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, westudy the gravitational properties of laser light and use other light rays to illustrate theseproperties. In the third part, light rays are used as a tool to determine the frequencyspectrum of an optical resonator in a background gravitational field. Finally, in the fourthpart, light plays both the role of the source of the gravitational field and the means toperform a measurement. As the gravitational field of light is weak, its effects are too smallto be experimentally measured. However, with the progress of technology, they might bedetected in the future. They are of conceptual interest, revealing fundamental propertiesof the nature of light.In the first part, we determine the gravitational field of a laser beam: The laser beam isdescribed as a solution of Maxwell’s equations and has a finite wavelength and circularpolarization. This description is beyond the short-wavelength approximation, and allowsto find novel gravitational properties of light. Among these are frame-dragging due to thelaser beam’s spin angular momentum and the deflection of parallel co-propagating testlight-rays that overlap with the source laser-beam.Further, the polarization of a test light-ray in the gravitational field of the laser beam isrotated. 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-reciprocalpart identified as the gravitational analogue of the electromagnetic Faraday effect. There-fore, letting light propagate back and forth between two mirrors, the gravitational Faradayeffect accumulates, while the effect due to the gravitational optical activity cancels. Inter-estingly, using only classical general relativity, our analysis shows gravitational spin-spincoupling, which is a known effect in perturbative quantum gravity.In the third part, we study the effect of a gravitational field and proper acceleration onthe frequency spectrum of an optical resonator. The resonator is modelled in two differentways: As a rod of matter with two attached mirrors at its ends, and as a dielectric rodwhose ends function as mirrors. The resonator can be deformed in the gravitational fielddepending on the material properties of the rod. The frequency spectrum turns out todepend on the radar length, which is the length an observer measures by sending a lightsignals back and forth between the mirrors and measuring the time difference. The resultsfor the frequency spectrum may be used for measuring gravitational fields or accelerationbased on frequency shifts of the light.Also in the fourth part we look at an optical resonator, this time a cubic cavity. Whilein the third part we considered a background gravitational field, now the light insidethe cubic cavity is the source of the gravitational field. With this setup, we consider anobserver making a specific measurement of the speed of light and analyze the precision ofthe measurement. Using quantum parameter estimation theory and analyzing the effect ofthe gravitational field, we determine the number of photons inside the cavity which leadsto the best precision of the measurement.