With lots of help from Vicky Xu, Kevin Kuns, and Erik Von Reiss I've been working on a script that uses the noise budget infrastructure to validate a quantum noise model, using squeezing measured with and without the filter cavity and at different squeezing angles. Other people have done some similar fitting of quantum paramters, in particular Dhruva's interactive fitting code and Wen's MCMC fits.  My goal was to make something we could use to quickly validate a quantum noise model for a noise budget, in the end this is a somewhat painfully manual processes to find a model, but I also find it informative.  The usual process for doing this is a little circular, we start with a model of quantum noise and subtract it from a measurement without squeezing to get an estimate of the non-quantum noise, (or we use the cross correlation, and subtract a model of QRPN), and use that to subtract the non quantum noise for different squeezer settings.  I was hoping to avoid doing this by using the noise budget terms, which is how the first 5 attachments to this alog were made,  but the noise budget residual is too large for that approach so in the end I'm doing the usual subtraction. 

SRC detuning

The squeezing angle is fit for each model by finding the squeezing angle that minimizes quantum noise at 3kHz with FDS, and then applying that as an offset to all the other squeezed or anti-squeezed traces.  This is needed because changing the SRC detuning or the homodyne angle changes the squeezing angle.

The first useful thing about this script is that it clearly shows that we need a SRCL detuning to explain the data from 77710. The frequency independent data clearly show this, without an SRC deetuning there is no explanation for the elevated noise with FIS around 200-80 Hz or so (compare the red measured trace in the first attachment to the yellow model, with no SRC detuning).  Adding a SRCL detuning clearly helps to fit this FIS trace, shown in the second attachment.  This FIS trace would provide us a nice constraint on the arm power, if there were not SRC detuning, but as it is these two parameters both have to be adjsuted to fit FIS.

SQZ and Anti-sqz level

Plotting this data set in dB of squeezing (ratio of the traces with squeezing to without squeezing, no subtraction done), we have 4.75dB of high frequency squeezing and 15.25dB of high frequency anti-squeezing. From alog 77710, the nonlinear gain was 16.9 impling that there was 17.1dB of injected squeezing at the time. We have 7.1% known injection losses (escape efficiency, HAM7 losses, OFI). To get this level of anti-squeezing with this nonlinear gain would require high total losses, 35%, which would not be able to produce this much squeezing even without phase noise.  As people have seen before, we need a lower estimate of nonlinear gain to explain our squeezing and anti-squeezing levels, which is annoying because it means we are adjusting a parameter that we would hope we could use a measurement for.  After talking with Begum and the squeezers about this, I went back to the time when were measuring NLG (16:00:50 UTC on May 8th), to compare the amplified/unamplified seed measurement to amplified/ deamplified, which Begum says been making more sense for LLO (In principle they should be the same).

amplified: 0.214  deamplified: 0.00383 unamplified: 0.0127 dark: 2.11e-5   nlg = ((1+sqrt(amplified./deamplified))/2)^2   gives us an nlg of 18.04, so this is too high.

We could get out of this mess by measuring and fixing phase noise, so that we can fit generated squeezing and total losses to fit our squeezing and anti-squeezing. I've set the phase noise to 30mrad, and adjusted the injected squeezing and total squeezer losses to match anti-squeezing and squeezing.

Models for high and low arm powers

I've started with the range of arm powers from the O4a paper, 364+/-10kW, and put together a low power (354kW) , mid power (364kW), and a high power (374kW) model. 

Semi-manual procedure: 

• Based on SQZ and anti-sqz, set total sqz losses (either assuming you know nlg or phase noise)
• set circulating power to what you want, set output losses to match shot noise level without squeezing.  Set sqz injection losses based on total sqz losses and output losses.
• adjust SRC detuning based on FIS at around 100-200 Hz

It turned out that the SRC detuning doesn't need to change when the arm power is changed and the losses are redistributed between injection and output losses, and I didn't adjust FC parameters for these.  So, for 354kW in the arms, I adjusted the output efficiency to 83%, to 80% for 364 kW, and 78% for 374kW.    In all cases the injected squeezing was 16.7dB, 30mrad phase noise, HD angle -10.7 deg, and the SRCL detuning was 0.29 degrees. 

This procedure will give us different predictions for the frequency indendent squeezing trace from 30-50 Hz, which should be able to give us a constraint on the arm power.  If the arm power is overestimated, the radiation pressure noise without squeezing would be overestimated; also we would assign more of the total sqz losses to interferometer output losses, and less to injection losses.  That means that there would be more anti-squeezing in the arm cavities increasing the level of raditation pressure noise with out the filter cavity.  So both of these effects go in the same direction, meaning that FIS at these frequencies is one way to verify an estimate of the arm power.   Clicking through these plots, it seems that the lowest powers in the range quoted in the O4a paper would be disfavored by looking at FIS.  (It will also be nice to use the no squeezing measurement to estimate the non-quantum noise instead of the noise budget known noises, this might favor the middle of the arm power range more).

Anti-squeezing at low frequencies looks wrong

Noticable in all of these plots is that the anti-squeezing model is wrong at low frequencies, we don't have the decrease in noise we'd expect from frequency independent anti-squeezing when the arm cavity is rotating the squeezed quadrature.  When this data is plotted without subtraction it's clear that this shouldn't be explained by the noise budget residual, that is too small.  We've taken data sets like this several times over the last few years, in all cases, the FIAS doesn't go clearly below the FIS curve around 50 Hz as the model here says it should (or sometimes the plots are cut off at these frequenices): 77133 77023 71902 67498

Using a non-quantum noise estimate based on subtraction of quantum noise model

In all of these above, I was only using the non-quantum noise estimates made by the noise budget, but as I said above there is too much noise which is not understood, particularly around 200Hz.  The estimate of the SRC detuning is fairly different if I instead estimate the non-quantum noise by subtracting the quantum noise model from the no-squeezing measurement, although the other parameters don't have to change.  The last three attachments show low, mid and high power models with an SRC detuning of 0.14 degrees and the non-quantum noise estimated by subtraction.  Looking at the frequency independent squeezing in these final three attachments, the slope isn't quite right from 90-200 Hz, which probably means that there is a mode matching effect that is not modeled here.    I've set the mid power model here as a quantum parameter file for the noise budget, as QuantumParameters_May2024.yaml  We can go ahead and use this to make a noise budget, while in parallel using Dhruva's interactive squeezer code to try to understand if there is set of mode mismatch parameters that can fit the data better.