Towards local measurements of space-time geometries with optical clocks

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The goal of the proposal is to develop proposals for experiments with which non-trivial space-time geometries can be measured locally, i.e. in a lab or with a satellite experiment, by using optical clocks. So far it is theoretically and even more so observationally unclear whether the global structure of space-time that describes the global expansion of the Universe is relevant in our local astronomical environment. But meanwhile, optical clocks achieve precisions that should make it possible in principle to measure Hubble´s constant that describes the expansion of the Universe on large scales in interference experiments. It is towards such kind of experiments that we want to work with theoretical analyses. To that end we will analyze three different kinds of situations: 1. The frequency shift of an optical resonator; 2. A satellite experiment similar to LISA (Laser Interferometer Space Antenna), the space-based gravitational wave detector that is currently being constructed; and 3. A fiber-optical experiment in which a phase-boundary created by a non-linear pulse moves with the speed of light in the fiber and is measured with a probe pulse. These three physical systems will be embedded in the McVittie metric, the simplest metric in which a gravitational central potential is superposed on an expanding space-time, and which represents one of the original proposals for our local space-time in the expanding Universe. Besides experiments with classical optics we also want to investigate possibilities whether multi-mode quantum metrology can help to measure the expected very small effects. We will also investigate whether with these setups other interesting gravitational effects can be measured, such as the presence of dark matter or geophysical effects, as e.g. terrestrial motion of matter (atmospheric and ocean currents, motion of tectonic plates). Applications for the synchronization of optical clocks via optical-fiber networks will be considered.