Ultra-stable lasers, characterized by high-frequency stability and extremely narrow linewidths, serve as vital tools in precision measurement and physics research. They find extensive applications in fields such as atomic clocks, gravitational wave detection, and quantum communication. With improvements in experimental precision, the demand for lasers with narrower linewidths and higher frequency stability has increased. Therefore, enhancing the frequency stability of ultra-stable lasers has become a significant area of research. Currently, the Pound?Drever?Hall (PDH) frequency stabilization technique is widely used for generating ultra-stable lasers. By employing this technique, the laser frequency is locked to a high-precision Fabry?Perot (FP) cavity to reduce the laser linewidth and improve frequency stability. If the feedback system has a sufficiently high signal-to-noise ratio (SNR), an appropriate loop bandwidth, and gain, it can fully suppress the free-running frequency noise and drift of the laser. Ultimately, the frequency stability primarily depends on the performance of the ultra-stable cavity (reference cavity), which serves as the frequency reference, and the servo system that controls the laser frequency. Thus, enhancing the stability of the reference cavity and optimizing the performance of the frequency-locking system are critical for improving the frequency stability of ultra-stable lasers.

This study theoretically investigates the influence of interference effects on PDH locking error signals and identifies optimization directions for the optical path. In experiments, a reflection mirror was initially used instead of the reference cavity to prevent data distortion caused by laser frequency drifts when the laser operates freely and scans through the resonances of the reference cavity. Subsequently, an Agilent 34401A digital multimeter was employed to measure the voltage values of the locking error signals under different optical path conditions. The stabilities of the locking error were calculated and compared under different optical path designs. Finally, the optimal design for reducing interference effects in the optical path was chosen. A self-developed photodetector and frequency-locking circuit were used to stabilize the laser frequency to a 10 cm reference cavity. To enhance the stability of the length of the reference cavity, it was enclosed within a vacuum chamber using a transportable mounting structure. Additionally, a Peltier temperature control system was installed inside the vacuum chamber to maintain the cavity temperature near the zero-crossing point of its coefficient of thermal expansion. The entire system was positioned on an active vibration isolation platform. We replicated this setup to create two independent ultra-stable laser systems. The two beams of ultra-stable lasers were combined using a fiber combiner and directed to a high-speed photodetector for beat-note detection. Beat-note frequencies were collected using a Microchip 53100A phase noise analyzer, which was used to evaluate the frequency stability of the locked lasers.

The study reveals that adding isolators and wave plates after an electro-optic modulator (EOM) can effectively suppress interference in the optical path (Fig. 2). After optimization, the relative stability of the locked frequency system reaches 9×10-7. The reference cavity's vibration sensitivity (Table 1, Fig. 7) and temperature instability (Fig. 9) are both sufficiently low, such that the impact of vibration noise and environmental temperature fluctuations on cavity length stability is overshadowed by that of thermal noise. With a reference cavity linewidth of 21 kHz (precision of 75000), the frequency stability of a 1.5 μm laser is locked at the 4.0×10-16 level (Fig. 10), which is approaching the thermal noise limit of the 10 cm reference cavity.

This study theoretically analyzes the influence of interference effects in the optical path on PDH frequency locking error signals and experimentally studies effective methods for reducing these effects. We develop two independent 1.5 μm ultra-stable lasers locked onto two 10 cm ULE reference cavities. Through mutual comparison, the short-term stability of each individual laser is evaluated. The stability reaches 4.6×10-16 for integration times of 1 s and 4.0×10-16 for integration times in the range 2?5 s. This ultra-stable laser system, which utilizes a 1.5 μm polarization-maintaining optical fiber output, is suitable for application in long-distance optical frequency transfer and quantum communication. The study on eliminating interference effects in the optical path provides a reference for future development of ultra-stable lasers with frequency stability at the level of 10-17.