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 Cryo Lab eLog, Page 2 of 61 Not logged in
ID Date Author Type Category Subject
3025   Thu Nov 10 14:53:38 2022 JCLab Infrastructurematerial propertiesInventory

I came into CRYO today to take inventory of the Flammables Cabinet.

Attachment 1: Screen_Shot_2022-11-10_at_2.54.55_PM.png
3024   Tue Nov 8 07:53:11 2022 JCLab InfrastructureGeneralparticle counts and temperature

There have been adjustments made with the programming system of the Cryo lab and this brought the room back to normal operating temperature between 71 - 73°F.  The next step to finding out the source of this issue is to set an alarming notification. If the temperature exceeds a certain threshold, Alex will be notified. From there, we can diagnose of whether the vents have stopped, the thermostat is malfunctioning, or any other issues. If this happens during a time where we will have to delay the diagnosis, Alex can turn on the AC manually to bring the temperature back down. Attachment #1 shows the temperature over the last 7 days. The system was reconfigured on 11/04/2022. Since this a reoccurring issue, I will be regularly checking the lab temperature. The graph below shows the temperature of in Cryo over the last 7 days.

Attachment 1: WB34_B250_SpaceTemp_11.07.22.pdf
3023   Fri Nov 4 11:55:17 2022 aaronDailyProgressVacuumvacuum components clean and bake

JC and I cleaned the vacuum components necessary for closing up and pumping down the PSOMA cryostat. (Wednesday) Unfortunately, there was no memory card in the camera so we lost most photos.

Maty showed us how to use the large sonicator bath at the 40m. We sonicated everything for 10 minutes, then air-baked for 24 hours at 200 C (since all parts were stainless steel).

When we unloaded the parts on Thursday. We wrapped all flanges with a lint-free cloth, covered with UHV aluminum foil, and bagged each component in a cleanroom bag (those laminate, silver ones).

The 4-way crosses had some dry, powdery residue on them after the initial bake out. Maty told us it is a wax leftover applied after the welding process. On Friday morning, Maty re-sonicated the 4-way crosses and placed them in the oven for another 24 hour air bake at 200 C. We'll retrieve them on Monday.

Here is the complete list of parts that were cleaned (also reflected in the PSOMA hardware inventory on google drive). We did not clean the vacuum hoses (too large, can bake in situ if needed) or the valves (contain plastics).

• 5x DN125CF blanks
• 4x DN35CF four way crosses
• 1x CF35CF to KF16 adapter
• 8x DN35CF blanks
• 2x DN35CF to KF40 adapter
• 1x KF16 standard tee
3022   Thu Nov 3 16:19:34 2022 ChrisComputingControl Systemupdated x1oma model, foton file broken

I fixed the busted foton file by removing the offending lines for obsolete filter modules from /opt/rtcds/tst/x1/chans/X1OMA.txt. If you ever want to start fresh, it should work to first remove this file before issuing the rtcds install command.

 Quote: I updated the X1OMA model to be more useful for the experiment. Attachments 1-3 show some relevant screenshots. The SIG block can create an excitation that is sent to the North laser's slow current control, and can be used to inject our acoustic signal. The N and S laser control signals are monitored in the NLD and SLD blocks, and slow temperature control is provided only if the cavity is locked. I will need to change the logic slightly to tune the N laser temperature only when the PLL is also locked. Because I deleted some unused channels, foton is throwing some errors when opening the x1oma filter file at /opt/rtcds/tst/x1/chans/X1OMA.txt. Could someone please remind me how to fix this? Can we generate a new foton file from scratch based on the new model? Attachment 4 shows a screenshot of the error messages when opening X1OMA.txt in foton. The last lines in the terminal are error messages when using the medm selector to try to open a specific filter module from x1oma.

3021   Wed Nov 2 13:36:32 2022 aaronLab InfrastructureGeneralparticle counts and temperature

Update with minute trend of temperature for the last week.

Attachment 1: Screenshot_from_2022-11-02_13-36-02.png
3020   Mon Oct 31 15:55:00 2022 aaronLab InfrastructureGeneralparticle counts and temperature

Here's a new temperature and particles trend. The lab temperature is back up to 87-88.

The temperature minute trend for 1 month and hour trend for 700 days are in attachments 2 and 3.

Attachment 1: Screenshot_from_2022-10-31_15-54-22.png
Attachment 2: Screenshot_from_2022-10-31_16-09-31.png
Attachment 3: Screenshot_from_2022-10-31_16-48-19.png
3019   Fri Oct 28 14:31:56 2022 aaronLab InfrastructureGeneralparticle counts and temperature

The weather is slightly warmer today, so the lab temperature has come down. I'll keep posting trends going forward. The daqd service died while I was updating the x1oma model this morning, but it is running now.

Attachment 1: Screenshot_from_2022-10-28_14-36-59.png
3018   Fri Oct 28 12:39:38 2022 aaronComputingControl Systemupdated x1oma model, foton file broken

I updated the X1OMA model to be more useful for the experiment. Attachments 1-3 show some relevant screenshots. The SIG block can create an excitation that is sent to the North laser's slow current control, and can be used to inject our acoustic signal. The N and S laser control signals are monitored in the NLD and SLD blocks, and slow temperature control is provided only if the cavity is locked. I will need to change the logic slightly to tune the N laser temperature only when the PLL is also locked.

Because I deleted some unused channels, foton is throwing some errors when opening the x1oma filter file at /opt/rtcds/tst/x1/chans/X1OMA.txt. Could someone please remind me how to fix this? Can we generate a new foton file from scratch based on the new model?

Attachment 4 shows a screenshot of the error messages when opening X1OMA.txt in foton. The last lines in the terminal are error messages when using the medm selector to try to open a specific filter module from x1oma.

Attachment 1: Screenshot_from_2022-10-28_12-38-52.png
Attachment 2: Screenshot_from_2022-10-28_12-39-01.png
Attachment 3: Screenshot_from_2022-10-28_12-39-11.png
Attachment 4: Screenshot_from_2022-10-28_12-38-32.png
3017   Fri Oct 28 09:21:08 2022 JCSummaryVacuumMoving the Chamber into Lab

We proceeded to remove the chamber from packaging and bring into the lab. This package came with 2 Separate pieces, the chamber and a bottom door.

To begin, we had to bring the engine hoist back from the 40m cage. When we brought this into the Cryo Lab, we had to turn the hoist onto its side and shimmy it in. During this, we encounter the issue of the hoist beginning to drip hydraulic fluid. Luckily, the fluid only fell onto the floor around the entrance area. After moving the hoist arm up and down a couple of times, the hoist stopped dripping hydraulic fluid.

Next, Shruti and Aaron garbed up and began to unwrap the chamber. This process went smoothly. Only the flanges were covered by foil, the rest of the chamber was cover by 2 sheets of mylar. Attachment #1, #2.

We followed by moving the hoist in and preparing to lift the chamber. I brought purple crane slings from 40m. We created a basket-type lift by hinging the sling around the bigger flanges on opposite sides. We slowly lifted to 8 in - 12 in above the ground and slid the hoist away from the bottom door. Attachment #3, #4.

Aaron and Shruti uncovered the bottom piece and came across a couple of smudges around the O-Ring. This is shown in attachment #5, #6, #7.

Afterwards, we moved the hoist back over and slowly set this down on the bottom door. This was a clean step.

Attachment 1: 48668D5B-9028-4438-A8CA-17B1AE00D098_1_105_c.jpeg
Attachment 2: 48DE9A2D-526B-4671-BE11-762CB0DABC91_1_105_c.jpeg
Attachment 3: 62C8FE1A-2B02-467F-B35C-97F343CF417A_1_105_c.jpeg
Attachment 4: 76D0DD1D-C98D-421F-A720-271B83EDF271_1_105_c.jpeg
Attachment 5: 7384721D-C5A8-460D-8D83-6876631D037B_1_105_c.jpeg
Attachment 6: 6A3EDBA2-0C25-453E-9AC0-775BC7072841_1_105_c.jpeg
Attachment 7: C547F640-DD5E-4731-990E-B7CE2F2F2722_1_105_c.jpeg
3016   Thu Oct 27 12:20:32 2022 aaronLab InfrastructureGeneralparticle counts and temperature

The temperature in Pasadena has started to go cold, which means the W Bridge HVAC has started to heat up the cryo lab. I wanted to post a temperature and particle trend, but the counter reset during the last power shutdown and I needed to adjust its baud rate and printer output for it to interface with our particle.service correctly.

For future reference, in the counter's settings I specified baud=19200 and the printer to "PRINT" (it defaults to RS-232). I also corrected what seemed to be an error in particle-0.5.py, where the channel for 0.5 um was listed after the channel for 0.7 um, resulting in the two channels being swapped (ie PEM-COUNT_05UM reported the particle counts at 0.7 um, and vice versa). With these settings, the particle count channels in nds report the same values as on the counter's front panel.

The USB hub we were using the send various slow signals to cominaux seems to not be working, at least I can get particle counts to nds when I bypass the hub but not when using the hub. Could just be that the baud or printer setting needs to be different when using the hub, not sure.

Will post a limited trend this afternoon. The lab temperature is 87 F.

3015   Thu Oct 27 11:04:59 2022 aaronNotesDrawingsPSOMA controls diagram

Wednesday October 26

Shruti and I drew up what we think is an accurate controls diagram of the PSOMA experiment as it currently stands. We'll be characterizing our system in this manner for a while, so please point out any issues. Next step is to write down its adjacency matrix, invert it, and figure out how to measure the transfer functions we're interested in (namely PDH error signal / signal amplitude [V/W]).

I'm turning this into an omnigraffle file that I'll post on the PSOMA github.

