Vicky, Sheila
Summary: Today we learned that frequency independent anti-squeezing is a very good way to determine which sign the homodyne angle is.
Background: I've been working on using code from Vicky's repo and the noise budget repo to do some checks of a quantum noise model, this is in a new repo here.
Details about how this model is made:
The first attached plot illustrates how these models and plots are made. It starts with a no squeezing time, and an esitmate of non quantum noises from the noise budget, (dark gray, this one is from Elenna's recent run of the noise budget: 80603 ) and an estimate of the arm circulating power along with other parameters set in a quantum parameters file in the same format that is used by the noise budget. It fits the readout losses by adding a gwinc model of quantum noise with the noise budget estimate of other noises, and adjusting the readout losses of the gwinc model, this is done from 1.5-1.8kHz in this case.
Based on this readoutlosses we get a model of quantum noise without squeezing, and subtract that from the no squeezing trace to get an estimate of the non-quantum noise. This is enough different from the noise budget one that I've used that as the estimate of the non-quantum noise for the rest of the traces.
By subtracting this subtraction estimate of the non-quantum noise, it estimates squeezing in dB, and finds a median level of dB from 1.5-1.8kHz for anti-squeezing and squeezing. This should be the same with and without the filter cavity, but in this data set there is slightly more anti-squeezing in the time without the filter cavity, so I've used FIS and FIAS to estimate the nonlinear gain and total efficiency for squeezing. The nonlinear gain is translated into generated squeezing for gwinc, and the injection losses for squeezing are set so that the injection efficiency* readout efficiency = total squeezing efficieny.
With this information we can generate models for anti-squeezing and squeezing traces, but fitting the squeezing angle to minimize or maximize quantum noise. Then for the mid angle traces, the squeezing angle is fit to minimize the residual between the data and the quadrature sum of the subtraction estimate of non quantum noise and the model. We can then look at these plots and try manually changing parameter in the quantum parameter file.
Homodyne angle:
We've been stumped for a while about the excess noise we see with low frequency anti-squeezing, in 79775 I went through old alogs and see that we've had this mismatch of model with our data for a long time. Today we tried flipping the sign of the homodyne angle and see that low frequency anti-squeezing is much closer to fit both with and without the filter cavity. Compare the 2nd and 3rd attachments to see this.
We still have more work to do on this model, including adding in the additional traces near squeezing and near anti-squeezing that Camilla took, and checking if it can give us any information about arm power (it doesn't seem very useful for that), or the mode mismatches.
I neglected to mention that this is based on the nice data set that Camilla collected here: 80664, and that three is more work to be done with this, checking SRC detuning, mode mismatch, and including the +/- 10 deg data.
Sumary: seems the current (+) side of DARM is better for FDS, although it is opposite of our previous quantum noise models. But given the current sign is actually better for DARM, the model error doesn't really matter, and it's not really worth changing signs.
The wrong HD angle sign seems to be why none of our quantum noise models, despite fitting all other SQZ angles well, have ever fit FIAS properly. We will update our quantum noise models for the noise budget. Attached are some quantum noise models and DARM plots for Camilla's recent SQZ dataset lho80664.
Plots with optimal FDS (optimal fc detuning) for both signs of the homodyne angle: showing 1st just the quantum noise models without adding back non-quantum noise (NQN), and 2nd showing QN models + NQN.
- Current sign of DARM (+) has solid lines. "Other" sign (-) has dashed lines.
- Homodyne angle is only really obvious for FIAS (freq-indep anti-squeezing, turqoise traces). It's almost indistinguishable for FIS otherwise (green, yellow, light blue). Marginally noticeable for FDS (but more sensitive to FC optimization).
- Sheila made a super important observation that FIAS has never fit quantum noise models properly.
- Quantum noise models with the "other" (-) sign expect FIAS < No SQZ between 15-100 Hz, and FIAS < FIS between 15-50 Hz. This is not what we have observed with FIAS, despite QN models fitting all other SQZ angles fine.
- Only flipping the HD angle sign was able to match the QN models to data, suggesting that previous quantum noise models used the wrong sign of the homodyne angle.
- It turns out this doesn't really matter in real life, but we will update the noise budget models.
- Confusingly, the current (+) side is better with FDS, but the "other" (-) side is better for unsqueezed DARM. See the grey (+) vs. black (-) traces for unsqueezed DARM at +/- 10 deg homodyne angles.
