Towards local measurements of space-time geometries with optical clocks

该提案的目标是制定实验提案，利用光学钟在本地，即在实验室或卫星实验中测量非平凡的时空几何。到目前为止，从理论上和观测上都不清楚描述宇宙全球扩张的全球时空结构是否与我们当地的天文环境相关。但与此同时，光学钟达到了精确度，原则上应该可以测量哈勃的S常数，该常数在干涉实验中描述了宇宙的大尺度膨胀。正是针对这样的实验，我们想要进行理论分析。为此，我们将分析三种不同的情况：1.光学谐振器的频移；2.类似于目前正在建造的天基引力波探测器LISA(激光干涉仪空间天线)的卫星实验；以及3.光纤实验，其中由非线性脉冲产生的相界随着光纤中的光速移动，并使用探测脉冲进行测量。这三个物理系统将嵌入麦克维蒂度规中，麦克维蒂度规是最简单的度规，其中引力中心势叠加在膨胀的时空上，它代表了我们在膨胀宇宙中的局部时空的原始提议之一。除了经典光学的实验外，我们还想调查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用这些装置测量其他有趣的引力效应，例如暗物质的存在或地球物理效应，例如地球物质的运动(大气和洋流，构造板块的运动)。将考虑通过光纤网络实现光时钟同步的应用。

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.