# High-Precision Single-Photon Laser Time Transfer with Temperature Drift Post-Compensation  
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1 State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China; [EMAIL_ADDRESS] (W.M. ); [EMAIL_ADDRESS] (Y.W.) Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China; [EMAIL_ADDRESS] (K.T. ); [EMAIL_ADDRESS] (Z.Z. ); [EMAIL_ADDRESS] (S.J. ); [EMAIL_ADDRESS] (Z.Z.) Department of Physical Electronics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, 115 19 Prague, Czech Republic; [EMAIL_ADDRESS]  
Correspondence: [EMAIL_ADDRESS]; Tel. : +86-21-62237211  
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1 State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China; [EMAIL_ADDRESS] (W.M. ); [EMAIL_ADDRESS] (Y.W.) Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China; [EMAIL_ADDRESS] (K.T. ); [EMAIL_ADDRESS] (Z.Z. ); [EMAIL_ADDRESS] (S.J. ); [EMAIL_ADDRESS] (Z.Z.) Department of Physical Electronics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, 115 19 Prague, Czech Republic; [EMAIL_ADDRESS]  
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Laser Timing (CLT) system onboard Chinese Space Station (CSS) and European Laser Timing + (ELT+) in space optical clock on International Space Station (I-SOC). The existing laser time transfer link T2L2 together with the onboard clocks has achieved a limiting time transfer precision better than 10 ps for integration time of 10 to 100 s, and 10 ps for integration time of several days [7]. The ongoing ELT project onboard the International Space Station (ISS) should provide an ultimate precision of 3 ps for 300 s of integration time with a clock stability of \(10^{-16}\)[8]. With the development of optical clocks, a frequency stability of \(10^{-17}\) was provided in several ground-based labs. The launch of space optical clocks is now under preparation [5; 9]. Optical clocks may approach a frequency stability of \(10^{-18}\) when operated in space. The time and frequency transfer of high stability between ground and space presents a fundamental experiment in physics. Laser time transfer ultimate precision, expressed by time deviation (TDEV) [10], is expected to be better than 0.3 ps over days in order to compare the frequency from the ground to space with \(10^{-18}\) precision [11]. The next goal of the laser time transfer system is now planned in the I-SOC mission by Europe and CLT mission by China to achieve a time stability of approximately 0.5 ps over 100 s and 1 ps over \(10^{6}\) s with optical clocks [5; 9]. With such high-precision requirements, both ground and space laser time transfer systems have great challenges. The onboard optics and instruments in space need to be especially well designed to achieve high accuracy and stability. In low earth orbit, the temperature on a satellite surface may change more than 100 \({}^{\circ}\)C. With some insulation methods, tens of degrees Celsius temperature variations may occur at the space-receiver side. The temperature changes have a strong effect on the delay of the laser time transfer chain. Therefore, it is important to control and compensate the system temperature drift to achieve better time stability performance [12]. The existing satellite laser ranging (SLR) technology was optimized to control the system temperature coefficient of a single instrument. The single-photon detector package based on a 25-um K14 chip from Czech Technical University achieved a temperature coefficient of 0.76 \(\pm\) 0.1 ps\({}^{\prime}\)C [13]. The event timer to record the time tags of the laser pulses has a drift of less than 2 ps\({}^{\prime}\)C [14]. The coaxial cable drift is within the range of 0.05 to 5 ps/\({}^{\circ}\)C per meter [11; 15]. The laser pulses emitting time also changes several picoseconds per Celsius degree.