Kevin, Sheila

We have various measurements of the parameters that determine the shot noise level in the interferometer without squeezing injected, some of them are incompatible and confusing.  Here I'm attempting to look at our shot noise level without squeezing, to see what constraints we can place on arm power and readout losses based on the various things that we do know.  Main messages from this alog are:

• for the homodyne angle and SRCL detuning we think that we have been running with for the last few months, our calibrated shot noise level combined with our known readout losses suggest that the arm power cannot be below 330kW if we have a DCPD QE of 99% or 337kW if we have a DCPD QE of 96%. 
• If we believe our higest arm power estimate (384kW based on the PRG), we need readout losses of 25% to explain our shot noise level with the homodyne angle and readout losses we think that we have (which would include IFO to OMC mode mismatch and misalignment).  This seems roughly compatible with the squeezing level seen in 67498
• We could potentially improve our shot noise limited sensitivty by a few % if we operate with a higher DCPD photocurrent (3% improvement at 200Hz by running at 30mA).
• An interesting check on the homodyne angle could be made by measuring the sensing function up to high frequencies for different SRCL offsets and DCPD photocurrents.

Information that we already have:

Readout losses: Sqz loss budget is here. The losses that should be included as readout losses are:

• 1 pass of the OFI (99% )
• the reflectivity of OM1 +OM3 (99.93% and 98.5%)
• OMC transmission of 95.7%
• DCPD QE of 96% (there are also documents saying this should be 99%)
• The product of these gives us a minimum readout loss of 10.5% if we believe the 96% QE or 7.7% if we believe the 99% QE.  The actuall readout losses could be higher and probably are due to imperfect mode matching and alignment into the OMC.

Homodyne Angle: 67305 Craig and Kevin found that 4.8mW of the light on the DCPDs is insensitive to DARM out of 23.3mW,  which gives an upper limit on the homodyne angle of 27 degrees. The estimate of 27 degrees of homodyne angle is based on assuming all of the 4.8mW is carrier 00 light, (Craig's calculation in 65000).

SRCL detuning: 67613 It seems that we have been running with a SRCL detuning of around 0.6 degrees.  

Arm power estimates for the current input power of 57-58W incident on PRM range from 270kW to 384kW:

• SRCL dither: 66860 270kW/263kW (X/Y) with 56.8W on PRM, which we could call 266kW average. 
• reflected carrier power: 66432   317kW for 47W on PRM, which would mean 387kW with our current 57.4W of input power if it scaled linearly. 
• CARM pole: 65093 estimated and 300kW from the CARM pole, with 48W incident on PRM, which would give 356kW from the CARM pole if it scales linearly with input power.  
•  PRG: 65095  337kW from PRG, with 48W incident and a PRG of 53.6 this implies an arm gain of 131, for the Feb 19th lock this would imply an arm gain of 384kW .  
• Modeling of hard loops with radiation pressure: 67528 290kW with current input power of 57W on PRM. 

Optical gain and sensing function:

• For now I've edited the noise budget to use a hard coded optical gain when calculating shot noise, scaled by kappa_c and the measured coupled cavity pole.  The calibration group reports optical gain in unit of DARM_ERR_cnts/ meter, Louis pointed me to the latest fits of the Jan 27 calibration sweeps in /ligo/groups/cal/data/H1/measurements/H1_calibration_report_None.pdf where the optical gain is listed as H_c 3.096e6 counts/meter.  Louis explained that this is the same sweep data as reported in 67063 but the fitting is restricted to frequencies above 80Hz instead of 20 Hz resulting in the slightly higher optical gain than reported in that alog.  This combined with my measurement of DARM_ERR counts per mA (DCPD sum channel) gives us an optical gain of 5.79e12 mA/meter, and a DARM pole of 425Hz. 

Comparison of gwinc quantum noise vs noise budget semi-classical quantum noise:

Starting with a script that Kevin wrote to compare the quantum noise as calculated by gwinc against the calcuation from our noise budget I'm attempting to use some of the times from Dhruva's nice sqz data taking times (67498) to use the measured quantum noise without squeezing to get some constraints on the readout losses and arm power. 

The first attached plot is just an example to show what the plot is (and explain the legend).  The noise budget traces are labeled shot and radiation pressure in the legend of these plots, shot noise is calculated from mA on the DCPDs, with the coupled cavity pole as reported by the calibration pipeline (425 Hz at this time, which is from Jan 28th because f_cc reported by the pcal lines isn't reliable until we push the calibration). This is no longer relying on pyDARM, other than using the values for optical gain and cavity pole that it fits. 

