Right-o. This is the kind of switching that existed in, e.g., the eLIGO OMC whitening box, but grounded-input is definitely better. I modified it to use the switching that's used for the VGA in the common-mode servo board. This avoids both floating inputs and also the potential loading that would come from leaving the inputs connected.

1) I think the relays ought not be a problem, judging by their performance on the OMC Z switch. I was under the impression that the MAX333 was an acceptable switch for low-noise signals (it is used immediately after the unity-gain input of the common-mode board, so it is presumed to have a noise floor much lower than an AD829's). That said, the CMB does show anomalously high low-frequency noise. I can do some testing to measure this, but what is the way around it? Use relays for everything? That would be OK, but it takes up a lot more space.

2) From my interrogation by EKG, I imagined that the balanced ISS PD would be its own specialized thing in a custom box. So, I didn't plan for that to be within the scope of this workhorse. Since we already know almost exactly what we will want from a balanced ISS setup, shouldn't we just make another design that is compact and best suited for that purpose?

3) I'm a bit confused here. Do you mean for the bias or for the offset? In either case, all we're doing is adding some extra active low-passing, right? The AD587 has a floor of ~100 nV/rtHz, so the filter brings this (and any junk from the potentiometer) down to the OPA140's floor of 5 nV/rtHz. As for drift, the AD587 is rated to ~10 ppm/K = 100 uV/K, while the OPA140's drift is well under 1 uV/K.

4) Yes.

Since we are thinking of using the MAX333 quad analog switch in a low-noise environment for the omniPD (see thread at CRYO:1016), we want to make sure it is not noisy.

I measured its noise tonight and found that the shorted-input noise of both NC and NO channels was limited by thermal noise from the ~130-ohm closed-circuit resistance, to the level measurable using a LT1128 preamp:

Here are a photo and sketch of the measurement setup:

In CRYO:1016, I alluded to the idea that it would be cool to have a concentrated binary input/output system with which to control our various electronics (with the omniPD as a first example). I thought about this some more and came up with the following idea, which I'm calling "microBIO".

It is an 8-bit BIO controller that takes as an input a single differential analog signal. An IC ADC (ADC0804) is used to convert this analog signal into 8 parallel digital outputs, which are then buffered (LMV324 --- low-voltage, single-supply, rail-to-rail quads) and used to drive switches, relays, or whatever. In a sense, the device under control is therefore effectively a digital storage medium. In this way, each device can have up to 8 independent binary control parameters all controlled with a single CDS output.

Some features and notes:

• The input to the controller will be one differential signal via BNC, and the output will be fed to the device via DB15. Power and ground for the microBIO will be provided over the same DB15, so it can be connected inline without any external power. Also, there is no ground connection between the CDS rack and the controller, so there is no potential for ground loops.
• The ADC is self-clocked, but it is triggered by a 555 timer rigged for very low duty cycle and a frequency of ~2 Hz. This way, the requested device state is only read twice a second or so, and not at the full rate of the ADC (> tens of kHz). This makes it highly unlikely that an incorrect state is written while the analog control signal is slewing.
• Setting it up this way gives an input range of 0-5V and a step size of 5V/255 ~ 20 mV. This seems OK, but I am doing some testing.
• I have not explicitly drawn it this way, but in cases where fewer than 8 bits are needed (e.g., the omniPD, which only needs 5), the bits should be addressed beginning with the MSB to ensure greatest immunity to digitization noise. In this case, the effective step size increases by a factor of 2^8-N.
• A preliminary current budget suggests that even if all 8 outputs are driving relays and they are all engaged, this should still not overload the 5-V regulator in the device.
• As shown on the omniPD schematic, there should be jumper switches on each microBIO-compatible device that allow the user to either hard-set any parameter or tie it to BIO control. So, this is a completely optional plug-and-play control scheme that may be added or removed at any time.

Here is a simplified diagram and a preliminary schematic:

I built a test circuit to make sure it all worked as expected. In the video below, I've wired up LEDs to indicate the 8 digital outputs (sorry---couldn't find enough bare LEDs so there are 3 red ones and 5 stacked green pairs, with the pairs tied together as one) and I'm driving the analog input with a triangle wave. At the start of the video, I'm not triggering, and you can see the digital outputs changing wildly. At 0:09, I engage the 555 triggering and you can see it starts sampling twice a second or so, with no apparent chattering. I plan to do a more detailed test of this with the real test stand in the ATF.

microBIO test from Zach Korth on Vimeo.

On Friday, I tested the prototype microBIO with the test stand in the ATF. To do this, I built a library part into the ATF model:

This takes EPICS binary inputs corresponding to each of the 8 controller bits and combines them into the appropriate analog signal to be decoded by the uBIO.

Everything seems to work as expected, but there is some sort of problem with the DAC not being able to maintain voltages above around 4 V (with the output gain [V/ct] being compressed before that point, as well). I do not think that there should be a problem with driving the ADC0804 with a differential signal, and that was the plan to avoid ground loops in the final scheme. I isolated the signal with a floating SR560, and, while it made it a little better, the problem didn't go away. More head scratching and testing required.

Here is a video showing where I switch bits 1-5 on and off with the MEDM screen. I didn't mess with 6-8 because the effect mentioned above leads to errors with them. Note that I turn them both on and off sequentially from 1-5, so different analog signal ranges are explored in each case.

microBIO test 2 from Zach Korth on Vimeo.

This is a shitty effect that Nic has found and mentioned before. The output stage of the PDH2 is a fancy-pants thing that was copied from the Rich uPDH design, and then we thought it would be fine to add the DAC_EXC injection without having any problems. We were wrong, in general, because adding a path to ground from this point through a resistance comparable to or smaller than the others in the stage's network changes the gain in the non-inverting configuration. This can be fixed by making R26 >> R24,R25 at the expense of lower excitation range.

There also appears to be a parasitic high-frequency path when the port is left open, which leads to a bump in the TF at 10 MHz, regardless of the INV setting. Therefore, it also creates a notch when out of phase with the main path. We don't know exactly how this happens, but clearly it's affected by what is connected to the DAC EXC input, so we terminate it.

Note that the former effect is what caused the oscillation when you plugged in the 50 ohm terminator (by changing the gain), while the latter is what caused it when you plugged in an open cable (by opening the parasitic path or by affecting the notch via the capacitance).

So, I would replace R26 with something bigger than 2.2k and terminate DAC_EXC when not in use.

To decide whether or not we can go with 1" windows (easier and cheaper than 2"), here is a conservative calculation of the expected cavity axis shift as a function of the (symmetric) g-factor we choose.

The mirror deflection angle is chosen to be a (rather high) 10 mrad, and the displacement is calculated at 20 cm from the cavity center, which is probably farther than the windows will be.

The calculation is made with one line from the formula in Siegman p. 769.

As you can see, the displacement for even this large angle should be on the 1-2 mm level for us, so we can use 1" windows.

I spent some time learning SolidWorks tonight by generating the following ideas for how to hold the wafers, etc., within the cryostat.

There are e-drawings attached to this log, but here are two screenshots from them:

The first one is our usual idea of pinning two wafers using steel rods. The second one has a single wafer pinned this way, but uses standard mirrors as the input couplers for the cavities, as this is an alternative we are considering. The large mounts take up a lot of real estate, so we would likely use smaller-than-standard ones to avoid making the cavities too short (they are 3" and ~2" here, respectively). Obviously, this is all upside down...

The clamp bases are just a first-pass idea I had for them. Our idea is that a long 1/4-20 cap screw would go through and compress the whole system.

(I realized that we should probably use the CRYO elog rather than the SUS one, so I've reposted this here).

[Nic, Zach]

Today, we unpacked the IR Labs cryostat that will be the centerpiece of the Cryo SUS experiment. 

Everything was more or less in order, except that the baseplate does not have any outward extensions with which to mount the cryostat to the table. Also, the holes for the screws holding the baseplate to the barrel are not countersunk. So, as of right now, the entire cryostat sits on these screws' caps, which is not ideal. We need to either a.) get a new baseplate made up with some wings on it and countersinking for the screws, or b.) work out another way to hold and mount the cryostat (for example, we might want some soft isolating material there anyway, though it will come at the expense of alignment drift).

I followed the instructions and removed the strange anodized heat shield bottom plate that comes with it during shipping, replacing it with the usual one and then resealing the chamber. As directed, I also pumped out the air again---the charcoal getter is not supposed to be exposed to atmosphere for long periods of time.

On Monday, after I did some inventory of all the parts we have received from various companies, Dmass helped me mount the RIO lasers into their mounts so that I could get started with the optical setup. We cleaned the surfaces with methanol, applied a small layer of silver thermal compound, and then screwed them in.

I then borrowed the following to run the lasers:

• The (separate) ThorLabs diode driver and temperature controller from Haixing's maglev setup
• An integrated ThorLabs diode driver / temperature controller from the TCS lab

After finding the right cables, I powered up the lasers and verified the P-I curve for each as listed on the spec sheets.

I then built a quick (temporary) optical beat setup, combining the two beams on an 1811. I had the temperatures (actually, thermistor resistances) set to what was listed as the testing set point on the datasheet, and as soon as I overlapped the beams and focused them onto the PD, there was already a strong ~50 MHz optical beat.

I have spent some time since then trying to lock various kinds of PLLs, both to interrogate the free-running frequency noise and to get used to controlling the lasers. Some things I've tried:

• Locking a Marconi to the free-running beat, which I think might be an exercise in futility due to the relatively small range of the Marconi FM
• Locking one laser to the other directly using a PLL, which I think might be an exercise in futility due to the bandwidth of the current actuation from the ThorLabs driver
• With Dmass's help, locking a Zurich PLL to the free-running beat. This appeared to work, and we saw a preliminary frequency noise spectrum that looked about right, but I'm skeptical because the control signal doesn't seem to respond to my slewing one laser's frequency.
• Briefly, locking one laser to the other at low frequencies using the Zurich PLL control signal as a frequency discriminator. This didn't work, adding to my suspicion.

The first two were not helped by the fairly basic loop shaping afforded by attenuators and an SR560.

I think my next step will be to simply use the I-Q demodulation method (like I did to measure the no-FM Marconi noise in ATF:1877) to measure the frequency noise. I'll compare that to what I get with the Zurich PLL.

 Yes, I noticed this effect. I'm talking about immediately after acquiring---or re-aquiring---PLL lock. I did this several times at different beat frequencies to see what effect it had on the noise (the spectrum changed considerably, which is another bad sign).

I spent some time tonight measuring the free-running laser beat noise in various ways. Recall that, as of yesterday, I had tried setting up a couple analog PLLs to no avail and I didn't trust the spectrum I was getting from the Zurich PLL. So, I wanted to measure it another way to see if I could corroborate.

