Clock Noise Cancellation in Heterodyne Links between Optical Cavities for Space-Borne Gravitational-Wave Telescopes

Space-borne gravitational-wave telescopes are key to extend the observation band below $10\,\mathrm{Hz}$. The use of inter-satellite optical cavities linked by heterodyne interferometry is a promising approach to reach the sensitivity level of $10^{-22}/\sqrt{\mathrm{Hz}}$ in the decihertz band. While heterodyne interferometry is advantageous for relaxing arm-length control requirements, it introduces susceptibility to clock jitter, which can be a significant noise source. In the back-linked Fabry--Perot (BLFP) interferometer aiming at the decihertz band, the required clock stability exceeds that of current space-qualified oscillators by more than an order of magnitude. We propose a clock noise cancellation scheme that uses two heterodyne signals with positive and negative beat-note frequencies, naturally obtained using both incoming and outgoing laser beams of arm cavities without additional clock modulation schemes. By forming a weighted combination of these signals with time-dependent coefficients, clock jitter contributions are eliminated while preserving gravitational-wave information. We present the theoretical framework, analyze performance under realistic arm-length drifts, and validate the approach through time-domain simulations using parameters from the B-DECIGO concept. Results show that the synthesized signal recovers the original sensitivity and even improves the signal-to-noise ratio by a factor of $\sqrt{2}$ for shot noise.