Quantum mechanics and general relativity are the foundational pillars of modern physics, yet experimental tests that combine the two frameworks remain rare. Measuring optical phase shifts of massless photons in a gravitational potential provides a unique quantum platform to probe gravity beyond Newtonian descriptions, but laboratory-based interferometers have not yet reached the sensitivity needed to access this regime. Here, we report the realization of a 50-km table-top Mach-Zehnder fiber interferometer operating at the single-photon level, achieving a phase sensitivity of 4.42×10^{-6}  rad  rms within the frequency range of 0.01-5 Hz. We demonstrate that this sensitivity is sufficient to resolve a phase-shift signal of 6.18(44)×10^{-5}  rad  rms at 0.1 Hz, associated with a modulated gravity-induced signal. Our results establish a milestone for quantum sensing with large-scale optical interferometry, demonstrating the capability to detect gravitational redshifts in a local laboratory, thereby paving the way for testing quantum phenomena within general relativistic frameworks.

The coupling between internal degrees of freedom of quantum systems and their overall motion in an external gravitational field plays a central role in multiple extensions of Einstein's equivalence principle to quantum physics. While previous models of such effects were predominantly restricted to linearized gravity and often required the motion of quantum particles to follow prescribed world-lines, this letter shows how such phenomena can be understood using generally covariant semiclassical approximations in the framework of quantum field theory in curved space-times. This method provides a unification and generalization of previously established results, but also predicts new effects such as an influence of internal energies on field amplitudes, as well as correction terms to the internal Schrödinger equation that give rise to Berry phases.

The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor, which unifies the Berry curvature and the quantum metric. In this work, we use the differential-geometric framework of vector bundles to analyze the properties of parameter-dependent quantum states and generalize the quantum geometric tensor to this setting. This construction is based on a general connection on a Hermitian vector bundle, which defines a notion of quantum state transport in parameter space, and a sub-bundle projector, which constrains the set of accessible quantum states. We show that the sub-bundle geometry is similar to that of submanifolds in Riemannian geometry and is described by generalized Gauss-Codazzi-Mainardi equations. This leads to a novel definition of the quantum geometric tensor that contains an additional curvature contribution. To illustrate our results, we describe the sub-bundle geometry arising in the semiclassical treatment of Dirac fields propagating in curved spacetime and show how the quantum geometric tensor, with its additional curvature contributions, is obtained in this case. As a concrete example, we consider Dirac fermions confined to a hyperbolic plane and demonstrate how spatial curvature influences the quantum geometry. This work sets the stage for further exploration of quantum systems in curved geometries, with applications in both high-energy physics and condensed matter systems.

Current models of quantum interference experiments in external gravitational fields lack a common framework: while matter-wave interferometers are commonly described using the Schrödinger equation with a Newtonian potential, gravitational effects in quantum optics are modeled using either post-Newtonian metrics or highly symmetric exact solutions to Einstein's field equations such as those of Schwarzschild and Kerr. To coherently describe both kinds of experiments, this paper develops a unified framework for modeling quantum interferometers in general stationary space-times. This model provides a rigorous description and coherent interpretation of the effects of classical gravity on quantum probes.

Single-mode fibers are used in fiber-optic gyroscopes to measure the Sagnac effect and are planned to be used in forthcoming experiments on the gravitationally induced phase shift in single photons. However, current theoretical models of such experiments are limited to ray-optics approximations or, if based on wave optics, to a restricted class of fiber alignments. To overcome these shortcomings, this paper develops a comprehensive perturbative scheme to solve for electromagnetic modes, i.e., monochromatic solutions to Maxwell's equations, of arbitrarily bent step-index fibers in general stationary space-times. This leads to transport equations for the electromagnetic phase and polarization that include the gravitational redshift, the Sagnac effect, a generalization of Rytov's law to curved space, a gravitational Faraday effect in the form of shift-induced gyrotropy, as well as inverse spin Hall effects caused by fiber bending, gravitational acceleration, and space-time curvature.