First, eye candy:

Now, an explanation of the various measurements.

I-Q demodulation method

This is a method I have used with some success in measuring the Marconi noise in its quietest state (with no modulation and therefore no means of feedback---see ATF:1877). It is done in the following way:

1. Split the beat PD output and send it to the RF input of two mixers (I used level-7 ZAD-1-1s), using equal path lengths.
2. Set Marconi to a frequency close to the beat (~50 MHz in this case) and an amplitude of +10 dBm
3. Split the Marconi output, send one splitter output to each mixer from (1), but with 90º rotation between them.
4. The outputs of the mixers are now at the difference frequency between the beat and the Marconi, but maintain their I-Q separation. (This is the reason for using the Marconi rather than beating the lasers at a lower frequency in the first place---the I-Q separation is maintained regardless of the differential laser drift, and it also only requires a short cable length.)
5. Acquire both I and Q signals and perform the I-Q analysis:
   1. Normalize the signals and atan2(I,Q) to get phi, then unwrap(phi) to get continuous phase evolution vs time
   2. diff(detrend(phi))/diff(t)/2/pi to get instantaneous frequency as a function of time
   3. pwelch

The main complication here is that, as you can see in the plot, the high-frequency RMS of the beat is several tens of kHz, which means you still have to sample at a high rate to get what you need. The best acquisition scheme I could think of was the Zurich box, which can do 460 kS/s. Still, to take meaningful data, I had to very carefully tune the laser beat to the Marconi LO and then quickly engage acquisition before the (wildly fluctuating) IF signals drifted above the Nyquist frequency (around one second of data was used to make this trace).

That said, the result doesn't look that crazy, and in fact it agrees very well with the DFD measurement that was carried out in a completely different way (see below).

Delay-line frequency discriminator (DFD) method

This is the usual scheme where one mixes a signal with a time-delayed version of itself to create dispersion. What I did:

1. Split the PD signal
2. Using one splitter output, find the appropriate combination of attenuators and amplifiers needed to obtain a LO-worthy +7-dBm signal (I needed -7 dB and then ~+25 from a ZFL-500-LN) and send it to a mixer LO input via a long (several-meter) cable.
3. Send the other output to the mixer RF input via a short cable (attenuate if necessary---wasn't in my case).
4. Verify that the DC level of the IF output varies sinusoidally with the beat frequency
5. Null the output and measure the frequency resolution. I measured 5.5 nV/Hz.
6. Amplify with SR560 and measure spectrum on spectrum analyzer
7. Divide spectrum by SR560 gain and the number in (5) to get frequency noise

This method worked swimmingly and reproduced exactly the result I found using the I-Q scheme. The noise floor (cyan in the plot) was measured by sending a quiet Marconi sine wave of the same amplitude and frequency as the beat through the pipeline.

Zurich PLL method

This method is incredibly straightforward. Simply plug the beat (ensuring it's < 1 V_rms and under 50 MHz) into the Zurich box and lock the internal PLL by pressing "ON" on the screen. Route the PLL control signal to one of the front panel outputs and choose the scale factor in V/Hz. I chose the same number as I measured for the DFD (including the SR560 gain) for ease of comparison on the spectrum analyzer.

Results

• All methods agree below ~50 Hz 
• The I-Q and DFD methods agree everywhere, but they are higher than the PLL result by ~2 from 50 Hz to around 10 kHz, above which they re-converge somewhat
• All traces (save for the PLL in a narrow band from ~50-500 Hz) are higher than those on the spec sheets sent with the laser (shown in black on the plot---note that the West laser is everywhere noisier than the East one).

I'm not sure what to believe. One would think the Zurich PLL is the most trustworthy, but a) I still am bothered by the time-domain behavior I see in the PLL control signal when I adjust the laser beat while watching it, and b) I've generated two nearly identical spectra that differ from it using completely different schemes from measurement to FFT.

All that said, I think the excess noise (and thanks to Dmass for saving me time by pointing this out) is just coming from the ThorLabs drivers, so this should be redone when we have our low-noise ones.

Tonight, I did some characterization of the Photline fiber-coupled amplitude modulators we will use for our experiment (MXAN-LN-10 --- datasheet attached nope google it yourself). These are electro-optic devices that work by using an internal mach-zehnder to convert phase modulation into amplitude modulation.

The test setup for all measurements was the same. I used the exact configuration that I have been using for the beat (see CRYO:1182), but I simply blocked one laser, so that only one beam was hitting the 1811 PD. The amplitude modulators were inserted (one at a time) between the East laser and its output coupler.

Insertion loss

The first thing I did was to investigate the insertion loss of the modulators. We chose the low-loss option, which just meant that the company hand-selected modulators with loss of < 3dB (= 50% power transmission).

I didn't go crazy with precision here, because systematics with fiber coupling can easily prevent a measurement to better than a few percent (an example of this: I installed a 1-meter patch fiber between the laser and the output coupler, instead of the modulator, and I actually saw a slight increase in output power vs. the case with the laser going straight to the output coupler… go figure).

In both cases, I measured very nearly 50% reduction in power (at the top of the MZ fringe---see below) vs. the case with no modulator. So, these things have a loss very close to 3 dB, as advertised. An important thing to point out is that we will need to bias these away from maximum transmission to get a linear PM -> AM coupling, so the real power reduction in our setup will be more than 50%.

DC response

These modulators have an SMA-connectorized "RF" input, as well as two bare pins connected to a separate set of "DC" electrodes (they also have two more pins connected to the cathode and anode of an internal PD, presumably at the other MZ output port, which is kind of cool). As far as I can tell, the RF input is also DC coupled, only it is 50-ohm terminated.

I did a DC sweep of both electrodes from 0-10 V while measuring the output power:

(The RF applied voltage range is lower due to sagging from the 50-ohm load).

Fitting these curves, I determined the following V_pis:

• S/N 03
  • DC: 6.46 V
  • RF: 4.19 V
• S/N 17
  • DC: 6.39 V
  • RF: 4.91 V

These are consistent with the numbers listed on the datasheet.

Transfer functions

Next I measured the actuation transfer functions ([RIN/V]) from 1 Hz to 100 MHz, driving the RF input while applying a mid-fringe bias to the DC input, and using

• Agilent 35670A FFT analyzer and the 1811 DC output for 1 Hz - 50 kHz, and
• Agilent 4395A RF analyzer and the 1811 AC output for 500 kHz - 100 MHz

Note the dead zone from 50-500 kHz---this was by accident, as I forgot to check the low-frequency resolution of the RF measurement. I will redo this sometime.

Here are the results:

Notes:

• The jump from 50 kHz - 500 kHz is from the measurement dead zone and carries no information
• The lag beginning around 10 kHz is from the stated ~50 kHz bandwidth of the DC output of the 1811. The AC output has a low end at ~25 kHz, so there isn't really a good way to make a measurement in this region with that detector. We could use a DC-coupled version to make a continuous spectrum.
• The slow rollup at low frequencies is well-sampled and repeatable. I'm not sure what causes it, but it appears to be real. In any case, it's pretty small.
• The delay at high frequencies is consistent with the optical path length from the modulator to the PD. I calibrated the cables' transfer function out, and what is left is this delay which has a 4.13-m free-space equivalent. There is ~64 cm of free-space travel on the table, plus well over a meter from the output fiber of the modulator.

The response very flat, and roughly what is expected from the DC sweep:

(1/P₀) * dP/dV|_mid-fringe = pi/Vpi ~ 0.5 ( = -6 dB).

To continue with the laser/modulator testing, I have added Dmass's old PMC to the temporary characterization setup. I have used the other output of the 50/50 BS that combines the two laser diode outputs, so that we can keep the beat setup intact while also being able to send either of the two beams into the PMC.

To do this, I:

• Made a cursory razor beam scan of the beam emerging from the BS
• Calculated a MMT solution to the PMC mode using some of our new lenses
• Installed the telescope and directed the beam towards the PMC
• Macropositioned the PMC by hand to rougly center it on the transmission of the single-pass beam, as measured using a power meter
• Scanned the PZT using a 0-10 V triangle from an SRS function generator, then used the diode temperature as a coarse adjustment to look for modes
• Maximized the first found mode (a horizontal HOM)
• Looked for nearby lower-order modes, then maximized them and iterated to get to TEM₀₀
• Installed HWP upstream and then maximized visibility by rotating polarization

The coupling isn't stellar yet, at roughly ~66%, but the MMT is fairly tight and I'm sure I can improve easily. The laser and cavity are stable to well within a linewidth at high frequencies, and only drift apart over many seconds.

Some things I plan to do with this setup:

1. Dither lock the PMC to the laser(s)
2. Characterize the phase modulators
3. Set up reflection PDH lock and feed back to lasers
4. More stuff

[Nic, Zach]

Yesterday, we opened up the small cryostat and installed the sapphire washers (SwissJewel SP-175). This is hypothesized to increase the resonator Q by reducing the strain energy leaking into the lower-Q steel clamp.

We found that the inner diameter of the washers is slightly too small to accomodate the inner lip of the lower part of the clamp. We were able to make do just by having the lower sapphire washer sitting on this lip---rather than on the full wider area of the lower clamp section---but it is not ideal.

Nevertheless, we clamped it, resealed and pumped the chamber down. As it pumped, I rebuilt the HeNe optical lever readout. When I finished, I was quickly able to tap the cryostat and see a mode ringing at almost exactly 250 Hz, which is known to be the frequency of this cantilever at room temperature. At a respectable pressure of several x 10^-5 Torr, I made a quick-and-dirty ringdown measurement using a scope and a stopwatch. I estimated  at roughly 2.5 seconds, giving Q ~ 2000. This was already a few times higher than Marie was able to measure at room temperature (see below).

I went down today and did an actual measurment, using the Zurich box sampling at 7 kHz as DAQ. Fitting the envelope by eye, I found a time constant closer to  = 5.55 s, giving Q ~ 4300 (I don't think my stopwatch method was all that wrong yesterday, but I do think the residual gas might have been contributing at the time---the pressure is now at 10^-7 Torr). This is not only much better than the previous result, but also within a factor of less than 3 of the expected result for Si, according to Marie's data. Given how cavalier we were with the clamping, I'm fairly confident that the sapphire washer idea (and therefore also the monolithic thicker-clamp idea) works as intended.

I ordered a new LN2 dewar and it has just arrived. Appropriately, for me, it is #305.

