High-precision and flexible laser frequency stabilization based on a self-referencing phase-lock module

We conduct a theoretical and experimental analysis for a self-referencing phase-lock module based on the delay-unbalanced Mach-Zehnder interferometer (UMZI) and optical phase-locked loop (OPLL). The self-referencing phase-lock module can be integrated with any system, allowing for linewidth narrowing and improved short-term laser stability without affecting the performance of the original system. In this paper, the laser noise detection principle based on UMZI is analyzed, accompanied by the development of UMZI response simulations and OPLL parameter design methods. Furthermore, we demonstrate one such application, where integrating the module with a saturated absorption spectrum (SAS)-based frequency stabilization system ensures both the long-term and short-term stability of the pump laser in a spin-exchange relaxation-free (SERF) atomic co-magnetometer. In the SAS system, the frequency modulation applied to the laser to generate an error signal for locking the laser to the atomic resonance line results in excellent long-term frequency stability, but also introduces significant modulation noise. Building upon this, the module further improves the short-term stability of the laser, effectively reducing its linewidth and enhancing the overall performance of the pump laser. Experimental results show that, in the absence of significant modulation noise, the self-referencing phase-lock module compresses the laser linewidth from 500 kHz to 108 Hz. When integrated with the SAS frequency stabilization system, the module compresses the laser linewidth from 3.3 MHz to 2 kHz, and the frequency stability is improved to 2.992 × 10^-13 at 10^-2 s, while maintaining the same level of long-term frequency stability as the SAS system. The research work is of great significance in improving the laser short-term performance with high flexibility, low cost and high precision.