【Kevin, Evan】
Summary: We applied the correlation technique described in Martynov et al. (2017) to find the noise in DARM that is coherent between DCPD A and DCPD B from 80 Hz to 155 Hz. The comparison with the expected thermal noise level (from previous budgeting efforts) is given in the attached pdf plot.
Measurement details: To do this measurement, we
- Turned the squeezer off and closed its beam diverter.
- Turned down the DARM gain by a factor of two and applied a series of elliptic bandstops, each with 40 dB of stopband suppression, so that we did not have to deal with the confounding effect of the DARM loop on the correlation measurement. (We needed a series of bandstops since trying an octave-wide bandstop in one go would take away too much phase even at the lowered DARM UGF.)
- Took 11 minutes of data with each bandstop, which enables 160 averages with 8 s FFTs and 50% overlap, and hence can resolve a coherence between the DCPDs down to less than 0.01. In fact the observed coherence in this region was more like 0.1–0.2.
- Took a pcal sweep after each bandstop measurement to ascertain the optical gain, which was about 5.7 mA/pm with a ~10% error. We ignored the effect of the cavity pole, which should introduce less than a 7% error in this frequency range (the pole should be >400 Hz).
The correlation also removes any dark noise uncorrelated between the DCPDs, but this is about 50× below the total DARM noise (LHO:67786).
Analysis: The amount of noise power in DARM coherent between the two DCPD should be 4 times the cross-spectral density. The attached plot shows this quantity, along with the spectral density of the DCPD sum (i.e., the total DARM noise). We also show the DCPD sum with the expected 20 mA shot noise subtracted off, which gives excellent agreement with the cross-spectrum estimate.
We also show the expected thermal noise level from the recent noise budget (LHO:68382), which is predominantly coating Brownian noise with small contributions from AMD noise and coating thermo-optic noise. Overall this estimated noise level is about 1.128×10−20 m/Hz1/2 at 100 Hz with a slope of f−0.455. Making the ratio of the cross-spectrum and the expected thermal noise, we can see that in certain regions the ratio is as low as 1.3, which seems in tension with the elevated thermal noise curve Gabriele posted previously (LHO:67452). We also know that some of the correlated noise in DARM here is jitter; if that were subtracted from this data, it would lower the ratio even more from its average value.
(An earlier version of this alog used outdated thermal noise estimates in the noise budget, and this has been corrected.)
The LHO noise budget uses pygwinc and takes the coating thermal noise calculation directly from gwinc. An old version was being used, however, which did not include an update to the coating parameters based off of measurements at MIT and LMA. The new loss angles are 3.89e-4 × (f / 100 Hz)0.1 for tantala and 2.3e-5 × (f / 100 Hz)0 for silica.
I added a jitter analysis to this estimate using the magnitude-squared coherence between the DCPD sum and IMC WFS A yaw, which gives the fraction of noise power in the DCPD sum that can be attributed to the jitter witnessed by this WFS channel (all four IMC WFS channels, A/B pitch/yaw, are highly coherent with each other).
Subtracting this estimated jitter from the cross-correlation gives a slightly tigher broadband constraint on the amount of unexplained noise above the expected thermal level. The tighest constraints, around 113 Hz and 127 Hz, remain at about 30% above the expected thermal noise level.
I am also attaching a plot of the expected thermal noise from the noise budget.
For anyone who wants to repeat this test, the foton design strings for the DARM notch filters I used are as follows:
- 80 Hz to 95 Hz:
ellip("BandStop",6,2,42,79,96)gain(1.25893)[currently DARM2 FM1] - 95 Hz to 115 Hz:
ellip("BandStop",6,2,42,94,116)gain(1.25893)[currently DARM2 FM2] - 115 Hz to 155 Hz:
ellip("BandStop",6,2,42,112,158)gain(1.25893)[currently DARM2 FM8]