Dmass helped me solve the Great Funnel Problem of 2015 by fashioning a foil extender to put in the tip of his metal funnel, since my glass funnel has a spout that is too narrow to get enough nitrogren through it. We spent some time yesterday afternoon filling the reservoir, after which I waited and then came back to see if it was still holding liquid. It was, so I added some more and left it overnight, and there still seemed to be some liquid by late this afternoon.

Assuming the cold volume had had enough time to reach low temperature, I made a quick ringdown measurement, only to find that the Q had only increased from ~4000 to ~8000 between room temperature and now. I think this means that the clamp integrity afforded by the sapphire washer sitting on just the lip of the steel clamp is not good.

I'm going to wait for things to warm up and then vent the chamber so that we can:

1. Improve the clamp
2. Fix our wiring issues

I monitored the reservoir level periodically over the day and night. As of the evening, there appeared to be ~1 cm of LN2 still there. As of around 4am, it appears empty, so it should be OK to open tomorrow. I've sealed the vacuum and shut off the pump in preparation.

I was having some issues with the beam(s) I had previously mode matched into the PMC. Apart from not having gotten great coupling to begin with, the alignment seemed to have drifted over a few days (I noticed this last week). I attributed this to 2 things: 1) the MMT I had was a pretty sensitive one, owing partly to the fact that I had to work with the beam far outside the Rayleigh zone due to the beam beat recombination being upstream, and 2) having the recombining BS in the way, I was susceptible to clipping in the output path I was using for the PMC. I don't really need the beat setup at the moment, and I can do the modulator characterization using a single laser, so I decided to rebuild the PMC test setup using a single laser.

As a first step, I simply remeasured the output beam profile of the West laser using the razor blade technique. The beam seems very circular and not astigmatic, so I only profiled in the horizontal direction. The result:

Using this, I recalculated a better MMT:

------------------------------------------------------------
Other solution:

mismatch: 0.00011786
w0x = 303.7849 um 
w0y = 303.7849 um 

lens 1: f = 103.2118 mm
lens 2: f = 206.4236 mm
Distances:
d1 = 6.161 cm
d2 = 14.3007 cm
d3 = 29.5383 cm
(Total distance = 50 cm)

I then installed this, aligned the PMC and was able to get ~96% coupling with little trouble. By locally optimizing the second lens, I pushed this to about 97.5%. While a bullseye was faintly evident on the card in the first case, it was very hard to tell what was reflected after the reoptimization.

I borrowed the RF electronics from the steel gyro PMC temporarily (splitter, mixer, bias tee and filters). For some reason, the 1-MHz dither I used with that PMC did not work with this one, but I was able to derive a nice error signal using a 300-kHz dither at 3 V_pp. I wanted to use the uPDH box I used to use before I had the digital servo for the gyro PMC, but I forgot that Eric Q had borrowed it for the 40m. Instead, I was actually able to lock robustly and stably with just an SR560 and a single pole at 10 Hz. The control signal stays within its output range over ~10 min+ time scales. (I didn't bother measuring the loop---all I needed for my phase modulator characterization is essentially a DC lock, and the bandwith was easily 10s-100s of Hz).

The transmission dither lock leaves the REFL port open so that I can measure the rejected sideband light pumped by the modulator as planned.

After rebuilding the PMC setup (see CRYO:1195), I was finally able to move on to characterizing the Photline fiber-coupled phase modulators we will be using (MPX-LN-0.1 --- datasheet attached nope google it yourself). I measured a couple things:

Insertion loss

As with the amplitude modulators (see CRYO:1187), I determined this simply by measusing the power straight out of the laser, then quickly connecting each phase modulator (one at a time) between the laser and the output coupler and measuring again. As I mentioned in the linked post, this is not an exact science due to the somewhat unpredictable behavior from connector to connector. Nevertheless, one can be confident at the one-to-few-percent level.

S/N 10:

2.66 mW out / 5.00 mW in --> loss ~ 2.74 dB

S/N 2:

2.88 mW out / 5.38 mW in --> loss ~ 2.71 dB

Supposedly, we had these two units hand selected for loss < 2.5 dB (for free, after we paid for the $500 low-loss selection of the amplitude modulators), while the standard typical loss from the datasheet is closer to what we have at 2.7 dB. An extra 0.2 dB isn't going to break the bank, but it's a bit disappointing that they didn't give us what they said. Probably too late to say anything anyway...

Response

My plan was to use the modulators to pump light into RF sidebands, then use the frequency selectivity of the PMC to measure the SB power and back out the actuation strength (Vpi). I was able to do this, to a degree, but I was thwarted by an unexpected issue: the modulators and the fibers coupling to/from them appear to change the output mode emerging from the collimator. What's worse, the mode seems highly sensitive to any touching of the fiber whatsoever. This was most egregious with S/N 10, with which my new cavity coupling maxed out at 83%(!), even after slight empirical MMT tweaking. S/N 2 wasn't as nasty; I got ~91.5% with it.

Given this, my new plan was to make a quick-and-dirty measurement in the following way:

1. Optimize the mode matching and record the contrast defect (17% and 8.5%, for S/N 10 and S/N 2, respectively, as mentioned above)
2. Drive the modulator at a chosen RF frequency (I chose 30 MHz since this is near where we'll be using them), and determine the amplitude necessary to double the reflected power.
3. The measured amplitude is associated with the modulation depth necessary to pump the same fractional power as the contrast defect out of the carrier (really, you could use any SB power level additively distinguishable from the contrast defect, but doubling it seemed the easiest thing)
4. Use the bessel function to infer that modulation depth, then scale the measured amplitude up to infer Vpi.

S/N 10:

Measured amplitude to double REFL power: 0.78 Vpp --> 0.39 Vpk.

2*J1^2 = 17% --> gamma = 0.611

Vpi = 0.39 * (pi / 0.611) ~ 2.00 V

S/N 2:

Measured amplitude to double REFL power: 0.52 Vpp --> 0.26 Vpk.

2*J1^2 = 8.5% --> gamma = 0.422

Vpi = 0.26 * (pi / 0.422) ~ 1.93 V

The datasheet claims 3.5 V typical, so this seems pretty good (though the spec is only officially at 50 kHz drive). Holding the amplitudes constant, I also swept the frequency down from 30 MHz to 10 MHz, and the reflected power was stable to around 5%.

Again, this is only really a quick-and-dirty measurement. Unfortunately, the only real way to get a good measurement is to reprofile the beam again with each modulator in place. Then, the contrast defect can presumably be brought down closer to 2% or better again, and the measurement can be made more cleanly. I'm hesitant to waste time doing so, though, given the observed mode dependence on the fiber resting position.

I vented the chamber today to redo the clamping and investigate our wiring issues.

Clamp

Since I observed relatively low Q even at cryogenic temperatures, I assumed there was some jankiness with how we clamped the cantilever when we installed the sapphire washers. Recall that the lower part of the steel clamp has a circular lip near the center around the screw hole, and it was too wide to allow the sapphire washers to fit around it. This meant that the lower washer was only being held by this lip, and not by the full surface area of the clamp. Also, when we installed the washers, we didn't remove the smallest can around the physics package, so we were doing a bit of guesswork as to how well aligned the entire clamp stack was. This meant that there could have been some slight rubbing, for example. Here is a photo of what it looked like in profile when I did remove the can today:

You can see what I mean about the lip, and it's also clear that the stack was not very well aligned. To fix the lip problem, I found a steel washer that was just about the right thickness and drilled the center hole out wide enough that it fit around the lip. This way, the lower sapphire washer will be supported by a larger surface from below (of course, the real solution will be to either design a new clamp or get wide-enough-ID sapphire washers). The picture on the left below shows the washer around the lip.

There was also some dust and other gunk visible to the eye, so I thoroughly cleaned all parts in the stack with methanol and isopropanol. I then carefully restacked the components and reclamped (a little tighter than we did last time, as well). The final stack is shown below at right.

Wiring

I checked each connection from the feedthrough to the heater or RTD, and found that everything seemed to be in order, so there must have just been a short when we closed up last time. I wrapped some extra kapton around each connector solder joint to provide insulation and extra strain relief, and everything stayed as it should be when I resealed the chamber. I *did* accidentally break a joint on the wire for the ESD while closing up---whoops---but I decided it was more hassle to fix it than necessary for this next run. I'll resolder it when we cycle again.

The chamber is under vacuum now and I filled the reservoir with nitrogen. The clamp was at 200 K when I left around 10pm, so I'm hoping things will be calm and cool when I come in tomorrow.

The cantilever was fully cooled by the time I got in this afternoon. I measured some quick ringdowns by looking at the amplitude on the scope, and estimated a Q of 2-2.5 x 10⁴. This is slightly better than what I measured the other day before improving the clamping (see CRYO:1193), but not good---still a few orders of magnitude below what we expect. I heated the system up near 120 K and found a slight reduction in Q.

Unlike before, I noticed a strange sort of sloshing of energy into a higher-frequency mode (~1350 Hz). It was hard to tell, but I got the sense that energy was being dissipated out of the fundamental mode through this higher-order one. I looked at a time-lapse spectrum of the ringdown, and it seemed to confirm this effect. If you look at the movie below (which is just about real time), you can see that the RMS of the two modes between 1-2 kHz pump up and down, while the fundamental mode around 215 Hz monotonically decreases. If you squint, it appears that the full RMS stays constant in most cases while the high-frequency modes ring up, while they all decrease together. This, coupled with the fact that everything rings down to zero if left alone, indicates to me that energy is leaking from the fundamental mode out through these others. As an order-of-magnitude estimate, the amount of energy pumped through these modes as the amplitudes increase and decrease is not inconsistent with the energy lost from the fundamental based on the observed Q.

I did some COMSOLing to try and figure out what is going on, and at first I couldn't explain it; it appeared that even the higher-frequency modes should have too little strain energy density leakage into the steel to explain the effect, especially with the sapphire spacers. In looking a little more carefully, though, I realized that we have not been careful enough in modeling our system: at the bottom of the clamp stack, there is a PEEK platform between the clamp post and the cold plate. This is there by design, to thermally insulate the clamp from the bath (for heating), but it also considerably softens the contact there.

This PEEK piece shouldn't have much of an effect on the fundamental mode, as the energy ratio for that mode is of order 10^-4. The second mode at 1350 Hz is nearly as well isolated. However, for the third mode around 1800 Hz, something like 70%(!!) of the energy is expected to reside in the PEEK layer. Since PEEK has very high loss, this is not good. Here are some COMSOL screenshots, with the first 3 showing the first 3 mode shapes, and the fourth showing the (log) strain energy density for the 3rd mode. Note that this model is run at room temperature, so the eigenfrequencies are somewhat higher than in my spectra.