Gravitational wave memory is said to arise when a gravitational wave burst produces changes in a physical system that persist even after that wave has passed. This paper analyzes gravitational wave bursts in plane wave spacetimes, deriving memory effects for timelike and null geodesics, massless scalar fields, and massless spinning particles whose motion is described by the spin Hall equations. We find that all such effects are characterized by four "memory tensors," three of which are independent. We also show that memory effects for null geodesics can have strong longitudinal components, even in vacuum general relativity. When considering massless particles with spin, we solve the spin Hall equations analytically by showing that there exists a conservation law associated with each conformal Killing vector. For the scattering of fields by gravitational waves, we show that given any solution to the massless scalar field equation in flat spacetime, a weak-field solution in a plane wave spacetime can be generated just by applying an appropriate differential operator-an operator that is constructed from the aforementioned memory tensors. Memory effects for scalar fields are illustrated for both incoming plane waves and higher-order Gaussian beams. We also present a numerical comparison between the spin Hall equations and the full evolution of localized wave packets with angular momentum. Although we work in plane wave spacetimes, which are physically idealized, similar results are also expected to apply for sufficiently small systems affected by distantly generated gravitational waves. Using the Penrose limit, our results may also apply to ultrarelativistic systems at arbitrary locations in arbitrary (even nonradiating) spacetimes.

Gravitational time dilation, a prediction of General Relativity, lacks confirmation alongside quantum mechanics. Our experiment aims to measure gravitationally induced phase shift of path-entangled photons between two vertically displaced arms of a fiber interferometer.

Laser-interferometric gravitational wave detectors are commonly modeled as being at rest in transverse-traceless coordinates (and thus geodesic). In this paper, we analyze what happens if the interferometer is mounted on a material that can undergo elastic oscillations caused by the gravitational wave. We thus compute the response of a two-dimensional elastic material to linearized gravitational radiation and compute the resulting response of a laser interferometer, mounted on such a plate.

We consider the propagation of light in arbitrarily curved step-index optical fibers. Using a multiple-scales approximation scheme, set-up in Fermi normal coordinates, the full vectorial Maxwell equations are solved in a perturbative manner. At leading order, this provides a rigorous derivation of Rytov's law. At next order, we obtain non-trivial dynamics of the electromagnetic field, characterized by two coupling constants, the phase and the polarization curvature moments, which describe the curvature response of the light's phase and its polarization vector, respectively. The latter can be viewed as an inverse spin Hall effect of light, where the direction of propagation is constrained along the optical fiber and the polarization evolves in a frequency-dependent way.

The equations of motion governing small elastic oscillations of materials, induced by gravitational waves, are derived from the general framework of Carter and Quintana. In transverse-traceless gauge, no bulk forces are present, and the gravitational wave is found to act as an effective surface traction. For thin rods, an equivalent description is given, in which there is no surface traction, but a bulk acceleration, which is related to the Riemann curvature of the gravitational wave. The resulting equations are compared to those of the Synge-Bennoun elasticity theory.

Experiments at the interface of quantum field theory and general relativity would greatly benefit theoretical research towards their unification. The gravitational aspects of quantum experiments performed so far can be explained either within Newtonian gravity or by Einstein's equivalence principle. Here, we describe a way to measure components of the Riemann curvature tensor with maximally path-entangled quantum states of light. We show that the entanglement-induced increase in sensitivity also holds for gravitationally-induced phases in Mach-Zehnder interferometers. As a result, the height difference between the two interferometer arms necessary to rule out flat space-time by measuring gravity gradients can be significantly reduced.

The theory of gauge-fixed Maxwell equations in linear isotropic dielectrics is developed using a generalisation of the standard R_ξ gauge-fixing term. In static space-times, the theory can be quantised using the Gupta-Bleuler method, which is worked out explicitly for optical fibres either in flat space-time or at a constant gravitational potential. This yields a consistent first-principles description of gravitational fibre-optic interferometry at the single-photon level within the framework of quantum field theory in curved space-times.

