Optimizing frequency noise calibration and manipulation in an active feedback control loop

Frequency noise is a key limitation factor for frequency sensitive ultra -high precision measurement. An excellent methodology for its calibration is the error signal extracting from a cavity length locking process via Pound-Drever-Hall (PDH) technique, and also can be applied as a noise discriminator for active feedback control. However, the stabilized laser frequency noise performance was poor to meet the applications for ultra -high precision measurement, and no literature has analyzed the cause in detail. In this Letter, we found that various of noise floors in the in-loop sensing and modulation depth in the PDH error signal should be responsible for the poor noise performance. Meanwhile, differing from the theoretical prediction (1.08), the modulation depth in frequency noise feedback controlling should be optimized by simultaneously considering the detector's gain and saturation power, cavity impedance matching, and control loop gain. In our case, it was fixed to be 0.17. The experimental results confirm our theoretical analysis well. Finally, the stabilized laser root root frequency noises are reduced to 10(-1) Hz/root Hz for out-of-loop and 3 x 10(-2) Hz/root Hz for in-loop. The results demonstrate an efficient settlement solution for active frequency noise feedback control.