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In this work, we have built an experimental setup to simulate the clock noise transmission with two spacecrafts and two optical links, and further demonstrated the extraction of picometer level signal drowned by the large laser frequency noise and clock noise with the data post-processing method. Laser frequency noise is almost eliminated by using the idea of time-delay interferometry (TDI) to construct an equal arm interferometer. Clock asynchronism and clock jitter noise are significantly suppressed by laser sideband transmitting the clock noise using an electro-optic modulator (EOM). Experimental results show a reduction in laser frequency noise by approximately 10^5 and clock noise by 10^2, recovering a weak displacement signal with an average amplitude about 60 picometer and period 1 second. This work has achieved the principle verification of the noise reduction function of TDI technique to some extent, serving the data processing research of space-borne gravitational wave detection.

Clock noise is one of the dominant noises in the space-borne gravitational wave (GW) detection. To suppress this noise, the clock noise-calibrated time-delay-interferometry (TDI) technique is proposed. In this technique, an inter-spacecraft clock tone transfer chain is necessary to obtain the comparison information of the clock noises in two spacecraft, during which an electro-optic-modulator (EOM) is critical and used to modulate the clock noise to the laser phase. Since the EOM sideband modulation process introduces modulation noise, it is significant to put forward the corresponding requirements and assess whether the commercial EOM meets. In this work, based on the typical Michelson TDI algorithm and the fundamental noise requirement of GW detectors, the analytic expression of the modulation noise requirement is strictly derived, which relax the component indicator need compared to the existing commonly used rough assessments. Furthermore, a commercial EOM (iXblue-NIR-10 GHz) is tested, and the experimental results show that it can meet the requirement of the typical GW detection mission LISA in whole scientific bandwidth by taking the optimal combination of the data stream. Even when the displacement measurement accuracy of LISA is improved to 1 pm/ $\mathrm{Hz^{1/2}}$ in the future, it still meets the demand.

In this work, we describe an updated version of single arm locking, and the noise amplification due to the nulls can be flexibly restricted with the help of optical frequency comb. We show that, the laser phase noise can be divided by a specific factor with optical frequency comb as the bridge. The analytical results indicate that, the peaks in the science band have been greatly reduced. The performance of the noise suppression shows that the total noise after arm locking can well satisfy the requirement of time delay interferometry, even with the free-running laser source. We also estimate the frequency pulling characteristics of the updated single arm locking, and the results suggest that the pulling rate can be tolerated, without the risk of mode hopping. Arm locking will be a valuable solution for the noise reduction in the space-borne GW detectors. We demonstrate that, with the precise control of the returned laser phase noise, the noise amplification in the science band can be efficiently suppressed based on the updated single arm locking. Not only our method allows the suppression of the peaks, the high gain, low pulling rate, it can also serve for full year, without the potential risk of locking failure due to the arm length mismatch. We finally discuss the unified demonstration of the updated single arm locking, where both the local and the returned laser phase noises can be tuned to generate the expected arm-locking sensor actually. Our work could provide a powerful method for the arm locking in the future space-borne GW detectors.

TianQin is a planned space-based gravitational wave (GW) observatory consisting of three earth orbiting satellites with an orbital radius of about $10^5~{\rm km}$. The satellites will form a equilateral triangle constellation the plane of which is nearly perpendicular to the ecliptic plane. TianQin aims to detect GWs between $10^{-4}~{\rm Hz}$ and $1~{\rm Hz}$ that can be generated by a wide variety of important astrophysical and cosmological sources, including the inspiral of Galactic ultra-compact binaries, the inspiral of stellar-mass black hole binaries, extreme mass ratio inspirals, the merger of massive black hole binaries, and possibly the energetic processes in the very early universe or exotic sources such as cosmic strings. In order to start science operations around 2035, a roadmap called the 0123 plan is being used to bring the key technologies of TianQin to maturity, supported by the construction of a series of research facilities on the ground. Two major projects of the 0123 plan are being carried out. In this process, the team has created a new generation $17~{\rm cm}$ single-body hollow corner-cube retro-reflector which has been launched with the QueQiao satellite on 21 May 2018; a new laser ranging station equipped with a $1.2~{\rm m}$ telescope has been constructed and the station has successfully ranged to all the five retro-reflectors on the Moon; and the TianQin-1 experimental satellite has been launched on 20 December 2019 and the first round result shows that the satellite has exceeded all of its mission requirements., Comment: 16 pages, 1 figure, invited article to a special section in PTEP