- Not sure where the notion of a "good side of DARM" comes from
- Pre-O4a, there was a quick test to lock on the other side of DARM, lho68080... But maybe this test just shows some technical noises change with the HD angle?
- In the test, see the plot of how unsqueezed DARM (purple vs. red) is very different below 100 Hz for the two signs, but not in the pway predicted by quantum noise models (grey + black traces).
- So, seems like this test suggests the +/- sign measured DARM noise differences are more likely technical (non-quantum) noises that change with homodyne angle.
Third attachment (3rd) shows a wider range of homodyne angles, from +15 deg to -10 deg. So far the code for these plots is living here.
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Altogether this is making progress on the quantum noise models for the noise budget!
Summarizing updates and what we're learning:
- As Sheila said, low freq frequency-independent anti-squeezing (FIAS) ---> homodyne angle (which sign it is + approx how many degrees): see light blue FIAS traces in 2nd plot.
- Elenna recently measured the contrast defect in lho80806, corresponding to a upper homodyne angle of +7.4 deg (down from the +10.7 deg measured in O4a (lho71913)).
- After subtraction, FIS matches reasonably well with this lower HD angle +7 deg.
- Still +10.7 deg is only marginally different, so FIAS is not really precise enough to tell at the ~degree level.
- As in lho80318 79951, can use the frequency-independent squeezing (+mid-sqz) bronchosaurus (FIS) ---> SRCL detuning.
- After subtraction, FIS matches reasonably well with SEC detuning between 0 and -0.2 deg.
- Subtracted FDS data still WIP as the low frequency quantum noise estimate seems not totally right.
- Maybe could fit the FC detuning at each SQZ angle (as SQZ angle can affect the RLF-CLF offset for such low (sub-linewidth) FC detunings), but haven't thought about this FDS data much yet.
- Important model degeneracies remain from having 4 model unknowns: [[ IFO arm power + readout loss, and SQZ NLG + injection loss ]] with which to fit 3 DARM measurements [[ unsqueezed shot noise + anti-squeezing (kHz level) + squeezing (kHz level) ]].
- Still need to factor in mode-matchings.
Vicky, Sheila
Based on the fit of total squeezing efficiency and nonlinear gain (which is based on subtracted SQZ and ASQZ from 1.5-1.8kHz), and known losses from loss google sheet, we can infer some possible maximum and minimum arm powers using the no squeezing data.
The first attachment shows the same plot as above, but with the latest jitter noise measured by Elenna in 80808 We noticed this afternoon that there is a problem with the way these jitter noises are being added in quadrature by the noise budget, but we haven't fixed that yet. In this data set, we have 15.1dB of anti-squeezing and 5.1dB of squeezing from 1.5-1.8kHz, we can use the Aoki equations to solve for nonlinear gain of 14.6 and total efficiency eta for squeezing of 73%. Since the known readoutlosses are 7.3% and the known squeezer injection losses are 8.8%, this gives us a minimum readout efficency of (eta/(1-known injection loss) = 79% and a maximum of 1-known readout loss = 91.2%. Using the level of noise between 1.5-1.8kHz with no squeezing (and an estimate of the non quantum noise) we can use these max and min readout efficencies to find min and max circulating powers in the arms.
These arm power limits will be impacted by our estimate of the non-quantum noise, the homodyne angle, and the SRC detuning. With 0 SRC detuning, and a homodyne angle of 7 degrees, this resutls in a range of arm powers of 324-375kW. the estimate of non-quantum noise is the most important of these factors, while SRC detunings large engouh to change these estimates significantly seem outside the range that is allowed by other squeezing mesurements.
- If I reduce the technical noise estimate from the noise budget by 10% in the ASD, the arm power range is 330-383kW, raising the non quantum estimate by 10% gives a range of 328-375kW.
- Using a homodyne angle of 10.6 degrees instead of 7 gives an arm power range of 331-383kW.
- using an SRC detuning of 0.48 degrees (which is clearly too large based on the mid frequency squeezing) results in a range of powers of 321-372kW.
I've run the comparison of the model to different squeezing configurations for the low and high range and the nominal parameters (0 SRC, 7 degrees homodyne angle). Frequency independent squeezing and both types of mid squeezing are sensitive to the arm power from 50-100Hz, this comparison shows that the low end of the arm power range seems to have slightly too little arm power and the high range slightly too much. However these frequencies are also sensitive to homodyne angle and SRC detuning.
