[Tanaka, Hirose, Komori]

Abstract:

We adjusted the common offset immediately after the input of the IMC LSC common mode servo (-5.0 ± 0.3 mV with 14 dB input gain) and the fundamental frequency to generate multiple RF sidebands (5.6243667(1) MHz) to keep the carrier and the RF sidebands just on resonance of IMC.
As the result, we achieved a precise estimation of the IMC length, accurate to 1 µm, L_IMC = 53.302438(1) m.

Details:

During the previous measurement in klog:29084, residual peaks at the modulation frequency of 1.023 kHz persisted in either I-phase or Q-phase demodulation signals even after tuning the RF sideband frequency.
We attribute this to an extra offset in the IMC length control, causing detuning of the carrier and either the upper or lower sideband.
To address this, we experimented with combinations of LSC offset tuning and sideband frequency adjustments.

The setup is the same as klog:29084.
Initially, we adjusted the sideband frequency to equalize the residual peak heights in both demodulation signals.
Subsequently, we fine-tuned the common offset of the IMC LSC common mode servo.
This method effectively reduced the height of both peaks simultaneously, although we have not understood yet an unexpected swap of the I-phase and Q-phase peaks with minor adjustments to the sideband frequency (approximately 10 Hz).
After several iterations of this procedure, the residual peaks nearly vanished (the red and blue lines), yielding the results described above.

However, one hour later, upon rechecking the peak height, we observed the reappearance of residual peaks (the magenta and cyan lines).
We were unable to eliminate these peaks by solely adjusting the sideband frequency and common offset, suggesting that both parameters had drifted during this hour.
The drift in IMC length may originate from the re-locking of the IMC, leading to differences in the locked point by a few um, and thermal expansion of the IMC mirrors and suspensions.
The offset drift may arise from electrical circuit and residual amplitude modulation due to slight mismatches in the input polarization to the EOM, caused by temperature drifts.
We must consider strategies to compensate for these drifts and assess their impact on interferometer sensitivity.