Here are some notes about the diagram

• We decided that f_LO doesn't need to be explicitly included at this stage of analysis. It's effectively just a parameter of the EOM transfer function and the plant gain of the PLL.
• P_amp is the plant gain due to the cavity. Pump carrier frequency fluctuations are converted to a voltage through the usual PDH. In our case, signal (and pump) amplitude fluctuations are also converted to a voltage by driving the cantilever, which also produces a PDH signal. We've drawn two mon points for "signal amp" and "beat freq" to indicate that the two quadratures act see their own transfer functions, so some of the control blocks are MIMO. In retrospect, it might be easier to work with a fully SISO system even though it makes the diagram more complicated.
• We've split up the actuators into two blocks, to reflect the fact that HF mon is not quite the same as either the Moku "control" point or the true laser frequency, and requires a straightforward calibration.
• The dotted box contains the entire PLL block, which effectively takes in the pump (S) laser PDH control signal and outputs the pump (S) laser's frequency and amplitude.
• As can be seen from the sideband picture above the loop diagram, the N laser doesn't produce an independent PDH error signal. The N laser's resonant sideband just mixes with the S laser's 33 MHz sidebands to produce some extra noise on the N laser's PDH error signal. If the PLL LO frequency is chosen to match the cavity's FSR, the N laser carrier would be coresonant... but so would its frequency sidebands, so I still don't think we'd get a clean PDH error signal.
Attachment 1: Y4Q1.pdf
3014   Thu Oct 27 10:32:38 2022 aaronUpdateVacuumPSOMA vacuum chamber moved in to cryo lab (tue)

[aaron, JC, Paco, James Gardner, Shruti, Ian]

Tuesday, October 25

We removed the sides from the shipping crate containing the new PSOMA vacuum chamber. We then used 4 people to lift the chamber body and lid (which are wrapped together) and move them onto a piano dolly. We rolled the body and lid into the cryo lab, on the west end of the PSOMA table. Two people carried the chamber base and placed it on four pieces of packing foam on the floor on the west end of the PSOMA table. Four people then lifted the PSOMA chamber from the dolly and set it down on top of the base in the same manner as it was packaged in the box.

All vacuum surfaces and openings of the chamber are covered in UHV foil. The lid and sealing surfaces between the base and body are covered in bubble wrap. The entire body and lid are wrapped together with plastic wrap. The entire base is wrapped in plastic wrap.

Photos of the unpacking are on the google drive.

3013   Sat Oct 22 11:04:46 2022 aaronDailyProgressPSOMAAcoustically modulated the N laser

I PDH locked our S laser to the PSOMA cavity, then locked the N laser 300 MHz away from the S laser with a PLL. (I did not check whether the N laser was detuned up or down from the S laser)

Several times, I phase modulated the N laser using the LO from the PLL. This should generate sidebands of the N laser resonant with the cavity and 600 MHz away from cavity resonance. The resonant sideband should be phase-locked to the S laser by the PLL (with a relative phase chosen by the PLL offset or LO phase).  I then used a function generator to drive the low-frequency "DAC" input of the N laser current driver around 1 kHz. The acoustic sideband appeared at the drive frequency in the PLL error signal and S current control spectra, but not in the PDH error or N current control spectra.

Was the acoustic sideband too weak? I think it would only be ~nW (2 mW N laser carrier - 30 dB EOM modulation - 30 dB current modulation). I increased the 300 MHz modulation depth and the acoustic modulation depth, but lost lock before seeing an acoustic peak in the N laser control signal. We'll need to investigate why it loses lock, I wasn't very careful here.

I instead drove the N laser EOM at (300 MHz - 300 Hz), so the its order sideband is 300 Hz detuned from cavity resonance. This should put a ~uW sideband 300 Hz away from the cavity resonance. The 300 Hz peak appeared in both the N and S laser control signals (see attachment, where the top plot is the N laser control spectrum and bottom plot is S laser control spectrum).

Driving the "probe" laser just outside cavity resonance isn't what we ultimately want. Because there is no phase-locked sideband on the other side of cavity resonance, both quadratures of the signal field will be amplified rather than just the amplitude quadrature. For a squeezed state, that means the antisqueezed quadrature would be amplified and overwhelm the squeezed quadrature. Still, might be useful for the classical demonstration.

Attachment 1: IMG_0138.jpg
3012   Fri Oct 14 15:36:10 2022 aaronDailyProgressPSOMABoth lasers locked to cavity, with 300 MHz offset

Based on the conversation above, we decided to first try locking the N laser to the S laser with a 100s MHz offset using a PLL. The tricky part is making a PLL with enough gain and stability to follow the S laser while S laser is locked to the noisy in-air cavity. We didn't need to change the optical path at all to try this. We simply stopped modulating the N laser at its EOM, and introduced a frequency offset to the N laser.

This method is convenient because we can phase-lock and mix the N and S lasers at the same beamsplitter. This lets us set the relative phase of the two lasers with the PLL, without being subject to acoustic noise between the beat note pickoff BS and the recombination BS. We also use all of the "signal" carrier field for locking the PLL, but don't send this carrier to the input port of our amplifier. Once we implement the Mach-Zehnder, this will let us avoid being limited by signal carrier RIN.

Today, I got both loops locking. Here were the important components that needed to work out:

• I increased the N-S laser offset frequency to 300 MHz (maximum LO frequency in Moku). This maximizes the plant gain for the PLL, and also keeps the N laser as far away from the S laser and its sidebands (and the cavity resonance) as possible.
• With the PDH servo off, the PLL locks with pure proportional gain, and is more stable with a bit of derivative near the UGF. However, with the PDH servo on, the PLL needs almost 60 dB of extra gain near the cantilever resonance to stay locked. I found that with an integrator at 2.674 kHz and integrator saturation corner below 10 Hz to avoid double integrating at DC, the PLL had enough low frequency gain to track the cavity frequency.
• Feeding forward the S laser's PDH control signal to the PLL reduces the frequency fluctuations of the NS beat note with the PLL servo off by a factor of 10. This is also necessary for the PLL to acquire lock.
• Originally, both the N and S laser control signals had +14 dB gain on the Moku's output stage to give them a bit of extra range (10 Vpp instead of 2 Vpp on the control signals). However, I noticed some digitization noise on the N laser control signal with the PLL locked and PDH servo off; discrete steps are visible in the control signal. To avoid this, I removed the +14 dB gain from the output stage of the N and S control signals. This makes the digital control signal internal to Moku +14 dB larger, avoiding the discretization.
• With the N and S lasers at different frequencies, we can't tell if the PLL is locked simply by looking at the DC fringing between the lasers. Instead, we can tell because the RF beat note and the LO will be phase locked just before the mixer.
• Used a 99-1 RF coupler to pick off some of the beat note to view on a spectrum analyzer. This was useful for tuning the N laser frequency while acquiring PLL lock.

The other choices when locking, like choosing the PDH loop parameters, were similar to in other recent elogs.

### attachments

1. Top level overview of the Moku setup. The loop shaping filters for both PLL and PDH controllers are in the PID instrument in slot 2. The PID instrument in slot 3 is just used to feedforward some of the PDH control signal to the N laser.
2. PDH and PLL error signals with both servos locked. The error signals are each dominated by 40 Hz noise from the cantilever resonance.
3. The PLL mixer, showing that the RF beat note and LO are phase locked (up to some fixed phase offset) when the PLL is locked
4. PID instrument in slot 3, showin that the PDH control signal is being fed to both the N and S lasers.
5. Detail of the PDH controller shape
6. Detail of the PLL controller shape
7. PDH mixer setup (servos off, lasers far from resonance)
Attachment 1: IMG_0132.PNG
Attachment 2: IMG_0130.PNG
Attachment 3: IMG_0131.PNG
Attachment 4: IMG_0133.PNG
Attachment 5: IMG_0134.PNG
Attachment 6: IMG_0135.PNG
Attachment 7: IMG_0136.PNG
3011   Thu Oct 13 11:46:28 2022 shrutiDailyProgressPSOMA1 to 2 loop locking

[aaron, shruti]

Today we began trying to lock both lasers to each other at a large frequency offset apart (~100 MHz) while the cavity remains locked.

The PLL remained stably locked for at least a few minutes without the cavity locked. The cavity also locked and remained locked separately a few times but the slow temperature control was causing issues. We spent time troubleshooting the slow control.

## Attachments

Aaron and I drew these diagrams post our discussion with Lee

1. Schematic for phase locking the two lasers a fixed frequency apart and using an AOM to then shift one lasers frequency by the same amount to get both at the same frequency to mix before entering the cavity.

2. Schematic for using one laser to split into both the signal and pump

update: the slow temperature control wasn't working because we took the control signal from the current driver's HF Mon instead of picking off the control signal directly before the driver. This is the right thing to do, but the HF Mon also contains a DC offset proportional to the frontpanel knob setting. We should instead subtract the LF Mon from the Cathode Mon to get a lowpassed version of the control signal that we can use as an error signal in the temperature loop.

Attachment 1: 54E0D1B4-D614-4D0C-8313-E09CE2EFC7BA.jpeg
Attachment 2: SingleLaserSingleCav-15.jpg
3010   Wed Oct 12 15:26:51 2022 aaronDailyProgressPSOMA3 loop locking

[aaron, shruti]

We worked out an expression for the PLL error signal starting from the fields on the REFL PD. See attachments for scratch work.

$\mathrm{error}_\mathrm{PLL} = E_{S0}E_{N2}\cos\phi_\mathrm{LO}[\omega_\Delta t\cos\phi_N + \sin \phi_N]$

From this, we can see that changing the PLL input offset changes the relative phase of the N and S lasers. It also slightly changes the PLL gain (which vanishes when the lasers are out of phase, and is only second order in phi_N when the lasers are in-phase).

Also, changing the LO phase changes the PLL gain.

Based on this equation, we can rationally set the LO phase and PLL input offset by:

1. With the loop stably locked, adjust the input offset to minimize the DC level on the BEAT PD (which implies the lasers are being locked in-phase and thus maximally interfering on the BS)
2. Slightly increase the controller gain until the loop starts to oscillate
3. Tune the LO phase in the direction of increasing loop oscillation until the lock breaks.
4. Decrease the controller gain, then reacquire lock and tune the LO phase in the direction of increasing loop oscillation. Repeat until changing the LO phase in either direction decreases the loop oscillation -- that's the optimal LO phase setting.