So, my hypothesis is that somehow energy is leaking from the (otherwise well-isolated) fundamental mode into these higher-order ones, where it is immediately lost to friction in the PEEK. One possible step is to get rid of the PEEK piece, but that doesn't address the question of why the cross-coupling exists in the first place. My intuition fails me, so I'm not sure what the right thing to do is.

It is a little tedious waiting for a full cryo cycle to iterate on the clamp. Also, in many cases we can learn a lot from just running at room temperature, but opening and closing the cryostat to get at the experiment takes a fair bit of effort. So, tonight I repurposed one of the gyro corner chambers to serve as a rapid-iteration room-temperature testbed. I used the northeast chamber since it had the pump connection. It has 2 KF flanges (on which I have put blanks) and 2 CF (one which goes to the gauges and valve, and the other which used to have a blank that I have replaced with a window).

I set it up next to the cryostat so that we only have to move 2 mirrors to switch between setups.

Given my revelation about the energy leakage and PEEK loss last night (see CRYO:1198), I resurrected the old rectangular block clamp to try a new idea. Namely, I just tried sandwiching the silicon cantilever (the central region with the hole, that is) between two sapphire washers, and then clamping the whole sandwich using the block clamp. The block clamp also has a PEEK base, but it should have provided a much stiffer clamp than the newer, cylindrical one, and that should result in less energy getting to the base. Here is what it looked like:

I pumped the chamber down and took a quick ringdown measurement. Unfortunately, the result was a Q in the ~2000 region, similar to what it was when we first installed the sapphire washers in the newer clamp and the bottom one was sitting on the clamp's lip (see CRYO:1191). Never fear---I have a new suspect: in looking at my photos, I'm noticing that the sapphire washers are not particularly flat. This could mean that the clamp contact is some strange shape and/or that the silicon is being stressed in some strange way.

Instead of the washers, I think I'm going to try sandwiching the cantilever between some other spare pieces of silicon that we have. If I use enough pieces to make a decently thick clamping region, this should serve the same purpose that we hoped the sapphire washers would. I'll try this tomorrow.

I sealed the cryostat vacuum line so I could use the pump for the new chamber. The LN2 reservoir was empty before I did so, and the clamp was registering around 250 K when I left. In any case, I'm going to keep iterating with the new chamber, and I think we shouldn't bother with the cryostat again until we can demonstrate a Q of close 10⁴ at room temperature.

As I planned yesterday (CRYO:1199), I tried out a new clamp using spare pieces of broken silicon instead of sapphire washers to sandwich the cantilever (as with the last run, I used the old, stiff rectangular block clamp---the newer cylindrical one is still in the cryostat).

I didn't take a photo, but this was basically just a sandwich consisting of the cantilever (still attached to the central wafer region) as the meat and two scrap broken-off cantilevers on each side as the bread. This was all put near the center of the steel block clamp so that the clamping force was normal, and I made sure that the protruding cantilever had enough room not to be clipped by the block as it swings.

I put it in the new chamber and pumped down, and immediately measured a fairly high Q of ~6800 (ringdown tau ~ 6.4 s, while the mode frequency is ~340 Hz---slightly higher than before due to the clamping being a bit further along the cantilever).

This is the highest room-temperature Q I've yet measured, beating the ~4300 I measured after we first installed the sapphire washers on the newer cylindrical clamp (see CRYO:1191), and is within a factor of 2 of Marie's prediction in the absence of clamping loss (also shown in that post). This is also by far the cleanest ringdown I've seen: there are a few high-frequency modes present when I first deliver the impulse, but they die away and do not return. The Q also seems far less amplitude-dependent than I've noticed before.

A lot of things happened tonight (mostly in the realm of setbacks followed by recovering frome them), but the take-home is that the measured Q of my silicon sandwich clamp seems consistently lower when measured in the cryostat, compared to in the new chamber from the gyro. Here's a rundown of what happened today/tonight:

• Before dinner, I made a first measurement on the silicon sandwich idea (cantilever sandwiched between a couple spare pieces of silicon on each side --- see CRYO:1200). This gave me the highest room-temperature Q I've measured yet at ~6800.
• After dinner, I wanted to port this to the cryostat and potentially do a cooling run. Unfortunately, to fit it in the cryo volume, I had to flip the sandwich around so that it was protruding from the clamp in the other direction (for the first run, I had it sticking out over the power resistor to avoid clamping in the region on the other side that has the groove for the Glasgow-style cantilevers, but there wasn't enough room for that orientation in the cryostat, so I had to flip back---I made it work so I didn't clamp over the groove anyhow).
• Unwittingly, I made the dumb mistake of not first testing this freshly-clamped system again in the simple chamber, and after I closed the whole cryostat again and pumped down, I measured a much lower Q (back down around 3000).
• So, I opened the cryostat again, and then spaced out and made the further mistake of still not testing this apparently bad clamp job in the simple chamber, just to verify that I got the same low Q. Instead, I went straight to cleaning all the pieces and re-clamping.
• This time, I put it into the simple chamber and immediately recorded a high Q around 7000 again.
• This is when some setbacks kicked in:
  • In opening the chamber, one of the RTD wires came loose from the feedthrough.
  • Not realizing that these were just press-fit sockets, I unscrewed the feedthrough to have access so I could reattach the single loose wire, only to have several others fall off.
  • So, I disconnected all the wires, spent some time mapping which one went where, re-soldered some and re-kapton shieled all, then reattached all wires, bunch taped them and taped the bunch to the feedthrough so that none could easily come loose. I also took this time to resolder the ESD wire that I broke the other day.
  • In moving stuff around, I accidentally tugged on the ribbon cable between the QPD and its vectorboard readout circuit, pulling a couple connections.
  • So I spent some time fixing that
• Now I was ready to do science again, so I transferred the (known good) clamp from the simple chamber back into the cryostat and carefully closed it all up again.
• After seal and pumpdown, I again measured a low Q around 3000.

So, it seems that the Q is repeatably lower for a particular clamp in the cryostat vs. in the simple chamber. To be sure, I'm going to do the final step of returning the clamp back to the simple chamber tomorrow and see if I again get a higher Q.

I'm not exactly sure why this could be happening. The only mechanical differences from one chamber to the other are:

1. The clamping block is screwed via holes in the PEEK base to the cold plate in the cryostat, while it is dogclamped to the breadboard in the simple chamber.
2. In the cryostat, there are wires soldered to the power resistor attached to the clamping block as well as a wire-attached Pt RTD kapton-taped to it. None of this is present in the simple chamber.

I'm tempted to think that (2) could be causing some excess damping, so one thing I will try is simply not connecting these just to see if that makes the probem go away.

Following my preliminary conclusion from yesterday (CRYO:1201), I set out to confirm or deny this seeming decrease in Q for a given clamp when going from the simple vacuum chamber to the cryostat.

One potential source of extra damping I considered was the wires attached to the block for the power resistor and RTD, so, while I still had the clamp in the cryostat assembly, I just disconnected these wires and pumped down the cryostat to see if I saw an improvement. I did see an increase in Q from ~3000 to ~5500, but not to the full 7000 I saw before in the standalone chamber. So, I conclude that there is some appreciable damping added by this kapton wiring. We need to use less rigid wire for the last stretch between the coldplate-mounted strain releif and the block.

The last step was to transport the clamp back into the simple chamber and see if I could recover the Q of 7000 that I measured initially. I did, completing the circle of repeatablility. I'm not sure what else could be causing the excess damping in the cryostat.

It is a shame, because I would be very interested to see what this particular silicon sandwich clamp looks like at 120 K, but I seem to have now way of doing so without the extra losses empirically associated with putting it in the cryostat.

Nic elucidated to me today Chris W.'s idea for getting truly wideband (~500 MHz) actuation out of our diode lasers. In case the reader isn't familiar, the lasers have two parallel linear actuation pathways converting current into frequency: one from current modulating the temperature, which is the strongest effect at DC and then dies off above ~1 MHz due most likely to the thermal response, and another, weaker but much wider-band, flat pathway arising from solid state effects that did not survive the elucidating. At some frequency (around 50 MHz, I believe?), there is a crossover between these paths, but there is a differing sign, which creates a "non-minimal-phase zero", leaving the phase at -180° and making the overall system a difficult actuator to deal with at high frequencies.

As I understand it, Chris's idea involves using the full, nonlinear current-to-temperature response to effectively circumvent the direct linear response at low frequencies. This can be done, for example, by pumping a strong RF carrier current (say, around 1 GHz) into the diode, and then using amplitude modulation on this carrier to produce baseband frequency actuation from the temperature beating. By choosing the phase of the AM correctly, one can make it so this pathway (now dominant at low frequencies) results in a nicer crossover with linear pathway #2 from above.

I performed a very simple proof-of-principle test today by doing the following:

• Dither lock my temporary diagnostic PMC to one laser using the setup described in CRYO:1195.
• Set the UGF fairly low (a few 100 Hz)
• Drive the laser current with a 1-kHz sine wave, strong enough to be clearly present above the noise in the error signal. I found that 200 uV_pp (= 2 uA_pp) gave me a nice SNR around 20.
• Using a Marconi into the SMA bias tee adapter directly on the diode, inject a fairly strong RF carrier current. I used 600 MHz at ~200 uA_rms, though the amplitude was determined empirically over the course of the test to see an effect.
• Engage amplitude modulation at 1 kHz and a pretty strong modulation (I chose "50%").
• (As I mentioned a couple bullets above, in reality, I removed the direct 1-kHz injection and pumped this RF-with-AM current up until I saw an effect in the error signal)
• With these two signals on, and adjusting the AM phase, I was clearly able to see modulation of the line in the error signal, indicating that the two drives were interfering as desired.

Trimming the RF amplitude and phase a bit to get a nice result, I was able to take the two spectra shown below. In the first trace, only the direct current line is present at 1 kHz. In the second one, the RF source is engaged and you can see an exact cancellation of the line in the error signal. Increasing or decreasing the RF (or audio) amplitudes led to the reemergence of the line (assuredly with 180º relative phase from one case to the other). To do the wideband actuation, one would simply make sure that the RF power is strong enough that the nonlinear path dominates.

So, it should work! We'll have to change the measurement setup to make a full transfer function showing clean actuation to very high frequencies, but it should be pretty straightforward.

Using the REFL PDH setup I built the other day (and that was detailed somewhat by Nic and Chris W. in CRYO:1204), I calibrated the error response so that I could make some further measurements. To refresh, this is using 30-MHz sidebands applied using one of our fiber phase modulators, sensing with a 1611 in reflection. The sideband drive was 0 dBm.

Using the sidebands as a reference, I calculated the slope at 6.4 nV/Hz:

Note that the error signal is slightly asymmetric, but there is no large offset.

