Long-distance frequency transfer over an urban fiber link using optical phase stabilization

We transferred the frequency of an ultra-stable laser over 86 km of urban fiber. The link is composed of two cascaded 43-km fibers connecting two laboratories, LNE-SYRTE and LPL in Paris area. In an effort to realistically demonstrate a link of 172 km without using spooled fiber extensions, we implemented a recirculation loop to double the length of the urban fiber link. The link is fed with a 1542-nm cavity stabilized fiber laser having a sub-Hz linewidth. The fiber-induced phase noise is measured and cancelled with an all fiber-based interferometer using commercial off the shelf pigtailed telecommunication components. The compensated link shows an Allan deviation of a few 10-16 at one second and a few 10-19 at 10,000 seconds

An absolute calibration system for millimeter-accuracy APOLLO measurements

Lunar laser ranging provides a number of leading experimental tests of gravitation -- important in our quest to unify General Relativity and the Standard Model of physics. The Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) has for years achieved median range precision at the ~2 mm level. Yet residuals in model-measurement comparisons are an order-of-magnitude larger, raising the question of whether the ranging data are not nearly as accurate as they are precise, or if the models are incomplete or ill-conditioned. This paper describes a new absolute calibration system (ACS) intended both as a tool for exposing and eliminating sources of systematic error, and also as a means to directly calibrate ranging data in-situ. The system consists of a high-repetition-rate (80 MHz) laser emitting short (< 10 ps) pulses that are locked to a cesium clock. In essence, the ACS delivers photons to the APOLLO detector at exquisitely well-defined time intervals as a "truth" input against which APOLLO's timing performance may be judged and corrected. Preliminary analysis indicates no inaccuracies in APOLLO data beyond the ~3 mm level, suggesting that historical APOLLO data are of high quality and motivating continued work on model capabilities. The ACS provides the means to deliver APOLLO data both accurate and precise below the 2 mm level.Comment: 21 pages, 10 figures, submitted to Classical and Quantum Gravit

Sound and Automated Synthesis of Digital Stabilizing Controllers for Continuous Plants

Modern control is implemented with digital microcontrollers, embedded within a dynamical plant that represents physical components. We present a new algorithm based on counter-example guided inductive synthesis that automates the design of digital controllers that are correct by construction. The synthesis result is sound with respect to the complete range of approximations, including time discretization, quantization effects, and finite-precision arithmetic and its rounding errors. We have implemented our new algorithm in a tool called DSSynth, and are able to automatically generate stable controllers for a set of intricate plant models taken from the literature within minutes.Comment: 10 page