Shruti used this procedure to tune the LO phase and offset.

Attachment 1: IMG_3513.jpg
Attachment 2: IMG_3514.jpg
3009   Wed Oct 12 11:34:08 2022 aaronDailyProgressPSOMA3 loop locking

Unfortunately, locking with 2x PDH and using the beat note signal to read out frequency noise is not as simple as it sounds. The problem is basically that the cavity can't distinguish between the N and S laser fields for the purpose of generating separate PDH signals for each laser -- and we don't want it to, or PSOMA wouldn't work as an amplifier.

Attachment 1 shows the loop diagram and the equation for the power incident on the REFL PD.

When trying to lock with two PDH signals, this is what happens:

1. One of the lasers (say the S laser) locks to the cavity
2. Bring the N laser closer to the S laser frequency.
• Because the cavity FSR is large, the N laser is far from the S laser frequency even if their free running frequencies were nearby. If f_N > f_1 and the N carrier amplitude is larger than the S laser's f_1 sideband amplitude, the cavity will lose lock when f_N=f_1
• Even if f_N < f_1 when the S laser is locked (or the N carrier amplitude is reduced to be lower than the f_1 sideband amplitude), once f_N is within the S PDH lowpass filter bandwidth of the cavity resonance, the S PDH error signal will contain an extra noise term due to the beat between the N carrier and S f_1 sideband. This noise term can cause the S laser to lose lock, so the N carrier must be small relative to the S carrier (or there must be some other scheme for removing this noise before feeding back to the S laser)
3. Supposing the N_0 x S_f1 term is small enough for the S laser to maintain lock, we can now engage the N PDH loop with the N laser near the cavity resonance
• If the N carrier was made small relative to the S carrier, the REFL signal at f_2 will be dominated by the beat between S laser carrier and the N sideband field. Again, maybe there's a clever way to remove this noise and recover the N laser's PDH signal, but I don't see it yet.

If instead we lock the two lasers with a PLL then lock to the cavity with one of the PDH signals (for example, the S f_1 sideband)

1. Phase lock the two lasers with the PLL loop such that they constructively interfere at the cavity input
2. Tune the S laser frequency close to the cavity resonance
3. Engage the loop to lock the S laser to the cavity.
• As long as lock acquisition is smooth enough and the cavity quiet enough, the PLL can maintain lock
• The PDH lock will need to deal with the extra noise due to frequency noise between the N carrier and S_f1 sideband
• Decreasing the N laser power reduces the coupling of N-S relative frequency noise into the PDH signal, but could also increase the residual noise of the PLL. There might be an optimal choice of N laser power.

The downside of using a PLL is that we can't directly read out the cavity's frequency noise at the beat note, since the note is being stabilized in a coupled loop. We need to do some complicated loop algebra to interpret the three available error signals.

Attachment 1: IMG_3512.jpg
3008   Mon Oct 10 16:07:53 2022 ranaDailyProgressPSOMA3 loop locking

Agree with final bullet: better to go for 2 PDH loops locking to the cavity, rather than something mixed. Having 3 loops on at the same time is pretty difficult to do since the PLL will modify the loop shape of the second laser loop.

Shruti, can you check that the modulation frequencies for the 2 PDH loops don't do something funny? i.e. regular mode scan plot.

3007   Thu Oct 6 16:26:04 2022 aaronDailyProgressPSOMA

This week, I've just been trying to get both lasers locked to the cavity. Here are some things I've tried / findings.

• Modulating the N and S lasers at different frequencies, so we can demodulate the PLL and PDH loops at different frequencies. The N laser is modulated at 77.37 MHz, while S laser is modulated at 33.59 MHz.
• With the S laser locked to the cavity, the direct beat note wanders on the spectrum analyzer. However, feeding some of the S laser control signal to the N laser mostly stabilizes the beat note to within 1 MHz. To offload some of the N laser control from the PLL to the PDH loop, I drive both the N and S lasers with the same PDH control signal (up to an overall gain).
• My procedure is basically to the set the S laser frequency close to the cavity resonance, then adjust the N laser current until the laser frequencies are close, with both loops engaged. The PLL typically acquires a noisy lock, and the PDH loop is able to prolong cavity flashes but not entirely lock. Eventually the PLL reaches its dynamic range and loses lock.
• I'll keep trying Lock loss does seem to occur when to improve the loop shape. Trying to note the frequency of oscillations just before losing lock, and reduce gain in either the PLL or PDH controllers.
• I did try locking with two PDH error signals (one for each laser) rather than first locking the lasers with a PLL then trying to lock the PDH. At the time, I was only mixing 10% of the N laser with the S laser, so the PDH signal for the N laser was much weaker. I've since removed the 10% pickoff BS from the N path, so I'll try again with full power from both lasers on the cavity.

Attachments

1. Overall moku configuration
2. PID servo controller in slot 2, showing the PLL controller settings
3. PID servo controller in slot 2, showing the PDH controller settings
4. PID servo controller in slot 3, which is just used to add the PDH control signal to the PLL control signal before driving the N laser
5. Mixer in slot 1, which demodulates the REFL RF signal
6. Mixer in slot 2, which demodulates the BEAT RF signal
7. Typical behavior where the PLL locks, then the cavity flashes until eventually the PLL oscilaltes and loses lock. The red trace is the PDH error signal, the blue is the PLL error signal.
Attachment 1: IMG_0120.PNG
Attachment 2: IMG_0117.PNG
Attachment 3: IMG_0118.PNG
Attachment 4: IMG_0119.PNG
Attachment 5: IMG_0121.PNG
Attachment 6: IMG_0122.PNG
Attachment 7: IMG_0116.PNG
3006   Mon Oct 3 17:14:56 2022 ChrisElectronicsPSOMACurrent driver repair/upgrade

Another one of the D1200719 current driver boards (S1600202) was in the EE shop for an upgrade to v7, to fix high frequency oscillations and crossover issues. An annotated schematic is uploaded to the board’s DCC traveler.

The upgrade went fine, but alas, the board then suffered a power supply reversal during final testing in the cryo lab, sending it back to the shop for replacement of several busted components.

Due to supply chain issues, a couple of substitutions had to be made:

• RB160M-60 → RBR1MM60ATR

Tests to check the basic functionality:

• A 25 Ω dummy load was connected for testing (note: this component must be rated for high power dissipation)
• The unit’s nominal current draw from the supplies was about 200 mA
• The response of the coarse and fine adjust knobs was measured. (Saturation occurs above a coarse knob setting of 7, when driving the 25 Ω load)
• Noise spectra were measured on the SR780 analyzer at the HF and total current monitor outputs, with a coarse knob setting of 4. (Both were nearly white, ~10 nV/rtHz HF and ~20 nV/rtHz total)
• A wideband transfer function from HF modulation input to HF monitor output was measured, using 4395A analyzer + ZSC-2-1 splitter into the differential input (which was driven single-ended)
• The transfer function from the DAC input to the total current monitor output was checked (showing the expected 40 dB/decade filtering above 10 Hz)

Attachment 1: knobs.pdf
Attachment 2: spectra.pdf
Attachment 3: AG4395A_16-09-2022_172805.pdf
Attachment 4: data.zip
3005   Thu Sep 29 15:59:45 2022 aaronDailyProgressNoise Budgetlasers phaselocked, but can't simultaneously lock cavity

Summary: I phaselocked the North and South Rio lasers and characterized their frequency noise, but I haven't been able to simultaneously lock the PSOMA cavity.

### Moku setup

I am phase modulating the South laser with our OCXO at 33.59 MHz. The LO signal is sent to Moku, which demodulates the beat note and REFL signals. The Moku produces a digital LO by locking a PLL (100 Hz bandwidth) to the analog LO from the OCXO.

By using a single RF modulation frequency, I have enough Moku IO channels to do all my locking and transfer function measurements (one input channel for excitation and two monitor channels for transfer functions remain after locking). The setup is in attachment 1, and channel list in the table below.

 Moku channel Signal In1 REFL In2 Beat RF In3 OCXO LO In4 Excitation Out1 S laser control Out2 N laser control Out3 monitor channel Out4 monitor channel

The PLL error signal is derived by demodulating the demodulating the beat note between the North DC field and South sideband field. The mixer and controller configurations are in attachments 2 and 3 respectively.

The other two Moku instrument slots are a mixer and controller configured as in our previous work with the PDH loop.

### Beat note PLL

I was able to lock the PLL with a PI controller, but found that the loop was more stable (smaller residual fluctuation in the REFL and beat DC signals) with a PID controller as in attachment 4.

My procedure for locking the PLL is

1. Tune the S TEC such that the cavity is flashing (not necessary for PLL, but we want the frequency close to the cavity resonance eventually)
2. Use the N laser current driver fine adjustment knob to tune the N laser frequency closer to the S laser frequency. When the direct beat note approaches 0 Hz, the DC level on the beat and REFL PDs will fluctuate at the detuning frequency.
3. Turn on the PLL at the output of the controller. I use the controller output because the Moku's integrator seems to windup even with its input disconnected (maybe a numerical precision issue).

I set the sign of the PLL such that when locked, the N and S lasers interfere constructively at the REFL PD and destructively at the beat PD.

### North laser actuator transfer function

I used the SR785 and delay-line frequency discriminator (DFD) to measure the transfer function from the N laser driver's HF input port to the DFD output. We calibrated the DFD from V to Hz earlier. I also measured the transfer function from the N laser driver's HF mon port to the DFD output. See attachment 5 and 6 for the transfer functions from control to laser frequency and HF mon to laser frequency for the S and N lasers (N laser data taken this week, S laser from earlier).

### PLL open loop transfer function

I used the SR785 and HP____ to measure the open loop transfer function of the PLL from 10 Hz to 10 MHz. Below 1 kHz, the measurement lost coherence. I tried many combinations of averaging and source amplitude shaping, but wasn't able to make a good transfer function measurement below 1 kHz.

The UGF of the PLL is ~201 kHz. Very stable! I can easily tune the temperature to find cavity resonances without losing PLL lock.

