Most systems used in quantum physics experiments require the efficient and simultaneous recording different multi-photon coincidence detection events. In such experiments, the single-photon gated counting systems can be applicable. The main sources of errors in these systems are both instability of the clock source and their imperfect synchronization with the excitation source. Below, we propose a solution for improvement of the metrological parameters of such measuring systems. Thus, we designed a novel integrated circuit dedicated to registration of signals from a photon number resolving detectors including a phase synchronizer module. This paper presents the architecture of a high-resolution (~60 ps) digital phase synchronizer module cooperating with a multi-channel coincidence counter. The main characteristic feature of the presented system is its ability to fast synchronization (requiring only one clock period) with the measuring process. Therefore, it is designed to work with various excitation sources of a very wide frequency range. Implementation of the phase synchronizer module in an FPGA device enabled to reduce the synchronization error value from 2.857 ns to 214.8 ps.

A theoretical formula for large-diameter rock-socket depth is developed to support pail embedding in a large bridge pile foundation project. There is a horizontal additional stress concentration at the place where the soil around the rock-socketed pile meets the soil layer under the horizontal load. When the rock-socketed tip stress and bending moment of the pile are relatively small, the pile shows favourable embedment effect and the pile foundation can be considered safe. The function curve of soil resistance around the pile under the action of horizontal force was obtained by finite element analysis. The force characteristics reveal the depth of the largediameter rock-socketed pile under the horizontal load. As the rock-socketed pile rotates under the action of horizontal force, the rock mass resistance around the pile changes according to the cosine. The distribution of pileside soil resistance is proportional to the displacement and distributed according to the sine. A comprehensive correction coefficient of pile shaft resistance beta is introduced to deduce the theoretical formula of the depth r h of the large-diameter rock-socketed pile embedded in the bedrock. It is verified through both experiments and numerical analysis.