With this information, I made some measurements:

Actuation transfer functions

I wanted to measure the actuation transfer functions afforded by:

1. The standalone ThorLabs laser diode driver (LDC201C) that is currently used to drive the west laser
2. The diode driver in the integrated ThorLabs laser controller (ITC502) that is currently used to drive the east laser
3. Simply driving into the bias tee on the diode

All measurements were done with the west laser head, driving as described and reading out at the error point, then correcting for the loop gain and calibrating to Hz.

Everything is more or less as expected:

• The LDC201C only claims 3 kHz bandwidth, which is actually a bit of a stretch as usual
• The ITC502 claims 500 kHz, and this is also a stretch (there is -45° at 40 kHz), but it's not so bad for some early locking
• Directly driving into the diode works across this measurement band and likely far, far beyond
• There are some common features, prominently at low frequencies and somewhat so at higher ones that likely arise from the current -> frequency response of the diode itself

Laser frequency noise

I now have another calibrated measure of laser frequency noise, wherever it dominates over the PMC length noise. I measured the error signal, corrected for the loop gain and calibrated to Hz. For comparison, I've added the measurement using the Zurich PLL on the beat between the two free-running lasers on 12/17/2014 (see CRYO:1185), as well as the RIO spec for this laser.

As you can see, tonight's measurement agrees quite well with the earlier one upt to ~1 kHz, above which the old measurement is probably marred by the relatively low-bandwidth PLL. It seems that the PMC is quiet enough to see the laser noise throughout, and the new measurement now sits closer to the spec up to the highest available point at 10 kHz. Below ~50 Hz, we are probably seeing the well-documented excess noise from the ThorLabs driver. Everything looks as expected.

Locking via laser feedback

Relatively early in the night, after having measured the actuation transfer functions, I sucessfully locked the cavity via feedback to the laser (as opposed to the PMC PZT) for the first time. Below is a comparison of the OLTFs for a 1-kHz loop using the same servo shape (a pole at 1 Hz) using both actuation schemes.

Because of what I had hooked up at the time, I only did this with the (low-bandwidth) LDC201C, so, while the absence of a ~10-kHz resonance is clear, the phase margin is not improved at all (worsened, actually). I only report this as a milestone, and the margin afforded by the ITC502 or by directly driving via the bias tee should be far better.

I wanted to do some intensity feedback testing, for two reasons:

1. Just to get used to using the fiber amplitude modulators
2. While I wait for the machined parts for the 1064nm M2 ISS testing on the old gyro table, I might as well use this basically perfect setup to do some initial runs with the M2 at 1550nm

So that I can have as much power as possible, I removed the fiber phase modulator and installed the amplitude modulator in its place. To generate the PDH sidebands, I simply drove into the laser bias tee with the 30 MHz oscillator signal and increased the amplitude until I got the same modulation depth as I measured with the modulator. I also had to readjust the demod phase via cable lengths, but after that the cavity locked just as before (and with an identical OLTF---not shown here). I don't claim that this locking technique is as good as using a phase modulator, in light of possible RFAM effects, but it is likely fine for intensity testing.

I also tried to increase the DC drive current of the laser, but it kept stalling after I tried to increase it above ~115 mA (the output power would increase in accordance with the plot on the datasheet, but then would suddenly crash and not return if the current was lowered until the driver output ON/OFF was cycled---not sure what gives here). So, I set it to 100 mA, where it seemed stable. The output of the laser head at this current is ~12 mW, so the max-transmission output of the amplitude modulator is about 6 mW (due to the 50% insertion loss). Adding a slight DC offset to the modulator, I reduced the output to ~92% to get some linear actuation strength for feedback.

I then tried to create an AC-coupled loop with an SR560, but had problems with stability on the low end. Eventually, I gave up and used the A-B function to subtract the measured DC level of around 4 V from the TRANS PD signal. I then put a pole at 300 Hz and scaled up the gain until I saw oscillations up near 100 kHz, and then slightly back down. Using this offset-subtracted DC-coupled loop, I was able to get solid in-loop performance, obtaining a UGF near 100 kHz and suppressing fluctuations to the dark noise level (consistent with the PDA255's noise) over a wide band.

The next step will be to use my low-noise readout optoelectronics and try out the Chachi servo.

I was preparing to do an initial test of the M2 ISS readout board with the 3-mm diodes on the SiFi test setup when I noticed some anomalously high noise on one of the diodes. So, I decided to make a more careful measurement and test all 4 diodes. I found that only one (S/N 7845) exhibits this very bad excess 1/f noise, but all four have it present at some level.

For this test, I had the transimpedance fairly high at Z = 2.7 k since I am only working with < 5 mW of power, and the diodes were completely blocked for this measurement and put in a dark box. The bias was 10 V at first, but then reduced to 5 V in an attempt to reduce the excess noise after I read on the datasheet that 10 V was an absolute maximum for some reason. I did not record the difference in noise from 10 V to 5 V, but this is a test I will likely try (though perhaps not up to 10 V anymore).

While 7845 is clearly bad, the others are probably OK for now; they are not acceptable for low-power/high-Z operation, but are likely just fine for our high-power testing since we will expect shot noise levels of >100 pA/rtHz, with SNR with respect to PD noise increasing as .

Tonight I succeeded in using the M2 ISS readout board and the 3-mm diodes to do some real intensity stabilization using the SiFi test setup.

First, I built a foam box to use as a temporary enclosure for the PMC and diodes until we get our real box finished:

There are holes for the input and REFL beams, and the diodes are held with makeshift mounts that clamp down on the sockets. Clearly, these aren't as stiff or stable as what we're having built, but they do the job for now. There is a steering mirror before the 50/50 BS so that the position on each diode can be adjusted separately with ease.

I didn't want to open the Chachi ISS box can of worms yet, so I just built my own temporary breadboard circuit. I had done some preliminary SR560 locking, so I knew roughly what I wanted, and I measured the modulator -> PD transfer function again today and verified that it was flat well above 100 kHz. I made a 2-stage pole/zero-style circuit, with a double (removable) pole at 300 Hz and a zero at 10 kHz to bring phase back to -90° around the target UGF of 100 kHz. It looks like this:

I wanted to DC couple, so I came up with an idea to pick off the stable 5-V bias supply from the M2 board and sum it with the (negative) output of the in-loop PD in the first stage of the servo. I had some current-related issues with the summer at first, but these went away when I increased the input resistors a bit (n.b., to fix the gain I had to change some other components, and as a result the controller TF is actually slightly different than shown above, but not much).

Hooking it up, it locked right away with the expected UGF of near 100 kHz (not yet measured, but inferred from the transfer functions and spectra). Here is the stabilization result:

As you can see, the out-of-loop signal is stabilized to the shot noise level (which is  higher than the bare shot noise for half the beam due to the well-understood correlated noise imprinted by the loop) from about 5 kHz down to just below 100 Hz. Below this, there is clearly some differential environmental noise between the PDs. I did some beam scanning to try and minimize with some success, but not much. I'm not sure what the coherence below 20 Hz indicates---the in-loop signal is suppressed to below the measurement noise level, while the OOL signal exhibits excess differential noise, so I don't see why there should be any coherence.

In any case, this is a nice verification that:

• The M2 readout board works with real optical signals
• The intensity feedback system for the SiFi experiment works
• The 3-mm diodes (save for the one bad one---see CRYO:1207) behave nicely, at least for these relatively low powers
• The PMC -> PD scheme shows promise for our future tests with nicer hardware

[Nic, Zach]

Nic got a Glasgow-style cantilever from a group in Taiwan, and a quick test in the rapid cycle chamber showed that it had pretty low loss, so we are running it in the cryostat now. As a reminder, these are the rough dimensions of this style cantilever:

Below is a photo of the box it came in, showing the actual 92-um thickness of this sample, as well as a shot of it in the vacuum chamber. For some reason, this particular sample's clamping tab did not fit in the groove that Nic had built into the clamping block for the other Glasgow cantilevers, so I had to mount it to the side against the flat faces of the clamp (as I've been doing with our larger samples).

This evening, we transferred it over to the cryostat and restored all the electrical connections for what will hopefully be a fruitful cryo run. Here is a ringdown of the fundamental mode (~106 Hz) at room temperature:

The measured decay time of 41 seconds corresponds to a Q of around 14,000, which is about as good as we expect at room temperature. This sample is probably better than our other ones for at least 2 reasons:

1. It is made from a better-quality (FZ) wafer, and
2. It has been manufactured monolithically with a thicker clamping tab, which our modeling suggests is a very effective way to evade clamping losses by keeping strain energy within the silicon.

Given that we didn't see much improvement at all with our other samples when going to low temperature, I believe (2) is by far the biggest effect. The Glasgow wafers only have the clamp-region thickness extended to one side, which is modelled to be worse than if you go both ways, but it is still much better than we can do with our discrete sandwiching.

I filled the LN2 reservoir and the volume is cooling overnight. I did some rough ringdowns at a point when the steel block was registering around 160 K and found greatly improved Qs already (approaching and perhaps exceeding 10⁵). We will continue to make measurements tomorrow.

Given that we see some excess noise in our 3-mm Laser Components diodes (IG17X3000G1i), especially with one of them, I went ahead and did a more careful measurement of both the dark currents and noise.

To make this measurement, I switched to OPA140 transimpedance amps on the M2 readout board and used a 1-M transimpedance.

Dark current

The OPA140 has a bias/offset current of 10 pA max and an offset voltage of 120 uV max, the latter which therefore limits the DC current sensitivity with this transimpedance to 0.12 nA. There is also some allowed current variation over temperature (±3 nA bias and ±1 nA offset over -40 to +125 °C), so this can add some more DC uncertainty if the lab temperature is a few degrees away from 25 °C. Plugging the outputs into the DMM without the diodes connected, I measured 0.0 mV and 0.2 mV on amps 1 and 2, respectively. This is consistent with the op amp spec.

The Laser Components spec for the dark current (at 5-V bias, where I measured it) is 20 nA typ, 100 nA max. Plugging in the diodes while keeping them in a blocked box and with the room lights off, I measured the following bias currents (output voltage divided by 1 M):

• S/N 7842: 78.9 nA
• S/N 7843: 61.7 nA
• S/N 7844: 43.8 nA
• S/N 7845: > 200 nA (started below 100 nA, increased continuously while energized---see below)

The first 3 diodes are within the max spec, while 7845 seems to be exhibiting some catastrophic failure mode where the dark current is avalanching whenever the bias is engaged. Below is a plot of the measured amplifier output after a turn-on of this diode, with one of a healthy diode for comparison to the right. This was taken in the middle of the testing, and the last measurement of the current before this turn-on was around 140 nA. As you can see, there is an initial slew (not inconsistent with the timescale of the bias turn-on), followed by a slow but monotonic increase of the dark current over time. When this was repeated, the initial slew brought the current again to the last-known highest level.