Result in attachment 7.

### NS beat note frequency noise

The frequency noise of the NS beat note should reflect the frequency noise of both the North and South lasers, as well as any additional sensing noise in the loop.

Attachment 8 is the raw in-loop noise measured on the error and control signals. Attachment 9 is the in-loop noise measured at the control point. I measured the actuator gain (HF input to laser frequency) but not the plant gain (laser frequency to error signal), so I can't estimate loop-corrected noises.

There are still some unresolved issues:

• I had to introduce a mysterious factor of -20 dB to the agilent spectrum analyzer data for it to match the SR785 data near 100 kHz. Need to investigate why
• still would like to measure the OLTF below 1 kHz
• It's somewhat surprising that the noise peaks near 1 kHz, when the OLTF measurement suggests the UGF is near 200 kHz.
• Once again, I don't think I measured enough transfer functions to fully estimate the loop-corrected noise using both the control and error signals. Makes it hard to draw conclusions about whether the UGF inferred from the OLTF is correct.
• The in-loop control signal should be a good measure of the loop-corrected noise below the UGF. I'm surprised that the low frequency behavior is not 1/f.
• The absolute frequency noise level around kHz to MHz looks OK... but given the other issues, I don't yet trust it.
Attachment 1: IMG_0108.PNG
Attachment 2: IMG_0107.PNG
Attachment 3: IMG_0109.PNG
Attachment 4: IMG_0106.PNG
Attachment 5: ctrl_to_freq.pdf
Attachment 6: HFmon_to_freq.pdf
Attachment 7: LoopTFs.pdf
Attachment 8: Spectra_VrtHz_20220929.pdf
Attachment 9: ClosedSpectra_HzrtHz_20220929.pdf
3004   Thu Sep 22 17:23:15 2022 aaronDailyProgressLasermodified fiber path

I modified the fiber path to send the North and South beams both to the cavity. I cleaned all fiber faces before attaching them, and also re-laid the fibers to run more cleanly (fewer loops and larger bend radii). The updated path is in attachment 1.

Attachment 1: 3F0DE399-F293-405C-9B68-550C93BE7446.jpeg
3003   Thu Sep 22 16:15:44 2022 shrutiComputingDAQUpdated x1oma

[shruti, aaron]

We updated the real-time model to read the HF mon signal of the laser current driver labeled '...SLD_PDH_CTL' from the "Analog Monitor" DB9 port instead of the "HF MON" BNC port.

Then, we built the model following instructions roughly in elog 2679 and elog 2624 (We had to 'make' all models first before building x1oma to get it to build without errors).

To verify that ndscope was showing what we wanted, I used a BNC-DB9 breakout board to drive pins 3,8 differentially using a function generator and saw that an expected sinusoidal signal was seen on the screen. We used documents linked in elog 2883 to determine which the right pins were.

But, weirdly, after disconnecting the cable from the function generator and reconnecting it to the current driver (while the driver was turned off) the counts on seen on ndscope were still ~22000. We will check this again when our lasers are back on after the fiber box modification.

#### Moku Pro

ip: 10.0.5.217

3002   Thu Sep 22 11:56:05 2022 aaronDailyProgressPSOMANorth laser locked to cavity

I measured the transfer function from the Moku control point to the DFD output this morning. The signal path was Moku control -> +14 dB output stage -> N current driver -> DFD -> SR560 (unity gain) -> Moku frequency response input. Attached is a screenshot of the measurement result. We can use this to calibrate the noise and transfer function data that Shruti measured yesterday.

However, note that the current and TEC setpoints were different during this measurement than our recent noise spectra. We needed to increase the laser power for both N and S lasers to get a 10 dBm beat note for signal for the DFD (even with our +20 dB RF amplifier). I think this is because we had been mixing 90% of the N beam with 10% of the S beam at the beat note PD, but switched to 10% of each beam in order to send more power from the N laser to the cavity for locking purposes. We could add a beefier (or second) amplifier next time to operate at the intended current and temperature settings.

Attachment 1: MokuFrequencyResponseAnalyzerData_20220922_114724_Nctrl_to_DFD_Screenshot.png
3001   Tue Sep 20 16:31:07 2022 shrutiDailyProgressPSOMANorth laser locked to cavity

#### 1. LIGO custom driver for North laser

I installed the LIGO custom current driver that Chris recently fixed and updated onto the rack. Once the laser was turned on, first I looked at the Beat DC output at the same settings the other driver was set to [Coarse: 4.89, Fine: 5.0] which showed -2 V. Moving around the temperature I saw the beat on the AG 4395A spectrum analyzer.

#### 2. Preparation for locking North laser with the "north" EOM

[Attachment 1: updated fiber setup diagram]

Then I turned down both knobs and turned off both laser current drivers.

In the fiber box setup, between the north Faraday and north 90-10 beat pick-off beamsplitter I connected the other EOM. So the North laser has its own EOM in its path.

To independently lock this laser, I switched south<->north at the input to their 90-10 beamsplitters, which seemed to be the most convenient point to do so.

#### 3. Locking

Then, using the same settings on the Moku multi-instrument setup with the exact same PID and filter coefficients, I was able to lock the laser to the cavity by moving around the temperature to a higher setpoint. The refl power without the cavity locked seems lower than for the south.

Also just noticed that the north laser, for the same current settings has a mode-hop region around 7.9 kOhm with the TEC. For the south laser, it was ~6.9 kOhm.

#### 4. OLTF

With the Frequency Response Analyzer in Multi-instrument mode, using the output to inject a small signal at the input of the PID controller and measuring the error signal before and after summation, I plotted the open-loop transfer function to find and found a UGF of ~126 kHz.

[Attachment 2: green plot is ChA/ ChB where ChA is error signal before summation 'err' (in red) and ChB is the error signal after the summation point 'diff' (in blue)]

Attachment 1: Y4Q1.pdf
Attachment 2: MokuFrequencyResponseAnalyzerData_20220920_172257_diff_err_OLTF_Screenshot.png
3000   Thu Sep 15 10:30:01 2022 aaronDailyProgressPSOMAnew noise spectrum

I'm measuring the noise spectrum. Here's what I want to do:

• Measure actuator response by measuring transfer function from control point to DFD output (and checking the DFD calibration)
• Measure plant response by recording a PDH error signal sweep
• Lock the cavity and record noise curve from 10 Hz to 10 MHz
• Measure loop transfer functions (directly measure ctrl/diff, err/diff, err/ctrl)

### Delay-line frequency discriminator calibration

The configuration for calibrating the delay line is Marconi signal generator --> DFD --> SR560 (unity gain) --> oscilloscope

I observed that the delay line output is sinusoidal when sweeping the Marconi carrier from 1 MHz to 200 MHz (attachment 1 shows from 1 MHz to 100 MHz). Here are the DFD critical points:

 Marconi carrier frequency (10 dBm) DFD output 37 MHz ~0 V 73 MHz 135 mV 109.01 MHz ~0 V 143 MHz -154 mV

Since 73 MHz to 143 MHz is pi radians for the DFD, and the amplitude of the sine response is 290 mV / 2, this implies the slope of the DFD at the 109 MHz zero crossing is 6.5e-9 V/Hz.

As a check, I can observe the response to a known FM signal from the Marconi. With the Marconi carrier set to 109.01 MHz and SR560 G=100, I introduced an 800 kHz FM deviation at 20 kHz and observed a 880 mV pkpk amplitude oscillations on the DFD output. This implies 880 mV / 2 / 100 / 800e3 Hz = 5.5e-9 V/Hz response of the DFD at 109.01 MHz.

For the analysis, I'll use the DFD calibration from the pkpk voltages and frequencies (6.5e-9 V/Hz), but would only trust this calibration to ~10%.

### Actuator calibration

Next, I measured the actuator gain (A) with the Moku frequency response instrument by exciting at the Moku control point and measuring the frequency response with the DFD. I measured the DFD output / control point and the HF mon / control point transfer functions.

I tuned the beat note between N and S lasers to 109 MHz. The TEC setpoint of the S laser is 7.260 kOhm during these measurements, and the SR560 provides a unity gain buffer after the DFD. I amplified the beat note signal to 10 dBm with a +20 dB RF amplifier before the DFD. The configuration is excitation -> actuator (Moku output gain + current driver) -> +20 dB RF amp -> DFD -> moku frequency response instrument.

I found an error in our previous actuator transfer function measurement (converted to dB a magnitude that was already in dB, which gave a deceptively flat transfer function). Attachment 2 has the correct transfer function from Moku (internal) control point to DFD output, as well as HF mon to DFD output in Hz (calculated by dividing control-to-DFD by control-to-HFmon). Note that the DFD itself has a 1.9 MHz lowpass filter, so these transfer functions aren't the same as the transfer functions to laser frequency above 1 MHz.

Since Chris has measured the laser driver transfer function to be flat to at least 10 MHz, I'm just assuming the actuator transfer function is flat above where the SR560 1 MHz LPF becomes visible in the transfer function... but this is not a great assumption, because you can see that the actuator TF falls off by more than a factor of 3 between DC and 1 MHz. I suspect this is due to the DC bias current drive being filtered by an RF bead (unspecified inductance) at the laser diode cathode; we may have a flatter current-to-frequency response by driving at the Rio laser's RF input.

### Plant calibration

Next, I set the PDH phase by introducing slightly more servo gain than we typically require and maximizing the loop oscillations as I tune the PDH phase.

I set the PDH offset to minimize the REFL RMS fluctuations with the laser locked on resonance. The PDH offset is the only setting I changed throughout the below measurements (typically minimizing REFL RMS fluctuations with a new choice of offset before each measurement, since I found the offset drift to be significant on O(10 min) timescales).

I then used the Moku function generator to provide a triangle wave at ~300 Hz and ~3 kHz, and recorded the PDH error signal as the laser frequency swept through the DC 00 mode resonance and both RF sideband resonances.

The fit of the PDH transfer function wasn't great, and I still need to extract the PDH response and cavity pole from the recorded curves. Stay tuned.

