A couple of weeks ago week Jeff and I took a series of measurements of the sensing function, cross correlation, and squeezing level for different phases, at different spot positions and different squeezing angles.  (51394,  and  51440) There is still more work to be done to understand the measurements, but some first conclusions are:  There are frequency dependent losses for squeezing which are larger above the cavity pole, and didn't change much with the spot position change, although the cavity pole and the reflectivity of the CLF sidebands did change with the spot positions.

Background:  We had tried before O3 started to move the SRCL offset and see a frequency dependence of the squeezing level, but we saw no impact.  I repeated this in July and found that with reduced frequency noise, and subtraction of correlated noise, we can see some frequency dependence, and a bit better squeezing at low frequencies for some SRCL offsets 50591

Lee has done some modeling of some frequency depenent losses, squeezing angle rotations, and an apparent frequency dependent phase noise due to SRC losses, SRC to ARM mode mismatch, and SRC detuning. 50610  Lee showed there that with SRC losses and a mode mismatch between the SRC and the arms, it is possible that the squeezing is flatter for a detuned SRC than for an anti-resonant one, and that SRC losses degrade the squeezing at high frequencies while SRC to arm mode mismatch degrade the low frequency squeezing.  Since we were planning to move our spot positions, and we know that this has an impact on the DARM pole, I wanted to try to get some measurements that could be usefull to compare to that modeling.

Optical spring /DARM pole: 

Jeff has posted some of the sensing function measuerments that he did in these alogs: 51440 and 51592.  The short story is that we can have much less of an optical spring effect with 100 cnts offset in SRCL for both spot positions, indicating that 100 counts offset is really closer to the SRC anti-resonance, and we are now running that way.  We lost lock trying a 200 count offset, which gave us an anti-spring based on the partial sensing function measurement Jeff was able to get.  (2nd attachment)  The calibaration group fits a single pole to the DARM cavity pole, this causes a few percent error in the calibration around and above the cavity pole for the kind of SRC detunings we have been running with in the first part of O3, which can be seen in the attachment linked above.  According to Jeff's use of Craig's model of the optical spring and DARM response here the detuning of the SRC that we have been seeing is around 6mrad, although something seems off here since the phase is not matched well above the cavity pole in those models. 

Squeezing:

The first attachment shows the squeezing level, based on DCPDs with the correlated noise subtracted as described in 50591  The first attachment shows all 4 sets of measurements, in all of them there is more squeezing and more anti-squeezing at low frequencies which would indicate lower loss below the DARM pole.  The measurements taken at phases intermediate between squeezing and anti-squeezing give us the best information about the frequency dependent squeezing angle rotation, although a little bit of thought is needed to interpret these. (In the legend I labeled each trace with sqz or asqz based on the sign of the CLF servo, and the phases are from the CLF phase shifter).  The three sets of stars are estimates of the mean squeezing level in three frequency bands.

The second attachment shows all measurements at the nominal squeezing phase and the nominal anti-squeezing phase, for easier comparison.  Abvove about 500 Hz all the measurements are basically the same, and at low frequencies the differences in the squeezing levels between them are small.  There is some suggestion of less loss (or at least more sqz/asqz) at low frequencies for the July spot positions and with the SRCL offset on, which could be compared to the first plot in Lee's alog.  Based on the level of squeezing and anti squeezing seen at these nominal angles (which are not very different from the best squeezing and anti-squeezing for each frequency), we can make an estimate of the total efficiency and phase noise for each measurement frequency.  Since there are many lines in the data which give impossible results if we interpret them as squeezing and anti-squeezing, I've limited the data used for making these estimates based on the level of squeezing and anti-squeezing.  The 5th attachment shows the resulting estimate of efficiency, with the budgeted losses divided out, which shows higher losses at frequencies above a few hundred Hz, which Lee's modeling suggests could be because of squeezing matching to the IFO or because of SRC losses.  We have basically the same result for frqeuency dependent losses for all the spot positions and SRC detuings, although the cavity pole increased from 409Hz to 415Hz when the spot position changed (for the measurements with no/small detunings 51466).  By comparing the change in the cavity pole to the lack of a change in frequency dependent losses using Lee's model we might be able to make a statement about if the cavity pole change was (or wasn't) due to a change in SRC losses, or perhaps could rule out SRC losses as an explanation for the frequency dependent losses that the squeezer sees.

The inferred efficiency increaes right around 2.3kHz, which is due to an increase in the anti-squeezing level, and is an interesting feature.  I wouldn't read too much into the infered phase noises in this plot, as there is a lot of scatter.

Squeezing level as demod phase rotates:

To estimate the losses discussed above, I used measurements made at the same demodulation phase for all frequencies.  There is a potential problem with this because the frequency dependence of the squeezing angle could be contributing a bit to the apparently higher losses at higher frequencies, but it should not be a large effect because none of the other squeezing angles had much more squeezing or anti-squeezing than the measurements used here. The third attachment shows the median squeezing in different bands plotted against CLF demod phase for each SRC offset/spot position combination.  These plots suggest that we could get better squeezing at low frequency if we continued to reduce the CLF demod phase, although this may not have much of an impact on our sensitivity.  I had hoped to fit each of these sets of measurements to get an estimate of loss, phase noise, and the squeezing angle rotation for each band to avoid the problem of using one demod phase to estimate squeezing and anti-squeezing for all frequencies.  The problem with that is understanding the relationship between the CLF demod angle and the squeezing angle (see Daniel's expression here 49026).  For most of these measurements the clf demod phase between anti-squeezing and squeezing is around 130 degrees, which I don't have an explanation for at the moment. 

LO Q signals:

Because the 130 degrees between squeezing and anti-squeezing made me wonder if the phase shifter calibration was off, I plotted the LO Q signals normalized by the CLF reflected power (the normalization is needed since there were CLF power jumps durring the measurements) and made fits (4th attachment).  Fitting these with an ellipse works well, and it seems that the calibration of the phase shifter is fine.  The most interesting thing to see is that the OMC 3 MHz signal ellipse has a larger semi-major axisis with the July spots than it does with the August spots, indicating that the reflectivity of the SRC for the CLF changed when the spot positions changed.  There were also small shifts in the demod angle of semi-major axisis when the SRC offset was changed, although this is small. 

Next steps:

There are several things that could be done next, including comparison to Lee's model for the cavity pole change, modeling of the 3MHz OMC DCPD error signal, infering a squeezing angle rotation from the intermediate squeezing angle measurements, measureing the squeezing at lower clf demod phases, and measuring squeezing at the intermediate angles for different SRC offsets.