[Aritomi, Yuhang, Yaochin]

We could see transmission of both coherent control sidebands (CCSB) from filter cavity at CCD camera with 40mW green. Pic.1 shows upper CCSB transmission at camera. We found that when CC PLL frequency is 7MHz, AOM frequency of upper CCSB is 109.04179MHz and lower CCSB is 109.02990MHz while AOM frequency of carrier is around 109.036 MHz. In CC locking of filter cavity, either of CCSB is on resonance and other CCSB should be separated by ~100Hz. So we tuned CC PLL frequency in order to have ~100Hz of CCSB separation frequency. Note that AOM frequency separation corresponds to twice of CC frequency separation.

Frequency separation with 6.997MHz of CC PLL is close to frequency separation that we want, but AOM frequency with 6.997MHz of CC PLL is not so precise since CC transmission seems not changing at camera around this region and we couldn't distinguish upper and lower sideband.

Pic. 3 shows plot of CC PLL frequency and CC frequency separation. The fitting result is

CC frequency separation (Hz) = -1907605 * CC PLL frequency (MHz) + 13347486

If you want to have 108 Hz of CC frequency separation, CC PLL frequency should be 6.996930 MHz or 6.997043 MHz.

After we set CC PLL 6.997MHz, we found that CC1,2 error signal oscillated since demodulation frequency of CC1,2 was not tuned. After we set demodulation frequency of CC1 6.997*2=13.994MHz and demodulation frequency of CC2 6.997MHz, the oscillation dissappeared and we could lock CC1,2. However, when we open the CC2 loop, CC2 error signal has low frequency oscillation (Pic. 2) due to residual frequency difference between CC PLL and demodulation phase and it is difficult to remove.