### Transfer function measurements

I used the Moku frequency response instrument to measure the loop transfer functions ctrl/diff, err/diff, and err/ctrl between 10 Hz and 10 MHz in increments of 2 decades. I'm still having trouble maintaining coherence and lock at low frequency during the measurement time, which was about 45 min total for the three transfer functions.

### Noise spectrum

Lastly, I recorded the noise spectra of the error and control signals with the Moku spectrum analyzer. The TEC setpoint was about 7.3 kOhm.

Don't trust the y-axis yet. Haven't applied new actuator calibration.  Updated noise spectrum is in attachment 4. The calibration methods discussed in NoiseSpectraCalibration.ipynb give consistent results. The closed-loop estimates from control and error points cross over around the UGF frequency implied by the OLTF. The frequency noise around 1-100 kHz is a factor of a few above the frequency noise claimed by the Rio laser data sheet; we should add some curves for expected noise sources to see what we expect to be limiting, but looks believable overall.

The noise budget is up to date on our git repo page.

### Attachments

1. Response of the DFD from 1 Mhz to 100 Mhz. Was actually operated on the next fringe at 109 MHz, but linearity held (missed the photo op)
2. Actuator transfer function
3. Loop transfer functions
4. Calibrated noise spectra
Attachment 1: 46563583-8EAE-4B6D-B91B-1C115D7E9C47.jpeg
Attachment 2: Actuator_TF_full.pdf
Attachment 3: LoopTFs.pdf
Attachment 4: AllSpectra_HzrtHz_20220915.pdf
2999   Wed Sep 14 11:13:44 2022 aaronDailyProgressPSOMAupdating noise curve

Attachment 1 shows that the cavity remained lock throughout the night, and I can confirm that the mode was 00 in the morning.

Attachment 1: Screenshot_from_2022-09-14_11-13-44.png
2998   Tue Sep 13 10:19:39 2022 aaronDailyProgressPSOMAupdated noise curve: configuration used

It does make sense to route the PDH error signal to the controller via the Moku's internal bus, do you have the data so we can compare to the previous configuration?

In the meantime, I'm repeating the noise and TF measurements with the 785.

I noticed a few unexpected changes at start of day

• 01 is now the dominant mode in the transmission spectrum (2.4 V on TRANS, compared to 1.29 V for the 00 mode).
• I'm seeing occassional lock loss in 00, even with the offset nulled and after adding an SR560 unity gain buffer with 10 Hz, -12 dB/oct LPF on the TEC tuning.
• Also saw 2 V on REFL MON with the cavity unlocked. I had been operating with 0.5 - 1 mW on REFL, because we had noticed saturation of the RF signal at higher powers. However, I didn't see peak distortion for the 33.59 MHz sidebands on an oscilloscope with the cavity unlocked/locked, and with the cavity locked the HP 4395A SA reports -10 dBm at the sideband frequency (well within the 1811's linear range). Seems fine for now.
• I noted 2.75 mW into the cavity without PBS in the launch path, and 2.064 mW into the cavity with PBS and HWP1 tuned to maximize the power in S (transmitted through PBS). The optimal HPW1 angle today was unchanged from the last time it was set, indicating negligible polarization drift (at least at this snapshot).

Then Moku detected a mandatory firmware update. After updating, the instrument configuration from yesterday was lost. If you did successfuly save the configuration yesterday, something about the firmware update reverted us to an older saved configuration. We should definitely prioritize scripting our Moku setup so we can operate in reference configurations most of the time.

### mode matching

I adjusted SM1 and SM2 to improve the mode matching by maximizing TRANSMON level with the cavity locked. However, the REFL MON was only 1.73 mW locked / 2.13 mW unlocked ~ 19% MM efficiency.

I then iteratively moved ML2 and adjusted SM1/2 in an attempt to find a better telescope solution, but was mostly unsuccessful. I did note that the beam is about halfway between center and the right edge of ML2, so we might need to do another round of telescope adjustment and from-scratch alignment to find a better solution that passes through the center of the modematching lenses. Or, could require on-axis adjustments to ML1.

Lastly, I adjusted SM1 and SM2 to maximize the ratio of TRANS MON / REFL MON. The best mode matching I found was still only 20-25% based on REFL MON, so this still needs some work.

Is this a good way to deterministically improve mode matching? I've started to doubt it and could use advice.

### Polarization cleanup

I added a PBS between SM2 and MC1, oriented to transmit S and reject P polarization downwards (toward the table). I directed the P beam to a beam dump mounted with 1/2" posts. The PBS is mounted in thorlabs' cage system cube prism mount, which seemed to work well for this application.

### Loop shape and setpoints

I also increased the PI corner of our controller to 70 kHz, closer to where I measured the cavity pole to be. I had to decrease the overall loop gain by 3 dB to avoid some oscillation. I observed qualitatively quieter locks (less rms noise on REFL and TRANS mons) and more stability (could tap the table and maintain lock).

I set the PDH phase by tuning to maximize the DC offset of the PDH error signal after the LPF while the cavity was flashing 00. I also checked that this choice of phase has the maximum PDH gain by locking the cavity with enough controller gain to observe some oscillation in REFL MON, then tuning the PDH phase to maximize those oscillations. The two methods gave the same PDH phase to ~degree.

I then set the PDH offset by minimizing the REFL RF rms fluctuations before the mixer (5-6 mVrms) with the cavity locked.

### Noise measurement

I used Moku's spectrum analyzer and frequency response instruments to measure the noise from 10 Hz - 10 MHz at the difference (error - excitation) point and the control point (Moku's internal control point, NOT the HF mon). The excitation was off during noise measurements, so the difference point is the same as the error point. I need to recalibrate the open loop control-to-frequency transfer function with the DFD for this new monitor point.

I also measured transfer functions from error to difference monitor points (open loop gain), and from the error to control monitor points (servo gain), though didn't extend these measurements to as low in frequency (only down to few 100 Hz).

### Analysis

I added a lengthier description of the calibration procedure to NoiseSpectraCalibration.ipynb, and am adding an option to save/load a reference noise curve for comparison. However, I wasn't able to calibrate the raw noise at the error point into Hz/rtHz with the data I took yesterday: I didn't measure the plant gain (either by PDH response, or above the UGF by driving the control point), so can't use |P| for calibration; and I didn't measure err/ctrl, so can't use |AP| for calibration.

I could estimate the noise below the UGF using just the control signal and an older measurement of |A|, but I'm not sure I can trust the actuator's Hz/V calibration at a new temperature setpoint. I'll be sure to make the complete set of measurements next time.

I measured a UGF at ~87 kHz

### Attachments

1. Loop transfer function measurements. I only measured the OLTF and controller gain, and the controller gain I accidentally measured diff/ctrl when I should have measured ctrl/diff. I'd like to repeat these across the full frequency span over which the noise is measured, and also measure the actuator*plant gain using err/ctrl.
2. Raw noise at the control and error mon points in V_rms/rtHz

Edit: By the way, I also briefly observed the 33.59 MHz AM fluctuations on the South laser using the 1611 beat note PD with the North laser off (so I saw only the South laser AM, with no beat note from the second laser). With 0 V DC offset on the RF modulation, the AM sideband was -82 dBm. I was able to reduce the sideband to <-90 dBm by tuning the DC offset to -800 mV. I saw that the REFL DC power was decreased after introducing this offset, but didn't investigate whether this was due to a polarization rotation or something else. Will probably continue this line of testing a bit more carefully later (add an RF amplifier, adjust HWP1 polarization, check the noise spectrum, etc).

Attachment 1: LoopTFs.pdf
Attachment 2: Spectra_VrtHz_20220913.pdf
2997   Mon Sep 12 16:32:16 2022 shrutiDailyProgressPSOMAupdated noise curve: configuration used

### Attachment 1

Following Chris' suggestion, I changed the error signal sent from the Lock-in to the PID controller to be a digital signal bus [Signal Bus 1] instead of the analog connection between two Moku ports (as it previously was). This was to prevent excess ADC-DAC noise. In order to account for -20 dB attn that was at the PID input, I changed the gain on the Lock-In from 40 dB to 20 dB. When we then tried locking, the cavity seemed to continue to lock easily. Therefore, I think that the previous servo gain was preserved.

Also, today, I tried to measure the noise spectra using the Moku itself. The second block on the Multi-instrument panel shows the spectrum analyzer with the Ctrl signal in Ch A and the error sig in Ch B.

### Attachment 2

There was still some non-zero input offset observed in the PDH signal either due to residual AM or some electronic offset. To me, it seemed that not adjusting this offset correctly really caused some sort of cascaded effect in the form of oscillations in the slow temperature control loop. Therefore, within the PID app, I adjusted the input offset to correct for the average DC level in the demodulated PDH error signal. Once this was done, turning on the slow servo maintained the lock properly and resulted in a control signal around zero. This attachment shows where the offset was adjusted and the red trace is the PDH error signal.

### Attachment 3

To measure the servo transfer function in-loop, I used this configuration. The small signal is being sent to the input of the PID controller, and the error point (after summation) and the control point were measured.

### Attachment 4

I used this setup to measure the open loop TF. The small signal is injected at the same point as in Attachment 3, and the PDH error signal is measured before and after the summation point where the signal is injected.

#### Edits (13-Sep-22)

The data is on gitlab, still working on the analysis.

The configuration saved to multi-instrument is what we had prior to my changes in this elog.

### Attachment 5

Raw noise spectral data with reference from previous elog.

Next To-Do:

• Calibrate the delay line with the HF mon for for the settings used while measuring noise/TFs
• Calibrate the control output of the PID to the HF mon (the difference is a buffer, but not sure what the gain is experimentally)

Attachment 1: 472F2108-9470-4E43-9A69-ECCA7CCF30D1.png
Attachment 2: 991F817C-11F3-4EF2-A7C9-2D6CA7E4F599.png
Attachment 3: A5C21049-D885-4A88-918D-2EB8F3F5A441.png
Attachment 4: 11C25142-9B68-46BA-98D2-1B363AED634D.png
Attachment 5: Spectra_VrtHz_20220912.pdf
2996   Fri Sep 9 10:19:25 2022 aaronDailyProgressPSOMAupdated noise curve

The noise spectra we took yesterday were surprisingly noisy and had very little low frequency resolution (they were full span SR785 spectra). I repeated the measurement at 1 Hz, 8 Hz, and 128 Hz RBW. I gave these data files descriptive names of what ch1 and ch2 are measuring so I can identify them; there were two files in 20220908 with only timestamps for identification, and I don't know how to use them.