Other than those two dashed lines, and the measured DARM trace, the rest of the traces on this plot are produced by Kevin's SuperQK branch of gwinc.  Each of these lines represents a souce of vacuum fluctations that come into the IFO and limit our noise, there are several traces in the legend that aren't shown for this time because there was no squeezing injected.  The two green traces represent two quadratures of vacuum fluctuations entering at the AS port, or more exactly at the point where squeezing would be injected if there were squeezing.  The one labeled SQZ misrotation is the quadrature that causes quantum radiation pressure noise, or what people sometimes call the amplitude quadrature, in this case since the homodyne angle is 0 this is QRPN but for a different homodyne angle or SRCL detuning noise from this quadrature can also contribute to the shot noise.  The trace labeled AS port SQZ is the other quadrature (sometimes called the phase quadrature), which is responsible for shot noise if the homodyne angle is 0.  There are also vacuum fluctuations entering through the readout losses, SEC losses and arm losses, although I haven't tried varying those losses from the gwinc defaults in this alog. 

Infering miniumum arm power based on known readout losses:

In the second and third attached plot I've fixed the readout losses to be our minimum possible, and adjusted the arm circulating power to match the shot noise which gives us lower limits on what the arm power could be. I've done this for our known losses, for a DCPD QE of 96% (10.5% minimum readout losses) and 99% (7.7% minimum readout losses).  Using these minimum readout losses we can find a minimum arm power needed to explain our shot noise level which depends on the homodyne angle and SRCL detuning, the readout losses could likely be higher which would mean we must have a higer arm power.  In each of the subplots the homodyne angle and SRCL detuning is changing, which leads to a different minimum circulating power.  The main point here is that with a homodye angle of 0, these plots are consistent with the lowest arm power estimates, but if we include a homodye angle of 27 degrees and a SRCL detuning of 0.6 degrees then our minimum circulating power to explain the shot noise level must be at least 330kW.  

 In each of these subplots plots the orange radiation pressure trace (from the current noise budget) is based on the same arm power, the arm power is only changing for the gwinc traces.  

Inferring readout losses based on arm power estimate:

The opposite approach would be to assume an arm power level, and from that we can estimate the readout losses that are required to explain our shot noise.  The 4th attachment shows this for our highest arm power estimate, 384kW based on PRG.  With a homdyne angle of 0, this gives us readout losses of 45%, but by including the upper limit on the homodyne angle and the SRCL detuning this gives us readout losses of 25%.  

In comments to 67498 Dhruva says that for 16.9dB generated squeezing (meaning if there were no losses, including an escape efficiency of 1 we would have 16.9dB), he is measuring 4.5dB of high frequency squeezing and 4dB at mid frqeuencies. Without phase noise this would imply the total squeezer losses are 44%, if we include phase noise the losses must be lower.  From the squeezing loss budget we have 7% known injection losses (6% losses in HAM7 plus one pass of the OFI), which means that the squeezing cannot expirience more than 30% readout losses, and likely that the readout losses have to be lower than 30% to allow for some phase noise.  While it might be possible that there is a mode mismatch situation that could allow the squeezer to have lower readout losses than the IFO beam, this story seems much more plausible since the squeezer losses seem compatible with the interferometer losses. 

Suggestion of a different way to check homodyne angle, slight improvement with higher DCPD photocurrent:

The second to last attachment here shows the quantum noise calculated by Kevin's branch of gwinc for a fixed readout loss and arm power, as we change the homodye angle and SRC detuning.  We have recently changed the SRCL detuning by we think about 0.6 degrees, if we compare calibrated shot noise at 1 kHz before and after we should expect to see a 5% improvement if our homodyne angle was is 27 degrees, while we would only expect a 1% change if the homodyne angle was 0. 

The last attachment suggests some tests that we could do.  With 4.8mW of contrast defect light, if we moved the DARM offset so that we have 10mA on the DCPDs, we would have an upper limit of 43.8 degrees on the homodyne angle (if all the contrast defect light is carrier 00), while if we moved to 30mA on the DCPDs we could reduce the homodyne angle to 23 degrees.  Based on 67613, if we move the SRCL offset from -175 counts to +175 counts (which should also be safe for ADC range on POP), we expect that the SRC (aka SEC) detuning can be changed from about 0 degrees to 1.2 degrees (it would be good to check this calibration by fitting the measured optical spring). The gwinc quantum noise calculation for these 6 scenarios are shown in the last  last attachment here.  The black traces represent what we think our current homodyne angle is, without the SRCL detuning we should expect a 3% improvement in shot noise at 200 Hz by moving to a DCPD current of 30mA.  

This plot also suggests a different way to check what our homodyne angle and SRCL detuning are, at 1kHz we'd see a 12% change in the sensing function by introducing a 1.2degree SEC detuning for a homoydne angle of 27 degrees, while we'd expect a 19% change in the sensing function at 1kHz with the same SEC detuning if we run with a homodyne angle of 44 degrees (10mA on the DCPDs).  Perhaps a useful constraint on the homodyne angle can be found by making 4 (or 6) measurements of the sensing function while changing the power on the DCPDs and the SEC detuning, and using an expression from Bunnano and Chen to fit the results (similar to what Craig did in 64928 but using the expected change in homodyne angle).