So, as you can see, S/N 7845 is clearly broken. Maybe we can get a replacement

Noise

I used the same transimpedance amp setup to measure the noise. All diodes show spectactularly higher noise than the advertised level of 3.2 x 10^-14 W/rtHz NEP (~3 x 10^-14 A/rtHz), with a 1/f characteristic that, if extrapolated, would not intercept the quoted spec until ~1 MHz. A frequency for this spec is not mentioned on the datasheet. In all cases, the circuit was allowed to equilibrate for a few minutes before a measurement was made. The spectra below were found to be stationary, with the exception of occasional glitches.

The readout noise is limited from several 100 mHz up to near 1 kHz by the Johnson noise of the 1-M transimpedance resistor, above which there is some noise peaking centered around 40 kHz that is not inconsistent with other measurements I have made with this op amp in very-high-impedance environments (c.f., 40m:8151).

What gives?

[Nic, Zach]

We measured the Q of the fundamental (~106 Hz) mode of the Taiwan cantilever in two ways. First, we used Nic's active steady-state method, and then we did a traditional ringdown. The results seem to agree, but the precision of the first method is much better due to the dynamic range of the readout for this mode: the motion becomes nonlinear at an amplitude only a few times greater than the background excitation level. Over a ~4-hr average, the loss is measured to be 1.45 x 10^-6 ± 2.9 x 10^-7, giving a Q of ~6.9 x 10⁵.

Here is a plot of the instantaneous phi from the calibrated control signal. This data has already been fed through a ~1-hr lowpass, and then the data from the initial settling time has been truncated away. The mean and standard deviation of the rest of the points are what is reported.

After this measurement was made, we shut off the servo and allowed the mode to ring down. Here is that ringdown, along with a predicted range of theoretical curves using the result from above. As you can see, they are fairly consistent with what is measured, considering that the system quickly reaches a regime where it is excited by the environment (that is, only the initial part of the ringdown, where the agreement is good, is very trustworthy).

This Q is a couple orders of magnitude lower than what is expected for this mode at this temperature, but it is also only a factor of 2-3 worse than the best measurements using a similar apparatus at Glasgow (to my knowledge).

It bugs me that we don't seem to have any information about what steel looks like at low temperatures. Given my COMSOL strain energy modeling, the energy ratio for this mode is about 3 x 10-^4, so this could be explained by clamp loss if the steel Q is as low as a few hundred. I'm looking into other modes to try and support or refute this hypothesis; since different modes have different energy ratios, we may be able to see what's going on. In parallel, I'm asking Matt and others to find out what is really known about cryogenic steel.

The most recent measurements on the Taiwan-sourced Glasgow-style cantilver (see CRYO:1213) are encouraging, but the best Q measurement at low temperature is still a couple orders of magnitude worse than what is theoretically achievable, and about one order of magnitude worse than our conservative clamp loss estimates. Also, I've done some measurements on other modes (that have different expected clamp loss contributions due to the relative strain energy ratios) to try and sort out what is going on, with little success. Finally, some modes---including the 2nd bending mode at ~650 Hz---exhibited very low Q for no known reason.

One thing I thought about is that, since the Taiwan cantilever did not fit in the groove that was built into the block for the Glasgow-style cantilevers and therefore is just sandwiched between the two large pieces making up the clamp (see CRYO:1211), the clamp is likely pushing down at somewhat of an angle, which could lead to all sorts of non-idealities. Since the other Si samples we have lying around are roughly the size of the clamping region of this cantilever (~300-500 um), I opened up the cryostat today and reclamped the cantilever using a spare broken-off 300-um-thick cantilever piece as a spacer on the other side:

Pumping it all back down, I immediately measured Qs a bit higher than what we saw last time around at room temperature. The last measurement I made before leaving was tau ~ 135 s ==> Q ~ 46000, though it had been increasing up to that point, likely from the residual pressure, which was at ~10^-3 Torr when I left. Compare this with the Q of ~14000 from the last time around, though admittedly I did not record the pressure at which this was measured.

I called the campus service yesterday morning to have the LN2 dewar refilled. They got around to it today. New dewar number is 102.

On Tuesday night, when I added the Si spacer to the clamp, I measured a Q of ~46000, but I noted that it had been increasing up to that point, likely due to the residual gas damping (see CRYO:1214). Last night, I made another measurement and found it to be much higher, at ~1.2 x 10⁵ (tau ~ 350 s). This is much better than we have seen at room temperature thus far, so it looks like my spacer addition has helped.

I remeasured this an hour or so later and saw no appreciable increase. I checked again today and it appears as though it may have increased slightly, but it was hard to say for sure due to higher environmental noise. Really, we need the steady-state ringdown to make a good measurement at this level.

The LN2 dewar was refilled today, so I filled the cryostat and we'll see how it looks at low temperature tomorrow.

The cantilever had cooled to around 100 K by this morning, so I set up the mode ringer and began an active measurement on the fundamental mode. The online loss angle measurement for a 3-hr period beginning around an hour after lock is shown below (this is the control signal filtered by a 2nd-order low pass at 0.2 mHz.

As you can see, the loss is hovering around 3 x 10^-6, giving a Q around 3 x 10⁵, which is slightly but significantly lower than what we measured before I added the Si spacer to avoid skewing the clamp (CRYO:1213). I would chalk this up to the spacer actually making the clamp worse, but we did in fact see a huge improvement at room temperature (CRYO:1216). So, like, what the hell man?

I've left it running to collect more data over the weekend. I haven't gone over the temperature readout/control system with Nic, so I set up a simple temperature readout in the meantime so that we can have at least a coarse Q(T) measurement as it warms. To do this, I simply put a 1k resistor inline with the RTD and put 5V across with a lab supply. The second set of RTD leads goes to the temperature readout input in the digital system, so this is now just a DC readout of the voltage across the RTD. The lockin input channel X1:SCQ-TEMPERATURE_LOCKIN_DEMOD_SIG_OUT is calibrated to volts, and is equal to 5 V * R_RTD/(1k + R_RTD).

It was a little unclear to me how the digital temperature control was supposed to work as it was built, so I made some modifications today.

Readout / Calibration

The previous implementation used a digital lockin setup (as does the new one), but the output of this was converted to an error signal for the temperature control loop using a relatively primitive calibration, so I added some math into the model to make it a little more exact. The changes can be divided into two sections: 1) the demod voltage to RTD resistance section and 2) the RTD resistance to temperature section.

Demod voltage to RTD resistance

To get a nice linear temperature signal using the 4-lead sensing method, the RTD current should not be determined solely by the RTD (otherwise, the readout just sees the excitation directly). So, I have added a 1-kOhm resistor in series with the RTD in the LO path, just as I did with the temporary setup described in CRYO:1217. The series resistor and the RTD now form a voltage divider where the RTD resistance can be inferred to high precision in the limit R_RTD << R_i (= 1 kOhm). This is almost always true, but the model does include the exact expression for R_RTD(V_out). To set the calibration, one must enter 2 values:

• RISET (aka Ri): The input series resistor (1 kOhm presently)
• VLO: The (pk) amplitude of the LO signal in volts across R_i+R_RTD. 

RTD resistance to temperature

For this, I have implemented the full, quartic formula from the ASTM standard (see our RTD manufacturer's page). Other than 4 preprogrammed empirical constants (and the Kelvin conversion of +273.15 at the end), this only requires one input from the user:

• R0: The RTD resistance at 0° C (100 Ohms for our RTDs).

Heater actuation

The heater actuation section was in pretty good shape, so I didn't really have to make any modifications there. One thing I did do was add a heater power calculation, which requires the user to enter the heater resistance.

On the hardware end, since I'm using the bigger steel block clamp which also has the higher-resistance (100-Ohm) power resistor, I found that I needed more juice than what the DAC -> voltage amp/buffer that Marie and Nic used could provide (this circuit was regulated to 15 V, giving a max power of 2.25 W, which just isn't enough). I stole my Sorensen HV supply back from the CTN lab for now, as it seems to be unused, and used it as a HV amplifier via the external control feature. Since this unit doesn't allow voltage range limiting in remote mode, I added a 1/10 divider between the DAC and it so that I didn't have to trust software limiters. Really, I should attenuate the HV output, but I couldn't think of an easy way to do that with the stuff I had on hand. Anyway, the railed heater voltage from a +10 V DAC signal is ~40 V --> 16 W.

Finally, I edited the SCQ master screen to reflect all these changes. Here, you can see the system being held at 120 K:

I reported in the replied-to entry that the Q of the Taiwanese cantilever at low temperatures actually appeared to have gotten lower at low temperatures, relative to the case before the Si spacer was added to the clamp to avoid skewness. However, the data from the longer run over this past weekend (see the ~20-hr stretch below) seem to suggest a Q not significantly different from that measured in CRYO:1213.

Interestingly, the online phi measurement starts out at the higher level I indicated in the previous post, but then slowly approaches a level not inconsistent with the ~1.5 x 10^-6 number from before the spacer addition. The title is misleading, as the system actually approached a minimum temperature of ~90 K on Saturday, but the thermoelastic noise prediction is roughly flat over this temperature band, so that shouldn't be a factor, and the associated deflection from this temperature shift should not be enough to account for this drift via calibration error.

As I discuss in the quote, I had hoped to make a continuous phi measurement as the system warmed leading up to today, but at the time I neglected to consider the thermal deflection, which over such a large temperature swing completely rasters the beam off the QPD. In retrospect, I'm lucky that this effect didn't break the cantilever as the sensing gain was reduced from the misalignment---thankfully, the loop destabilized quickly enough that the watchdog script killed the feedback before anything happened.

So, it looks like we'll have to make this measurement the old fashioned way, point-by-point, which is why I spent time reconfiguring the temperature control today. I'm running an active measurement overnight at 120 K to see if we see a Q bump there.

I brought the cyrostat up to room temperature today to do some work inside, and there appears to have been a minor disaster.

The 100-Ohm heater was was glued to the large steel clamping block with (I'm assuming) conductive epoxy, and it appears as though there was enough heat to dissociate it at some point during the latest run.

When I opened the cryostat, there was a strong noxious smell, which was my first indication that anything had gone wrong. Upon opening the top of the can, I found that the power resistor was now attached to it and not the block (the whole thing hangs upside down, so the resistor fell of, then grabbed onto the lid as it cooled).

