Gravitating waveguides

Experimental tests of general relativity typically involve very large scales. Among the most prominent examples are corrections to the orbital motion of Mercury in the gravitational field of the Sun, time dilation on satellites caused by Earths gravitational field, and the recent ground-breaking direct detection of gravitational waves by kilometre-sized laser interferometers. The development of new tabletop experiments capable of testing the predictions of general relativity could provide massive simplifications in this research area, and is simultaneously expected to open up new possibilities to study the interplay between gravitational and quantum effects. Experiments involving waveguides appear as an interesting way to proceed. Indeed, an interferometer with 100 km long arms can be built out of two coils of optical fibre mounted on a desk. Given that there has been tremendous progress in controlling noise and reducing losses in optical fibres, the time is ripe to study the theoretical possibilities of using waveguides to test and study general relativistic effects on light. This is especially interesting within the context of gravitational wave detection: the signal from three mutually orthogonal interferometer arms would allow for a precise determination of the source location using only a single observatory, at a fraction of the cost of the existing devices. Another fascinating aspect is the possibility to send single photons into the waveguide, or entangled pairs of photons, in order to test quantum field theory on a curved background. The aim of this project is to explore the influence of weak gravitational fields on the propagation of light in waveguides. The focus is on the interaction of single photons with a (post-)Newtonian gravitational field, as well as with gravitational waves inside an interferometer. The project will answer the question, how photons in a cylindrical waveguide respond to quasi-static deformations of the medium, in a weak gravitational field. These minute effects are negligible in current experiments, but might become important in experiments involving the gravitational field. We will also determine the response of spooled electromagnetic waveguides to gravitational waves. The starting point will be the general relativistic Maxwell equations, which provide a fundamental description of light in curved spacetime.

Experimental tests of general relativity typically involve very large scales. Among the most prominent examples are corrections to the orbital motion of Mercury in the gravitational field of the Sun, gravitational time dilation on satellites caused by Earth's gravitational field, and the groundbreaking detection of gravitational waves by kilometer-size laser interferometers. The development of new tabletop experiments capable of testing the predictions of general relativity could provide massive simplifications in this research area, and is simultaneously expected to open up new possibilities for studying the interplay between gravitational and quantum effects. For this, an interferometer with 50 km long spooled fibers-optic arms has been built in collaboration between the University of Vienna and MIT. This interferometer provides a tool for testing and studying general relativistic effects on light. The instrument has been devised to send both classical light, and single photons, and entangled pairs of photons into the waveguide, to test the predictions of quantum field theory on curved spacetimes. In the current project we have been exploring the influence of weak gravitational fields on the propagation of light in instruments as above. The focus has been on the interaction of single photons or pairs of photons with a classical gravitational field, as well as on gravitational wave detectors. We have analyzed how single-mode fibers deform in weak gravitational fields, and how this influences the propagation of photons in the fibers. These minute effects are important in state-of-the-art experiments testing gravitational effects on fiber interferometry. We have also determined the response of spooled optical fibers to gravitational waves. While the resulting signal is out of reach of current technology, it is conceivable that the development of hollow-core technology will make waveguide-based desktop gravitational wave detectors a reality.