A test of time dilation with an optical atomic clock on a stratospheric balloon

最先进的光学晶格钟的性能为改进测试广义相对论的基本效应之一-引力势中的时间膨胀提供了机会。对这一效应最精确的测试是在40年前进行的，方法是比较两个高度相差10000公里的微波钟。一种新的、具有竞争精度的非卫星测试这种效应必然意味着需要在实验室外操作光学钟。在这里，我们建议建立一个Yb光学晶格钟，并将其用作重要高度上的探测钟，通过与地面参考钟的频率比较来精确测量引力时间膨胀。我们的目标是测量精度好于即将到来的太空任务ACES(2017-18年)，后者使用冷原子Cs微波钟。为了实现该项目的目标，我们提议开发一种可飞行的光学时钟(FOC)，这是一种特别紧凑和坚固的仪器，它首次额外包括两个原子子系统，从而能够针对我们的具体实验进行深入的表征和性能优化。为了放宽对探头和参考时钟的精度要求，在我们的应用中，我们预见在每次实验期间，首先在地面上比较它们，然后将FOC提升到高空并重复比较。因此，主要要求是焦点和参考频率的重现性。此外，为了最大限度地减少测量过程中的积分时间，实现高频率稳定度是至关重要的，测量过程的持续时间是有限的。在一个长达7年的项目中，我们计划进行越来越复杂的实验，包括垂直距离和两个时钟之间的链接。在演示实验中(第4年)，FOC将在杜塞尔多夫电视塔的全景水平上运行，地面参考时钟上方160米，通过光纤链路连接并进行比较。这将提供在1E-3水平上的引力时间膨胀的测试。在该项目的最后部分(第7年)，将执行一项任务，在35公里高度的平流层气球上运行FOC大约10个小时。与地面参考时钟进行比较的频率链将是一种基于频率梳的双向自由空间激光链路，将在第4-6年与NIST和Viallight的同事合作实施。通过将FOC和参考时钟频差的统计不确定度平均到2E-18水平，我们的目标是测量引力时间膨胀，相对不确定度为5E-7，大约比ACES任务的预期目标好4倍。

The performance of state-of-the-art optical lattice clocks offers an opportunity for an improved test of one of the fundamental effects of General Relativity, the time dilation in the gravitational potential. The most precise test of this effect was performed 40 years ago by comparing two microwave clocks on a 10 000 km height difference. A new, non-satellite test of this effect with a competitive precision necessarily implies the need to operate an optical clock outside of the laboratory. Here we propose to build a ytterbium optical lattice clock and to use it as a probe clock on significant altitudes to precisely measure the gravitational time dilation through a frequency comparison with a reference clock on the ground. We aim at a precision of the measurement better than that of the upcoming space mission ACES (2017-18), which employs a cold-atom Cs microwave clock. To achieve the goals of the project, we propose to develop a flyable optical clock (FOC), a particularly compact and robust apparatus, which additionally comprises, for the first time, two atomics subsystems, allowing for in-depth characterization and optimization of performance towards our specific experiment. In order to relax the requirement of accuracy for both the probe and the reference clock, in our application we foresee that during each experiment they are first compared on ground, before the FOC is brought to altitude and the comparison is repeated. Thus, the main requirement is the reproducibility of the FOCs and the references frequency. Furthermore, achieving high frequency stability is crucial in order to minimize the integration time during the measurement campaign, whose duration is limited. In a 7-year long project, we plan to perform experiments of increasing complexity, concerning both the vertical distance and the link between the two clocks. In a demonstration experiment (year 4), the FOC will be operated in the panoramic level of the television tower in Düsseldorf, 160 m above the reference clock on ground, which is connected through a fiber link and intercompared. This will provide a test of the gravitational time dilation at the 1E-3 level. In the final part of the project (years 7), a mission will be performed in which the FOC will be operated on a stratospheric balloon at an altitude of 35 km for approximately 10 hours. The frequency link for comparison with the reference clock on ground will be a frequency-comb-based two-way free-space laser link, to be implemented in collaboration with colleagues from NIST and ViaLight in years 4-6. By averaging down the statistical uncertainty of the frequency difference of the FOC and reference clock to the 2E-18 level, we aim for a measurement of the gravitational time dilation with relative uncertainty of 5E-7, approximately a factor of 4 better than the expected goal of the ACES mission.