The response of Michelson interferometers to weak plane gravitational waves is computed at one order of accuracy beyond the eikonal equation. The modulation of the electromagnetic field amplitude and polarisation are taken into account by solving the transport equations of geometrical optics with boundary conditions adapted to laser interferometry. Considering both DC and balanced homodyne readout schemes, explicit formulae for the interferometer output signals are derived. These signals comprise perturbations of the optical path length, frequency and amplitude, and are shown to be insensitive to polarisation perturbations.

We analyse the response of laser interferometric gravitational wave detectors using the full Maxwell equations in curved spacetime in the presence of weak gravitational waves. Existence and uniqueness of solutions is ensured by setting up a suitable boundary value problem. This puts on solid ground previous approximate calculations. We find consistency with previous results obtained from eikonal expansions at the level of accuracy accessible to current gravitational wave detectors.

The response of optical fibre modes to plane gravitational waves (GW's) of low frequency is computed. By solving perturbatively the Maxwell equations for step-index optical fibres in a GW background and implementing appropriate boundary conditions to describe single-mode fibres, explicit formulae for the perturbations of the phase and the polarisation of the fibre modes are obtained.

Some previously published expressions for the perturbation of light by gravitational waves exhibit pathological behaviour in the limit of parallel propagation. We show that this is caused by similarly pathological initial or boundary data and can thus be remedied by implementing better-behaved initial conditions.

We analyse the influence of Earth's rotation on the propagation of light in optical media. This is done using both geometrical optics and a perturbative calculation based on Maxwell's equations in rotating coordinates in flat spacetime. Considering light propagation in cylindrical step-index waveguides in particular, the first order correction to electromagnetic modes is computed. The calculation shows that Earth's spin causes a weak mode coupling, giving rise to sidebands, whose amplitudes are computed as well. The correction to the dispersion relation derived here allows to assess the anisotropy of light propagation due to Earth's rotation. The linearisation of this result is found to agree numerically with a simple formula derived from geometrical optics.

In dieser Arbeit wird der Einfluss der Erdrotation (sowohl um die eigene Achse, als auch um die Sonne) auf Lichtausbreitung in optischen Medien analysiert. Dies geschieht sowohl im Rahmen der geometrischen Optik, als auch anhand von perturbativen Rechnungen basierend auf den Maxwell-Gleichungen (Wellenoptik) in rotierenden Koordinaten in flacher Raumzeit. Insbesondere werden Korrekturen erster Ordnung zu den elektromagnetischen Moden in zylindrischen Stufenindex-Wellenleitern berechnet. Die Rechnung zeigt, dass die Erdrotation eine schwache Modenkopplung hervorruft und daher Seitenbander anregt, deren Amplituden ebenfalls bestimmt wurden. Die hier hergeleitete Korrektur zur Dispersionsrelation erlaubt es, die Anisotropie der Lichtausbreitung aufgrund der Erdrotation zu quantifizieren. Die Linearisierung dieses Resultats stimmt numerisch mit einer einfachen Formel uberein, die aus der geometrischen Optik abgeleitet wird.

Noether’s theorem states that every differentiable symmetry of the action corresponds to a conserved quantity. Considering classical electrodynamics, two symmetries immediately come to mind: Poincaré invariance (Lorentz transformations and translations) and gauge invariance. In the absence of sources, Poincaré invariance implies the conservation of energy-momentum and angular momentum of the field, but in the presence of electric charges and currents, these quantities are no longer conserved. In this article, we will derive the corresponding equations using Noether’s theorem.

Experimental research has become complex and thus a challenge to science education. Only very few students can typically be trained on advanced scientific equipment. It is therefore important to find new tools that allow all students to acquire laboratory skills individually and independent of where they are located. In a design-based research process we have investigated the feasibility of using a virtual laboratory as a photo-realistic and scientifically valid representation of advanced scientific infrastructure to teach modern experimental science, here, molecular quantum optics. We found a concept based on three educational principles that allows undergraduate students to become acquainted with procedures and concepts of a modern research field. We find a significant increase in student understanding using our Simulated Interactive Research Experiment (SiReX), by evaluating the learning outcomes with semi-structured interviews in a pre/post design. This suggests that this concept of an educational tool can be generalized to disseminate findings in other fields.