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 Earth’s 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.