To convert the in-loop noise measured at the PDH error point to in-loop noise measured at the control point, I needed to inject a 1 MHz tone and compare its amplitude at the PDH error and at HF mon (same measurement as earlier, but we were using the LB servo). I found PDH error / HF mon control signals were separated by 33.92 dB, and updated this calibration factor in calpar.yml.

Attachments

1. Screenshots of PDH error signal. The separation of the sidebands and width of the DC error signal lets me estimate the cavity pole at 79 kHz. The PDH error signal for the DC field is 522 mVpp, so the PDH response is 657 mV/MHz.
2. Raw noise at the HF error mon and PDH error mon points in Vrms/rtHz
3. In-loop frequency noise in Hz/rtHz. The HF mon curve is the control signal, and has been calibrated using our reference voltage-to-frequency response measured by the DFD. The PDH error mon curve has been calibrated by undoing the cavity pole (estimated at 20 kHz) and applying a flat 33.92 dB gain to refer to the HF mon point, then applying the same HFmon-voltage-to-frequency response. The loop correction has not been applied in attachment 2
• The error and control curves cross just above 10 kHz, which is unexpected because we estimate the UGF to be ~31 kHz.
• However, it makes sense that the noise falls approx like 1/f^2 between 100 Hz and 1 kHz
• The in-loop noise is comparable or maybe somewhat lower than our last measurement with the LB servo controller, but we didn't take a OLTF measurement then so can't make a direct comparison of the plants
4. Open loop frequency noise in Hz/rtHz. I couldn't get the estimates at the error and control points to match. Will try to remeasure and reanalyze next week.
Attachment 1: E6F0429E-A3B6-4A72-8F10-518C8C29C770.png
Attachment 2: Spectra_VrtHz_20220908.pdf
Attachment 3: ClosedSpectra_HzrtHz_20220908.pdf
Attachment 4: OpenSpectra_HzrtHz_20220908.pdf
2995   Thu Sep 8 10:08:34 2022 ranaDailyProgressPSOMAcavity locking for hours

that's great that its now stable to allow for characterization. But I think if you change the DC light level on the RFPD it changes the overall gain, but not the shape of the plant.

It would be cool if there's a way to make a state machine so that we could have Guardian like logic to click buttons for us, internally to the Moku. The other way is to make a MEDM screen that controls the Moku through a pymoku interface, and then we can acquire the data in CDS and control the lockinig that way.

2994   Thu Sep 8 09:24:53 2022 shruti, aaronDailyProgressPSOMAupdated noise curve

[aaron, shruti]

With the slow temperature control on, the cavity had remained locked for hours. Today, we also noticed that the temperature must be at a good place (~7.3 kOhm on the TEC) for the slow loop to function properly. It kept getting the cavity out of lock when the temperature roughly corresponded to 7.1 kOhm on the TEC display. This might have been due to the PDH offset being slightly different at the two TEC setpoints, as we later observed O(V) drifts in the PDH offset over hour timescales.

Measured a few noise spectra. With the fans turned off, the transmission looks the quietest it has been in the past week.

#### Added offset to get a less noisy lock and zero control signal

With the cavity flashing, we noticed that there was a ~-422 mV offset at the output of the Lock-in amplifier used to get the demodulated PDH signal and we compensated it there before sending it to the PID controller for locking by adding a 422 mV offset. This reduced the offset in the control signal (on ndscope the counts decreased from -3000 to -100, also a Moku screenshot to be attached), and then with the slow temperature control, the control signal mean returned to 0 while locked.

#### Also measuring transfer functions.

After we measured a set of transfer functions, we noticed the control signal level drift back to 400 mV. So we reset the offset to zero.

### Afternoon

We repeated the noise spectra measurement at HFmon and PDH error points (picking off the PDH error with a BNC T from the Moku front panel output #3). We also measured several transfer functions (see attachment 1 for definitions, attachment 2-4 for state of Moku during measurements):

• PDH error / excitation
• HF mon / excitation
• Diff mon / excitation
• PDH error / Diff mon

Before each measurement we ensured a stable lock by nulling the PDH offset (turned off the loop with the integrator reset, and introduced an "Output offset" after the mixer+lowpass+gain in the Moku lock-in instrument). We noted that the PDH offset drifted by 100s of mV within one measurement time O(10 min). The transfer function measurements are in attachment 5. Notes about the transfer functions:

• The UGF ~31 kHz, and the phase margin is large (275 deg). This suggests we could increase the gain 10-20 dB and still have a stable loop.
• There is some phase advance near the 26 kHz PI corner, suggesting our cavity pole is higher than estimated (makes sense, since I didn't account for losses). We could increase the PI corner for some free gain at low frequency.
• We only measured the control / exc transfer function below 1 kHz, because the coherence fell off sharply at lower frequency. Increasing the excitation amplitude caused lock loss, and increasing the averaging taxed my patience.
• I made two estimates of the OLTF, and both agree. The curve between 1 kHz and 100 kHz is calculated by dividing two transfer functions: (PDH error mon / exc) / (difference mon / exc). The curve that extends from 1 kHz to 10 MHz is directly measuring (PDH error mon / difference mon), and splices data from both the Agilent and SR785 SAs.
• The TFs look OK to me, but I need to do more sanity checks

still need to plot the frequency noise we measured today, including new loop corrections.

I also swept the current drive HF input while measuring the PDH error signal on the Moku, but haven't yet plotted the data.

Attachment 1: 41835C83-4332-4E7F-AFDE-DB208B22E392.jpeg
Attachment 2: DF36ED03-67C1-4BE8-9CE8-F30D11F73A94.png
Attachment 3: 604CC6A6-710F-4B42-94E6-0D9201ECAA6B.png
Attachment 4: 23BB07E8-7C02-4496-BEC2-86184D3B5DB1.png
Attachment 5: LoopTFs.pdf
2993   Wed Sep 7 13:31:13 2022 shruti, aaronDailyProgressPSOMAcavity locking for hours

[shruti, aaron]

We were able to get the cavity somewhat locking after re-aligning SM2, i.e., the lock would flicker intermittently and the trans/refl looked quite noisy. Played with adjusting the gain and loop shape.

afternoon

Continued improving the loop shape. Found that changing the polarization at HWP2 to change the DC level on the REFL PD is an easy and smooth way to change the low frequency gain. By increasing the power incident on REFL PD, we were able to reduce the integrator gain and low frequency gain limit (but kept the proportional gain about constant, since above the cavity pole the noise is not much affected by the DC level of REFL PD).

With some empirical testing and adding slow temperature control from the CDS system, the cavity maintains lock for O(hours). Attachment 1 are minute trends showing some cavity locking activities for the first hour, then over an hour with the cavity locked.

The lock can also be maintained or reacquired with both HEPA FFU set to 'low'. Setting to 'high' causes lock loss.

The control signal at the HF mon point has about 300-400 mVrms fluctuations while locked. The signal continues to be dominated by the 40 Hz cantilever mode.

I tried to measure the noise at HF mon point using Moku, but the spectra looked suspicious. I don't believe the curves so I'll repeat the measurement tomorrow.

Update: cavity remained locked for most of the night, and was able to reacquire lock without assistance. The temperature control loop also properly shut itself off during lock loss. Attachment 2

Attachment 1: Screenshot_from_2022-09-07_17-11-06.png
Attachment 2: Screenshot_from_2022-09-08_09-22-50.png
2992   Wed Sep 7 09:27:35 2022 aaronLab InfrastructureHVACparticle count

quick particle trend, goes back 21 days to cover the time since the last trend was posted.

Attachment 1: Screenshot_from_2022-09-07_09-31-33.png
2991   Tue Sep 6 17:51:39 2022 aaronDailyProgressPSOMAmoved SM2

[aaron, shruti]

We locked the cavity throughout the day, but repeatedly couldn't re-acquire lock at the same nominal settings after trying different gain/corner frequency/etc.

Eventually we moved the second input steering mirror (SM2) NW to attempt to improve the mode matching. Still getting the cavity flashing.

2990   Fri Sep 2 14:48:35 2022 aaronDailyProgressLab Workcalibrating error and control signals

[rana, shruti, aaron]

We added the new box around the cavity. Also rested a label from our label maker against the back of the cantilever to damp its motion.

After adding the box, had to adjust the input alignment again. We adjusted the mode matching throughout the day, but found that the second input steering mirror (SM2) needs to be translated slightly. The yaw alignment wants to move off the left edge of the mirror (perspective of the incoming beam). Nonetheless we were able to get O(seconds) lock on the 00 mode.

While adjusting alignment, we were locking with the LB servo controller. The box is broken in several ways: the integrator reset switch has stopped working, the pot knob lock for the input offset no longer fully locks, and the switching knobs were loose. Nonetheless, we were able to get somewhat stable locks a few times to 00 mode. The latest settings with decent locks are in attachment 1-2 (we also had the analog boost filter between the controller and current driver).

Next switched over to Moku locking. We set up the Moku as in attachment 3-5. We originally had an additional digital filter module with an elliptic lowpass filter to reject noise above 1 MHz, but found the module was glitching and causing the control signal to flip from rail to rail at kHz even with the filter input and/or output disconnected. With these settings, we were able to lock on 00 mode for O(seconds). We noted that the dominant noise on the control signal is at the cantilever resonance, as expected.