It's unclear when this happened. I had been running the cantilever at constant amplitude over varying temperature over the last 2-3 days and there was no significan event to indicate the time when the resistor must have fallen. My best guess was that it happened as I provided a steady power of ~10 W to it this morning to speed up the heat-up. The RTD, located on an adjacent side of the block some ~3 cm away, never registered above room temperature, and that was at the very end before I vented the chamber.

Thankfully, this stuff dissolves readily in isopropanol. I've been going through the entire system, starting with the Taiwan cantilever itself, and cleaning everything. There is a very slight (and typically invisible) residue apparent on most parts of the chamber, so I'm getting that all off.

The power resistor on the smaller (radial) clamp is screwed on, which I think is a better solution in light of this.

[Den, Chris, Nic, Zach]

Since my snafu before the LVC meeting (CRYO:1225), the small cryostat has been in pieces being thoroughly cleaned and aired out. Nic wanted to have the ringdown setup rebuilt so that we can demo the steady-state Q measurement technique for our visitors, so we did some work today to make that happen.

This morning, I re-lined the main chamber walls and floor with aluminum tape. This model came with some thin foil lining the walls, attached by periodic thin strips of double-sided paper tape. We have been intermittently scraping some foil off each time we cycle, and since a nasty residue was present on the floor of the chamber after the epoxy incident, I figured it was time to replace the lining. I just used aluminum tape since a.) it is stronger and will be less prone to scraping off, and b.) if and when we need to replace it again, it should come off much more easily.

This afternoon, we rebuilt the cryo package on the cold plate (clamp with Taiwan cantilever installed, ESD, and 45º mirror). Since we don't want to use epoxy to mount the power resistor anymore and we don't have any tapped holes in the clamp, we have not equipped any heat source or temperature sensor. This is fine, since we really just want to use it as a demo this time around, and room temperature should be sufficient. If we want, we can still cool it down to LN2 temperature, but we won't have any actuation or readout.

Upon pumpdown, we noticed that the pressure had stalled at around 20 mTorr after a good 20 mins of pumping, indicating that we had a leak. We checked the top seal and electrical feedthrough (which had also been freshly reattached during the rebuild), and found no issues. With nothing else to try, we decided it was most likely the seal between the chamber floor and the main section (I had to foil this with rectangular sections of tape, which I then XActo cut into a circle at the o-ring groove, so it was possible that a foil flake was blocking the seal). With everything still in place, we flipped the cryostat over and removed the bottom. We found a couple places where a tiny piece may have extended into the seal, so I re-cut the circle more conservatively. When re re-sealed, we found the pumpdown profile to be much closer to what we usually expect. The pressure was a few mTorr after ~10 minutes and showed signs of healthy decline.

We rebuilt the optical readout, then tested the MODERINGER amplitude sensing and found everything seemed to be working. We did not want to test the ESD at this high pressure. When I left, the Q was relatively low at maybe a few thousand, but gas damping was likely still a limiting factor. Also likely is that there is still some residue on the cantilever that I didn't get off, or perhaps even that some irreparable damage might have been done. We should be able to tell when the pressure is low enough.

Before the LVC meeting, I had just done a long steady-state Q measurement on the Taiwan cantilever. I got too distracted by the melted epoxy disaster (CRYO:1225) to actually post the data.

Below is a plot of the ~16 hour stretch of data (second trend), showing the temperature and instantaneous loss angle. The temperature was stepped in 10-K increments from 90 to 130 K, holding at each temperature for 3 hrs to allow the system to equilibrate and integrate (except for some of the early steps which required some manual intervention).

The main result is that the loss seems relatively constant at ~10^-6 from low temperature to ~120 K, where it starts to increase. Towards the end of the 130-K stretch, the LN2 ran out, and the system started heating to room temperature uncontrolled (i.e., heater output was railed at zero).

This level is too high to be from the Si, so I assumed it was some residual clamping loss. I was dubious that the figure from the one reference that Matt A. found and gave me for the cryogenic Q of stainless steel would be applicable to our particular clamp, so I thought I might try to measure it directly, in parallel with the cleanup of mess in the cryostat. To do this, I got some spare steel wire from Gabriele and made a makeshift suspension, hanging the top piece of the clamp, hoping to measure the loss of its lowest vibrational mode. I knew it was a long shot, since this mode should be around 17 kHz, but I set it up in the simple vacuum chamber anyway, and tried to excite it and read it out optically. The first bending mode should have nodes *near* the suspension points, so I thought I might get some kind of meaningful results if I could actually see a ringdown.

I was unsuccessful. I tried various excitation schemes, from broadband (banging stuff) to narrowband (bandpassed white noise, amplified with the boom box and blasted out of a speaker touching the chamber), and none revealed any mode excitation. I was able to see broadband noise increase with the excitation profile, but no lines, so most likely I was seeing some alternate path.

I still think it would be nice to get an empirical measurement of the cryogenic Q of the steel we use for our clamps. Maybe we can set up a laser vibrometer measurement like Norna and her student did a few years back on the steel gyro PMC?

Today, I installed the shelves into our rack and moved the electronics that were on the table into it. I then cleared the table and started setting things up the way they will be.

The cryostat is now on the south side of the table, and the lasers are set up on the north side. I connected and placed the AM and PM modulators in both laser chains, then placed the output couplers. I used posts to protect the fibers and strain releif the SMA cables going to the modulators, and installed the BNC patch bay on the end of the table near the rack. I'm waiting on our 3/4" posts to continue with the optical layout.

With everything connected, I trimmed the AM DC voltages to maximize the transmission and verified that the output power for each was ~25% what it is directly out of the laser, as it should be (since each modulator has loss ~3 dB).

I roughed our cryostat back down tonight. Remember, this model has a getter that degrades over time when exposed to air, so we should minimize the time that it's not under vacuum.

Apparently, the getter is made by IRLabs themselves. They've quoted me $690 for a replacement (see attachment *removed since I was informed that's not allowed*).

Seeing Hartmut's talk at the last LVC meeting about innovative DC photodetector designs (something necessary for future squeezed IFOs) reminded me of some investigation I did into the same while at LLO. One thing I did a fair bit of work on while there was the DC current subtraction idea (c.f. LLO:6449 and 6532), but another thing I spent time modeling was the concept of using an RL network, as Hartmut is exploring now.

The circuit I was considering differs somewhat from Hartmut's idea. In his circuit (at left below), the inductor ("L1") and input resistor ("R1") perform a current branching: at low frequencies, the photocurrent sees low impedance to ground through the inductor, and therefore does not pass through the transimpedance amplifier and get converted into an output voltage; at high frequencies, the inductor looks like an open circuit, and all the current passes through the TIA. Ideally, this leads to an effective frontend whitening that allows for a high Z at audio frequencies. In practice, one would use either the DC resistance (DCR) of the inductor, or perhaps an extra resistor in series, to set the DC Z, which would be , where R_DC is the DC resistance of the inductor path. One problem with this design is that, since R_DC cannot be arbitrarily low due to the DCR of the inductor, one must choose an R1 that is high enough to set the DC Z to a low enough level. Roughly speaking, this means that the value of R1 must be approximately the ratio of the desired AC and DC transimpedances (typically a factor of 100 or so), times R_DC. Since RDC will be on the order of 100 Ohms, R1 must be on the order of 10 kOhm. This in turn means that the current noise of the amplifier is fully converted by this high impedance at all frequencies, which ruins the SNR of the detector at low frequencies (you could use a low-current-noise part, but then the voltage noise kills you directly).

The circuit I had in mind is at right below. As you can see, the amplifier in this case is only used as a unity-gain buffer for the passive readout circuit (though one could consider adding a switchable flat gain for low-current operation, as in the ZSWITCH feature of the currently used DCPDs). This design works simply by having a passively different transimpedance at different frequencies: at low frequencies, the inductor shorts the large resistor and the transimpedance is just the inductor DCR plus the additional series resistance to ground (50 Ohms in the schematic); at higher frequencies, the impedance increases until it is limited by the parallel resistance (10 kOhms here, plus the series 50 Ohms). With this topology, the current noise always sees the same impedance to ground as the photocurrent does (i.e., the transimpedance), and there is no extra reduction in SNR. The "DC" section is not necessary in principle, and in fact it always has worse SNR for a finite inductor DCR, but it could be used as a calibration path for the DC response due to potential nonlinearity of the inductor.

As a side project, I've started doing some testing of this design. To start, I bought a ginormous 4-H inductor from DigiKey:

Transfer function

The first thing I did was to verify the transfer function. To do this, I biased one of our 3-mm diodes with the M2 circuit bias supply, then sent the anode into a breadboard version of the RL circuit. The parameters were slightly different: L = 4 H (DCR ~ 60 Ohm), R_AC = 10k, R_DC = 39 Ohm. I then put one of our SiFi lasers on it and modulated the power using its fiber amplitude modulator. Here is the result:

As you can see, it performs just about as expected. A couple notes:

• The LISO trace above has been adjusted using the inductance and diode capacitance as fit parameters, since they are not known precisely a priori.
• The slow upturn at low frequencies is fairly well explained by the amplitude modulator response at low frequencies (see CRYO:1187).

Noise

Of course, the biggest concern with using such a big inductor is the additional noise it might inject, particularly due to pickup. Below is a summary plot of some measurements I made on this circuit, together with some theory curves and the currently used DCPD for comparison.

Notes:

• Obviously, there is a strong presence of pickup here. These traces are also the result of wrapping the inductor in metal and orienting it to minimize noise. Yes, the pickup is prohibitively bad as it appears here, but I have an idea to get rid of it (see below).
• Below a few Hz and above ~1 kHz, the circuits behave as they should, except that the LT1128 exhibits excess current noise in the high-frequency region. This is no surprise, as we have never acheived the "typical" noise performance advertised by Linear (see ATF:1890---Rana points out that this could potentially be due to our not following proper electrostatic discharge practices, but it seems that they are always out of "typ" spec---not "max"---in the exact same way). In this case, though, the noise is even worse than the "max" level, which is an extra party foul. My proof of this is that the OP27-stuffed circuit does what it says it should at these frequencies. Note also that I had only some modest thermal shielding, and that's why the noise shoots up below a few 100 mHz.
• Given the typical LT1128 performance in the real world, it may be that the OP27 is the ideal buffer amp for this circuit, since it adds a factor of a few at high frequencies (where we are most likely to be sensing noise limited). It's also only a factor of a few worse than the fantasy LT1128 curve at low frequencies.
• For all its nascent imperfections, this is still already a detector with 10x better noise both at 1 Hz and above 1 kHz than what we have in aLIGO, so that's already promising. 

