Gravity of Light, Light in Gravitational Fields, and Metrological Implications

Abstract

This thesis deals with the interplay of gravitation and light. It is split into four parts, each of them giving an overview of one of our projects: In the first and second part, we study the gravitational properties of laser light and use other light rays to illustrate these properties. In the third part, light rays are used as a tool to determine the frequency spectrum of an optical resonator in a background gravitational field. Finally, in the fourth part, light plays both the role of the source of the gravitational field and the means to perform a measurement. As the gravitational field of light is weak, its effects are too small to be experimentally measured. However, with the progress of technology, they might be detected in the future. They are of conceptual interest, revealing fundamental properties of the nature of light. In the first part, we determine the gravitational field of a laser beam: The laser beam is described as a solution of Maxwell’s equations and has a finite wavelength and circular polarization. This description is beyond the short-wavelength approximation, and allows to find novel gravitational properties of light. Among these are frame-dragging due to the laser beam’s spin angular momentum and the deflection of parallel co-propagating test light-rays that overlap with the source laser-beam. Further, the polarization of a test light-ray in the gravitational field of the laser beam is rotated. This is analyzed in the second part. The rotation consists of a reciprocal con- tribution associated to the gravitational analogue of optical activity, and a non-reciprocal part identified as the gravitational analogue of the electromagnetic Faraday effect. There- fore, letting light propagate back and forth between two mirrors, the gravitational Faraday effect accumulates, while the effect due to the gravitational optical activity cancels. Inter- estingly, using only classical general relativity, our analysis shows gravitational spin-spin coupling, which is a known effect in perturbative quantum gravity. In the third part, we study the effect of a gravitational field and proper acceleration on the frequency spectrum of an optical resonator. The resonator is modelled in two different ways: As a rod of matter with two attached mirrors at its ends, and as a dielectric rod whose ends function as mirrors. The resonator can be deformed in the gravitational field depending on the material properties of the rod. The frequency spectrum turns out to depend on the radar length, which is the length an observer measures by sending a light signals back and forth between the mirrors and measuring the time difference. The results for the frequency spectrum may be used for measuring gravitational fields or acceleration based on frequency shifts of the light. Also in the fourth part we look at an optical resonator, this time a cubic cavity. While in the third part we considered a background gravitational field, now the light inside the cubic cavity is the source of the gravitational field. With this setup, we consider an observer making a specific measurement of the speed of light and analyze the precision of the measurement. Using quantum parameter estimation theory and analyzing the effect of the gravitational field, we determine the number of photons inside the cavity which leads to the best precision of the measurement.