Towards local measurements of space-time geometries with optical clocks

该提案的目标是制定实验提案，通过使用光学时钟，可以在实验室或卫星实验中本地测量非平凡的时空几何形状。 到目前为止，理论上和观测上都不清楚描述宇宙整体膨胀的时空整体结构是否与我们当地的天文环境有关。 但与此同时，光学钟达到的精度应该使测量哈勃常数成为可能，哈勃常数描述了干涉实验中宇宙的大尺度膨胀。 这是对这样的实验，我们希望与理论分析工作。 为此，我们将分析三种不同的情况：1。光学谐振腔的频移; 2.与目前正在建造的天基引力波探测器丽莎（激光干涉仪空间天线）类似的卫星实验;以及3.一种光纤实验，其中由非线性脉冲产生的相边界在光纤中以光速移动，并用探测脉冲测量。 这三个物理系统将被嵌入到麦克维蒂度规中，这是最简单的度规，其中引力中心势叠加在膨胀的时空上，它代表了膨胀宇宙中我们的局部时空的原始提议之一。 除了经典光学实验之外，我们还想研究多模量子计量学是否可以帮助测量预期的非常小的效应。 我们还将研究是否可以通过这些设置测量其他有趣的引力效应，例如暗物质或地球物理效应的存在，例如物质的陆地运动（大气和洋流，构造板块的运动）。 将考虑通过光纤网络同步光学时钟的应用。

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.