of an ideal clock is interpreted as the elapsed proper time along its classical trajectory through spacetime. In contrast, quantum theory allows the association of many simultaneous trajectories with a single quantum clock, each weighted appropriately. Here, we investigate how the superposition principle affects the gravitational time dilation observed by a simple clock – a decaying two-level atom. Placing such an atom in a superposition of positions enables us to analyze a quantum contribution to a classical time dilation manifest in spontaneous emission. In particular, we show that the emission rate of an atom prepared in a coherent superposition of separated wave packets in a gravitational field is different from the emission rate of an atom in a classical mixture of these packets, which gives rise to a quantum gravitational time dilation effect. We demonstrate that this nonclassical effect also manifests in a fractional frequency shift of the internal energy of the atom that is within the resolution of current atomic clocks. In addition, we show the effect of spatial coherence on the atom's emission spectrum.
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.
A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special relativistic kinematical time dilation. Here, we extend this proposal to a weak gravitational field in order to investigate whether the weak equivalence principle holds for quantum matter. We find that for general quantum states the quantum time dilation in a weak gravitational field obeys a similar gravitational time dilation found in classical relativity. However, unlike the special relativistic case, the time dilation involves the external time (a background coordinate time at the observer on the Earth) as well as the proper times of two clocks. We also investigate a quantum time dilation effect induced by a clock in a superposition of wave packets localized in momentum space or in position space and propose the setup to observe the gravitational effect in the quantum interference effect in the time dilation.
Atomic clocks can measure the gravitational redshift predicted by general relativity with great accuracy and for height differences as little as 1 cm. All existing experiments, however, involve the comparison of two independent clocks at different locations rather than a single clock in a delocalized quantum superposition. Here we present an interferometry scheme employing group-II-type atoms, such as Sr or Yb, capable of measuring the gravitational time dilation in a coherent superposition of atomic wave packets at two different heights. In contrast to other recent proposals, there is no need for pulses that can efficiently diffract both internal states. Instead, the scheme relies on very simple atom optics for which high diffraction efficiencies can be achieved with rather mild requirements on laser power. Furthermore, the effects of vibration noise are subtracted by employing a simultaneous Rb interferometer that acts as an inertial reference. Remarkably, the recently commissioned VLBAI facility in Hannover, a 10-m atomic fountain that can simultaneously operate Yb and Rb atoms and enables up to 2.8 s of free evolution time, meets all the requirements for a successful experimental implementation.
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.