Here are some next steps:

• Translate SM2 so the beam can be centered on the mirror
• Adjust the mode matching to maximize 00 mode
• Will probably then need to reduce the loop gain, and do some shaping to improve stability
Attachment 1: 6ED37C86-0947-42CD-AC27-2633C3F46F11.jpeg
Attachment 2: F9FCC0EA-F7EB-40EF-826E-4AA4D4FD7AA6.jpeg
Attachment 3: IMG_0057.PNG
Attachment 4: IMG_0056.PNG
Attachment 5: IMG_0054.PNG
2989   Thu Sep 1 18:52:44 2022 aaronDailyProgressLab Workcalibrating error and control signals
• finished measuring in-loop transfer functions for yesterday's configuration
• tried to add a box
• moved REFL PD north 1" so I could avoid HWP2 impinging the box
• Moved TRANS PD and TRANS BS 1" west to avoid impinging the box
• MC3 mount is too tall for our existing box. Tried a few things to options to add some height to the box, but ended up finding a taller box with the same footprint in EE shop. Added the holes in the same locations as the old box... the fit was too tight and I badly misaligned MC3.
• Realigned MC3 by rotating laser polarization to P and locking the cavity the low finesse state
• Found a good set of filter settings that actually seemed to have more robust lock than yesterday (could tap the table more vigorously; 300 mVpp PDH signal full span compared to 15 mVpp rms while locked). However, after further "improving" (as indicated by TRANS DC / REFL DC ratio, adjusting input alignment with cavity locked) mode matching, I couldn't acquire a steady lock for the rest of the day
2988   Wed Aug 31 12:49:10 2022 aaronDailyProgressLab Workcalibrating error and control signals

After nulling the PDH offset, I locked the cavity. I noticed that the PDH error signal was actually more like 240 mVpp close to the 00 mode (the error signal had >300 mVpp when the 00 is not flashing, probably due to sideband or HOM).

As mentioned above, I wasn't sure the ratio of HF mon to LB error mon for a 1 MHz tone was giving us the right calibration for the control signal. The overall loop gain is surely small, but the gain due to the cavity pole should already be rolling off by 1 MHz. To see what's going on, I injected tones at a few frequencies at the sweep point

 Frequency HF mon (dBm) LB mon (dBm) difference (dB) 1 MHz -92 -76 16 900 kHz -91 -74.7 16.3 500 kHz -85.89 -64.9 20.99 100 kHz -69.59 -38.121 31.47 50 kHz -65.44 -31.597 33.84 10 kHz -81.1 -42.4 38.7

I drew the diagram in attachment 1 to help with the loopology. P_1 takes us from V at HF mon to Hz at the cavity input, which is the transfer function we measured with the DFD. P_2 is the PDH response in V/Hz, appears in (HF mon / LB mon), and falls off at high frequency due to the cavity pole.

Because the sweep injection point has its own gain knob, I don't know the ratios (HF mon / sweep) or (LB mon / sweep) directly, just their ratio. However, I think if I inject a tone well below the cavity pole I'll have made the measurement I want -- the loop suppression is cancelled out in the ratio (HF mon / LB mon), so I'll just see the slope of the PDH error signal.

Along the way, I measured some in-loop transfer functions with the HP spectrum analyzer and Moku from 1 Hz to 1 MHz, injecting both at the sweep and excitation points in attachment 1. I did get a satisfactory transfer function at low frequency. Maybe should try with the digital system so I can check the coherence (I've just been heuristically looking for the phase to converge).

[rana, shruti, aaron]

Rana helped us improve the transfer function measurement. Also pointed out that our previous estimate of the in-loop noise looked fine -- the control signal had noise above the electronics floor at low frequency, crossover b/w error and control traces showed that the UGF was approx in the right place, about 40 dB difference between control and error at 10 Hz, and 40 kHz/rtHz noise at 10 Hz is consistent with our estimate of the actuator gain + 1e-4 Vrms/rtHz noise on the control signal at 10 Hz. All consistent with slightly more than laser noise.

• I was already injecting at the error point and measuring after the summation point (LB error mon), which is good because we won't be comparing two signals that differ by G/(1-G)~1 in the high gain region, but instead signals that differ by 1/(1-G)
• Switched to the SR785, since we are measuring at low frequency
• Added a low passing SR560 to the swept sine injection path. Because we are injecting at the error point where our noise is ~1/f, shaping the excitation like 1/f will maintain a more uniform SNR for the excitation.
• Exciting with 10 mVpp does not give quite enough coherence below 1 kHz; exciting with 100 mVpp causes the loop to lose lock
• Eventually we gave up trying to get the LB servo to relock. Rana suggests adding a pomona box with a switch at the input to the servo so we filter out the step function transient a bit when engaging the loop.

### Update

magnitude part of the transfer function attached in #2 (I know I know, what use is it without the phase...)

This is LB mon / excitation as measured as described in attachment 1. The magnitude is

$|\frac{1}{1-H}|$

I don't know why I had GAP_1P_2 in the numerator in my handwritten note, obviously wrong today.

From the plot in attachment 2 and the ~10 Hz/rtHz @ 1 kHz in-loop noise from yesterday's elog, we can estimate that the frequency noise at 1 kHz is about (1e1 Hz/rtHz + 50 dB) = 3 kHz/rtHz. This is suggests ~ MHz/rtHz noise at 1 Hz, if the noise is falling like 1/f.

Attachment 1: 2403E02B-FC71-4C16-9A82-482A4B3E0B8E.jpeg
Attachment 2: mag_TF_coherence.pdf
2987   Tue Aug 30 10:00:12 2022 aaronDailyProgressLab Workcalibrating error and control signals

This morning, I locked the cavity and finished measuring the PDH response.

### PDH response

With the cavity unlocked but flashing 00, I observed the PDH error signal fluctuating with 330 mVpp (note-- more than yesterday, but I didn't change anything from end of day yesterday).

I was able to get the LB servo switch working well enough to lock the cavity. With the cavity locked, there are 28.5 mV rms fluctuations in the PDH error signal, which is less than 10% of the full range (though pkpk is almost half the PDH range). The fluctuations on the control signal (measured at the HF mon point of the current driver) are dominated by compensating the cantilever's 40 Hz mode, and are 713 mVrms (2.92 Vpp). See attachment 1, where the cavity is locked.

Note that I see 40 Hz fluctuations in the transmitted and reflected DC signals with the cavity locked, indicating some nonlinearity in the loop (I did change the PDH offset while acquiring lock, so I could be locking slightly off resonance). See attachment 2.

With the cavity locked, I injected a 1 MHz modulation from a function generator to the sweep port of the LB servo controller. The tone was -95.158 dBm at the current driver's HF mon, and -78.986 dBm at the LB servo's error mon, indicating the gain from the HF mon point to PDH error point is 16.17 dB (see attachment 3). This tells us the PDH response (since we already know the frequency response of the HF mon point in Hz/V).

### actuator response

Attachment 4 is the actuator transfer function measured yesterday, calibrated into frequency in Hz of the South laser per volt measured at the HF mon point. Our DFD calibration assumes a flat frequency response, so I don't think the phase should be believed.

The actuator transfer function plot was generated by cryo_lab/scripts/calibrate_noise/LaserTF.ipynb. The transfer function data are in data/calibration/220829_Imon_to_DFD.txt. Parameters and single-number measurements related to calibration are in cryo_lab/scripts/calibrate_noise/calpars.yml. We'll be describing the calibration pipeline on the PSOMA wiki soon.

### Frequency noise spectrum

Attachment 5 is the noise ASD measured in V/rtHz at the LB controller's error mon point and at the current driver's HF mon point.

I did the following to turn this into a frequency noise ASD at the cavity input:

• for the control signal trace
1. Multiplied by the fitted magnitude transfer function in attachment 4. This is immediately referred to laser frequency.
• for the error signal trace
1. Divide by the cavity pole and the PDH sensitivity as measured at 1 MHz (above the UGF) to refer the error ASD to the HF mon point
2. Multiply by the fitted magnitude transfer function in attachment 4 to get the frequency ASD

The procedures for the control and error traces don't agree (attachment 6). I'm uncertain about going from error signal -> HFmon

• I found the PDH sensitivity by driving the control signal at 1 MHz, which is above the loop UGF. However, my cavity pole is something like 20 kHz (I think, based on fineses ~ 10,000 for a ~18" traveling wave cavity). I would think the PDH response below the cavity pole should be larger than my measurement at 1 MHz.
• Might have just applied the cavity pole incorrectly? We had a function that reversed the cavity pole that seemed needlessly vectorized, but maybe I simply broke it.

### loop TFs

I also tried measuring the transfer function of the loop with the Moku and HP SA, but couldn't get both coherence and a stable loop.

Update: found a flat scaling error, updating noise spectra.

Attachment 1: 8801783F-A0A5-4D5F-BBDF-741C5F4CB082.jpeg
Attachment 2: F9311819-28A5-4557-A4D1-34FCD3580F52.jpeg
Attachment 4: Actuator_TF.pdf
Attachment 5: Spectra_VrtHz_20220909.pdf
Attachment 6: Spectra_HzrtHz_20220909.pdf
2986   Mon Aug 29 14:38:04 2022 shruti, aaronDailyProgressLab Workcalibrating error and control signals

[aaron, shruti, chris, rana]

### delay line box returned to 'high sensitivity' configuration

Changed delay line length on the RF side in the delay line box from 20 cm to 1.5 m (Attachment 1).

Attachment 2 shows a sweep of the Marconi frequency just to roughly locate a null in the delay line output.

Attachment 3 is the transfer function of the new box used with a buffer SR 560 and low pass at 1 MHz.

For 300 kHz/V FM dev. 50 mV

We calibrated the DFD by observing a 300 mVpp output range (with a G=1 buffer). There is a peak at 210 MHz, a zero at 182 MHz, and a trough at 146 MHz, so the full range frequency span (pi radians) is 64 MHz. This implies that the slope of the DFD response near the null is 7.4 mV / MHz.

### Actuator transfer function

We sent the beat note through an RF amplifier and -5 dB mixer to drive the DFD with a 10 dBm signal, and tuned the North laser TEC to put the beat note near a null of the DFD.