Reducing the pickup:

So, we are left with the problem of being highly sensitive to a signal injected into the coil, but not to one induced by external fields. Luckily, the guitar industy has had a solution for almost exactly the same issue for about 80 years now: the humbucker. Of course, it's slightly different, since in the guitar case you want to be sensitive to an induced signal (i.e., the signal from the string, which is deliberately made differential-mode by reversing the polarity of the magnets inside the coils), but I believe the same principle should apply. In our case, we'll put the inductors in series electrically, but adjacent and flipped spatially. In that case, the pickup-induced voltages should cancel while the current-induced voltages should add, as desired. It's hard to find CMRR values for high-end humbuckers, especially since they are usually intentially imbalanced for tone considerations, but I would venture a guess that the ~40-50 dB required in this case is not completely out of the question. I've ordered another identical inductor to see what we can do.

Tonight, I got to do an experiment that I've wanted to do for some time now.

For years, I've heard in conversations with people who shall remain nameless (unless they care to contest this work) that the 3/4"-post-on-rectangular-1/4"-thick-base optic support method (used at the 40m and adopted into LIGO) is better than the standard 1"-pedestal-and-fork method (used by many experiments in our own labs and elsewhere). After many attempts, I have never succeeded in getting any hard data to support that claim. So, I decided to make a measurement myself.

I set up a simple michelson using one of the SiFi beams, once using each support scheme for the beamsplitter and end mirrors:

There is a HWP to find the polarization for which the "50:50" BS is closest to balanced, a lens to focus into the IFO, a second lens to focus the AS beam onto the PD, and the PD itself, which is a PDA255. There is an ND=0.7 filter on the PD.

Below is a scope screenshot of some fringing action when pushing on an end mirror. The contrast defect in each case was pretty low at ~2.5 x 10^-3.

Once the IFO was aligned in each case, I pushed on one mirror a bit to creep it into a half-fringe state. This took some time, since I had to push and wait a few seconds for it to settle. After doing that, I took a spectrum (actually 3 at different spans from 1 kHz to 100 kHz). The results are below, with a zoomed plot to the right.

Conclusion

As you can see, the difference is pretty minimal. The post-and-base setup has slightly higher RMS below ~1 kHz, owing to two high-Q resonances (at 340 Hz and, to a lesser extent, 920 Hz). My detractors will accuse me of bias (e.g., in tightening, etc.), but I invite anyone to come test this with their post-and-base clamping chops.

With this, I'd like to put to rest the notion that the post-and-base method is somehow fundamentally superior. I DO acknowledge that there are definitely wrong ways to use the pedestal-and-fork, and this can lead to the non-idealities noted in the folklore. The post-and-base method is foolproof in a way, since the proper procedure is somewhat manifest (use two screws, use washers, etc.), while the pedestal-and-fork requires some diligence to get just right. However, with just a little bit of care up front, the pedestal-and-fork offers huge advantages:

• Arbitrary placement (most importantly, the ability to always work along table hole axes, which makes alignment incredibly easier).
• Free-hand alignment, since the fork can be placed without jostling of the optic (see below).
• Space, since it takes up way less of it.

How to fork

To mitigate the potential recklessness of this post, I offer the Zach-Approved™ Forking Method.

First of all, this is the only fork you should be using, the Newport PS-F (maybe there actually are other acceptable ones, but none that I've found that don't apply horizontal forces on the pedestal upon clamping):

Now, the forking method (accompanied by the GIF below):

1. Locate where you want to place the optic.
2. Place the optic and align by hand. The pedestal is heavy enough to hold itself in place with friction.
3. Locate the appropriate screwhole and set the fork gently onto the pedestal, slightly un-engaged. Of crucial importance is that you pick a hole that will be somewhere close to the middle of the slot. Working along the table hole axes ensures there should be several options in every case.
4. Using your finger, engage the fork on the pedestal. If you use just enough force to move the fork, it will come to a stop when fully engaged and you won't have moved the pedestal (and optic) at all.
5. Insert the screw and hand-tighten a few threadlengths.
6. Use a ball driver to finish screwing almost until tight.
7. Just before tightening, give the fork one final nudge against the pedestal. Sometimes I use the ball driver tip, but this can also be done with your hand so that you can keep the driver in the cap.
8. Tighten as desired.

At no point after initial alignment should you have to touch the optic, and, if you follow the procedure above, the optic orientation should not have shifted by more than a mrad or so. You can see how little the optic moves over the operation in the GIF.

I bought and received the last optics I was missing (90R/10T BSs) last week, so I began building the real experiment today. Here is what it looks like so far:

Frontal beat

The first thing I did was build the frontal beat, which we will use to locate and adjust the beams' frequency offset without having the cavities locked. This is fit in a rather compact layout between the main beams, using a 10% pickoff from the second mirror in each path. The beat alignment DOFs are matched by the actuation offered by 1) the extra steering mirror in the E (left above) beam path and 2) the combining beamsplitter. A further steering mirror puts the beam on the PD after a focusing lens, and the (small) reflection is dumped. Here are the beams beating near 50 MHz:

Test cavities

We want to use some dummy cavities to set up and test our electronics. To make these, we've used some of Dmass's spare fused silica ATF-coated optics (coating run V6-593/594---scans attached). I chose to use two 50-cm mirrors for each cavity, with a length of ~4" (this is just roughly as big as you can make it with two big mirrors within the vacuum area---note the cryostat boundaries drawn onto the table). The transmission of these mirrors is 0.016%, giving a finesse of ~20k. Here are the arbcav plots:

I temporarily relocated the cryostat to the central table so I could put the dummy cavities within its boundaries on the main table. Installing only the cavity end mirrors first, I finished the main beam paths, aligning the beams along the holes and level at 4" for the main stretch, then installing the steering mirror zigzags to bring the beams in to the cavity longitudes. With the beams centered on the cavity output mirrors, I then calculated a modematching solution. Modematchr came up with plenty of options, but I chose this one because it used only f=100mm lenses (which I had bought specifically for mode matching) and left plenty of room near the cavities for the circulating optics:

------------------------------------------------------------
Other solution:

mismatch: 0.0002397
w0x = 222.7609 um 
w0y = 222.7609 um 

lens 1: f = 103.2118 mm
lens 2: f = 103.2118 mm
Distances:
d1 = 11.8781 cm
d2 = 26.4822 cm
d3 = 72.1297 cm
(Total distance = 110.49 cm)

As you can see, the predicted best mismatch is 0.02%.

I installed these (on slotted bases, so they can be adjusted), then verified that the output beams were roughly as expected---they were. I then used the cavity output mirrors to retro-reflect the beams, which served as a further modematching sanity check (since the retroreflected beams agreed transverse-spatially). Next, I mounted and installed the circulating optics (PBSs and QWPs), tuning the initial HWP and the QWP to maximize forward transmission and backward rejection, respectively. Finally, I focused the E REFL beam on a PDA255 for temporary testing.

Now the input beams and end mirrors were aligned, so all I had to do was install and align the cavity input mirrors. Before doing so, I borrowed the 1550nm-sensitive CCD camera from Dmass's setup and placed it behind the E cavity end mirror. With all the lights off, I could very faintly see the transmitted beam, and I centered the camera onto it. The REFL PD gave me a good reference, so just installed the input mirror and directed the prompt reflection back to the PD. Immediately upon doing this, I saw strong transmission flashes on the camera.

Tweaking the cavity and input beam alignment somewhat while scanning the laser frequency, I did a rough TEM00 maximization. The REFL dips indicate ~80% coupling, which I think is as good as I'll bother going before locking. 

For tomorrow:

• Repeat the last step above for the W cavity
• Install and tune the gyro RFPDs
• Determine appropriate PDH servo TFs and modify boards
• Lock cavities
• Build transmission beat setup

Well, I got partway through the plan for the day, anyway.

Rather than align the W cavity as I had done the E, I decided to continue working on locking the E cavity so that I could copy all the work wholesale to the other side at the end. The first thing I did was to install the gyro RFPDs. To facilitate this, I installed a NIM crate in the bottom of our rack (one of the spares that was stored under the gyro table). This will be used to power the PDs, the PDH2 board, and some of my homebrew filters/preamps if necessary. After powering what became the E REFL PD up, I installed it and focused the REFL beam onto it.

I checked to see if either of our crystal oscillator frequencies were within the tuning range of the PD as it's stuffed now. They weren't, so I just tuned it to 30 MHz (and notched 60 MHz) for temporary testing. Recall that these are aLIGO-style PDs that don't have maximal gain at the resonant readout frequency. In practice, they are tuned by looking at the notch seen by the anode, rather than looking at the readout node as seen below. (Note: the delay seen is consistent with the optical path lengths through the fiber and free space).

I then did some playing around with an SR560 servo, moving the pole and gain until I got some weak locking action. Then, I systematically searched the parameter space until I found the best stability (still bad, though). Using that information, I built into the uPDH box (#1437) a TF that had similar gain in the UGF target region of ~50-100 kHz, but much more low-frequency gain. This ended up being something like zpk([10k,10k], [50, 50], 1000), where the cavity pole at ~40 kHz returns the loop to 1/f above there. I would have put one of the servo zeros at this frequency, but I had too large a capacitor for it to make sense due to the smallness of the resistor needed---this is something I can change if necessary.

Plugging that bad boy in and playing with some attenuation before and after the servo, I got a reasonably stable lock, but nothing too stellar. It holds for many minutes, but it is in a delicate balance (often not very balanced) between lots of unsuppressed audio noise and some instability in the ~100-kHz+ band due to the plant. This is exacerbated by the low bandwidth of the driver (see CRYO:1205---I'm using the ITC502 at the moment). I tried doing some feedback using the bias tee input, but I wasn't able to lock at all with this method. Maybe I need to do some high-frequency crossover to it while keeping the low-frequency actuation going through the driver. Here is a shot showing the transmitted beam on the camera and card, as well as a scope trace of a lock acquisition:

In the above, GREEN is TRANS, CYAN is error, and MAGENTA is actuation. The error signal is dominated by periodic oscillations at >100 kHz, while the transmission shows plenty of audio-band noise.

Given the measurement that I made the other day on essentially the same physical system (CRYO:1238), it looks like the audio-band RMS is on the order of almost a nanometer, which is ~50x the linewidth of this cavity. So, I need more gain or less noise at 1 kHz. There are two options:

1. Switch to the PDH2 and add rapid rollup below ~30 kHz with up to 4 P/Zs
2. Just go to vacuum already, since we don't really need to contend with this much noise in the end

Since I want both sides to be roughly balanced (i.e., same loops, etc.), I'm tempted to just do (2). I've already got everything pretty well aligned and I know the electronics TFs are not crazy, so I think that's what I'll do.