Then, we used the HP spectrum analyzer to drive the HF input of the S laser current driver, while measuring the DFD output on the A input and the current driver's HF monitor point on the R input. We recorded the transfer function from current monitor to DFD output, and we can use the calibration above to turn this into Hz/V as measured at the current monitor point.

### Switched from moku laser lock instrument controller to LB servo controller

Switched the PDH error and control cables from the Moku to LB servo controller.

We reconnected the REFL RF cable to the analog PDH mixer box, and delivered a 7 dBm LO from our OCXO. The EOM is driven by a -16 dBm modulation from the OCXO, which is about 100 mVpp (same as we had before from the Moku controller). I turned off the HEPA FFU and blocked the cavity to set the LB controller's input offset. Messed with the gain until I saw flashes.

We sometimes acquire lock with the loop left unattended, but found that the on/off switch of the LB servo controller is not functioning, and can't reliably be used to turn off the control loop. This basically made it impossible to actively acquire lock, since turning off the servo could not be used to reset the controller's integrator.

We did note that with the cavity flashing 00, the PDH error signal was 230 mV pkpk on an oscilloscope.

Attachment 1: E9974E28-397F-45BE-91DA-20B1FCEC3DFD.jpeg
Attachment 2: B915931B-DE9C-4404-BBCC-40211D48D5A9.jpeg
Attachment 3: MokuFrequencyResponseAnalyzerData_20220829_150342_Screenshot.png
2985   Thu Aug 25 20:01:23 2022 aaronUpdateControl Systemclosed loop noise spectrum

Based on my updated calculation of the modulation depth above, I increased the amplitude of the RF modulation from 50 mVpp to 100 mVpp. I then observed that the ratio between the f_0 and f_1 beat notes was about 26.4, which my calculation suggests is modulation depth 0.096.

I observed that the amplitude of the 33.59 MHz tone on REFL AC is maximized when REFL DC is around 1V, so I'm keeping REFL DC less than 1 V to avoid saturation.

I'm able to lock with the same filter parameters, and find a very stable lock (>10 minutes, doesn't lose lock when tapping the table, etc). I note

• REFL DC ~ 925 mV
• TEC ~ 7.749 kOhm
• PDH error signal fluctuating +- 2 mV (mostly at 40 Hz)
• control signal fluctuating +- 200 mV (mostly at 40 Hz)

Note that this is without the boost filter in place.

I recorded the error and control signals at 1 MHz sampling for 1 minute, and verified that I have all of the data. I also located the .li files containing the full recorded data from Aug 23.

To get a rough calibration of the closed-loop frequency noise, I recorded the beat note frequency (unlocked, but with the same settings) with the Moku phasemeter while driving the control point at 10 mVpp at 1 Hz.

I transferred the files to my laptop for analysis, but frankly if I do it tonight it will be rife with errors. I'll post the closed-loop noise spectra from today and Aug 23 first thing tomorrow.

Update

Attachment 1 is the closed-loop noise mentioned above as measured at the control point. The plotting script is in cryo_lab/scripts/calibrate_noise/LaserNoise.ipynb, and the data are in cryo_lab/data/NoiseSpectra/20220825/ and cryo_lab/data/calibration. The calibration from control point to frequency deviation of the S laser is estimated at 408 MHz/V at 1 Hz, which I applied across the spectrum assuming a flat actuator response. There are probably a number of issues, and it's hard to say if it's plausible without the loop transfer functions... but it doesn't look consistent to me compared to the last time we made such a measurement with the lower finesse cavity. To estimate the open loop gain without transfer function measurements:

• The control filter provides about +46 dB, and the Moku input stage attenuates -20 dB
• Actuator is 408 MHz/V
• The PDH error signal before we increased the cavity finesse was O(MHz/V), and the finesse increased two orders of magnitude.
Attachment 1: 20220825_ctrl_ASD.pdf
2984   Thu Aug 25 18:57:41 2022 aaronUpdateControl Systemlocking again

I tried modifying the DFD to let me measure the frequency noise spectrum directly from the beat note, but was unsuccessful. The mixer in the DFD is a ZFM-3-S+, which "only" operates up to 1 GHz. I had been using a 500 MHz RF amplifier to get my beat note up to the required +10 dBm, but switched to a ZHL-2010+ which also functions up to 1 GHz.

Since the RF electronics in the DFD work up to 1 GHz, if I place the zero crossing of the delay line interferometer at 1 GHz I'll be losing half of the linear range (or a bit more). To calculate the appropriate delay, refer to Rana's note. One half cycle of the delay line is over $\delta \phi = \pi$, which means if we want the frequency difference across 1/2 cycle of the DFD output to be  $\delta f_\mathrm{span}$, we should set the cable length difference at

$\Delta L=\frac{c_\mathrm{cable}}{2\delta f_\mathrm{span}}$

Where $c_\mathrm{cable}\approx 2e8$ is the speed of light in coax.

I made two versions of the high dynamic range DFD, first with $\delta f_\mathrm{span}\approx 1 GHz$. The short cable is about 15 cm long, so I cut a 25 cm length of coax cable and crimped on two SMA connectors. I then drove the DFD with a 10 dBm carrier wave from the Marconi, and swept the frequency from 1 MHz to 1200 MHz. I measured the output of the DFD with the SR560 sent to an oscilloscope. The result is in attachment 1. I must be missing a factor of 2 in the DFD output, because attachment 1 shows one full cycle over 1 GHz. The DFD is only "by-eye" linear for about 50 mV around its zero crossing.

Since I could get some extra range by looking at only 1/2 cycle in 1 GHz, I shortened the 'delay' cable to 20 cm, so $\Delta L = 5 cm$. Attachment 2 shows the same frequency sweep from the Marconi driving the new DFD. We can see that the high frequency part of the sweep is flat, presumably because some of the electronics don't function above 1 GHz. The response looks about linear from 613.8 MHz to 698.8 MHz.

I then sent the +20 dB amplified beat note to the DFD. With the cavity unlocked and the beat note tuned to the center of the DFD linear range (about 650 MHz), the RMS noise on the DFD output is about 25.6 mV (similar to the noise driven by the Marconi, though I forgot to note it). However, with the cavity locked the frequency deviations drove the DFD to nearly twice its linear range, with clear signs of saturation at the extremes of the 40 Hz tone (see attachment 3).

Attachment 1: 6D4F474B-D9B1-47C6-930F-76AA76AA9746.jpeg
Attachment 2: 64A841B6-2694-4AA9-B79E-60CE5BB3C1B3.jpeg
Attachment 3: 8EA729B3-2E01-4216-B0D9-BC30EE2F0D5E.jpeg
2983   Wed Aug 24 19:05:17 2022 aaronUpdateControl Systemmodulation depth

I measured the modulation depth of the 50 mVpp, 33.59 MHz modulation provided by Moku's laser lock box driving our iXBlue MPX-LN-0.1 EOM.

### cavity wasn't locking

Cavity wasn't locking initially.

I had turned the HEPA FFU off. The polarization was still nearly pure S (1.883 mW before MC1 without PBS, 1.501 mW before MC1 when PBS is inserted between HWP1 and ML2, rotating HWP1 recovered 1.524 mW before MC1. Only about 1% misalignment).

Qfter adjusting input polarization, I noticed that the Moku input impedance had changed to 1 MOhm. I should really set up a script to control the Moku's multi-instrument setup over ethernet so I have an unambiguous starting state, because the load function doesn't seem to always load what I expect (and always will load the 'last saved' configuration, which is dicey). After changing the Moku's input impedance to 50 Ohms, the cavity locks again.

### Finding the beat note

On Moku spectrum analyzer, the f_1 sideband amplitude on the S laser is only -95 dBm, so I wouldn't expect to see that sideband on the 4395A at full span and 1 MHz RBW (the floor was -85 dBm). I expect the (f_{0, south} \times f_{0, north}) sideband to be somewhat higher amplitude than (f_{0, south} \times f_{1, south}) because the north laser doesn't see the loss of an EOM before the beat note PD. Nonetheless, I sent the beat note through a ZHL-1A RF amplifier (+18 dB gain) before the 4395A. With the extra gain, I quickly found the peak... though the amplifier wasn't necessary, as the f_0 and f_1 signals on the south laser mixed with north laser f_0 both appeared with plenty of SNR even after removing the amplifier. Must have just been unlucky and impatient yesterday.

### modulation depth

I observed the beat note between the north and south carrier fields at -33 dBm, while the beat notes between the north carrier field and south f_1 sideband had amplitude -67 dBm.

The intensity ratio of the North carrier x South carrier beat note to the North carrier x South sideband beat note is

$\left( \frac{J_0(\beta)}{J_1(\beta)}\right )^2$

Where $\beta$ is defined in the equation for the modulated field

$E(t)=E_0e^{i(\omega_0 t + \beta \cos (\omega_m t))}$

Hm. This seems wrong, since it implies a modulation depth $\beta$ below 0.001. Found at least one mistake, redoing this morning. I think the above is now correct, but possibly off by a factor of root 2. See my modulation depth notebook on the cryo scripts repo

This implies a modulation depth index $\beta$ of 0.05. Because there are two sidebands and the modulation depth is defined as the maximum deviation over the mean value, the modulation depth is $m=2*\beta$, implying that the modulation depth I observed was indeed 0.1.

As a sanity check, the spec sheet for our EOM suggests that 3.5 V at 50 kHz modulates a 1550 nm beam by pi, so a 50 mVpp modulation should be closer to modulation depth 0.01. That said, the actuation strength could be stronger at higher frequency, or maybe I'm misinterpreting the specification.

Attachment 1 is a photo of the spectrum analyzer with the data I'm referring to above. The scan is from 20 MHz to 100 MHz with RBW=300 Hz. The narrow peak between the left sideband and carrier is the direct sideband on the south laser at 33.59 MHz (the other peaks are wider because the north carrier is wandering relative to the south carrier).

### Side note -- moku cross coupling

Made an observation about the Moku cross coupling. I noticed that the 33.59 MHz sideband sent to Moku's input 1 shows up in the power spectrum for input 2 as measured by Moku's spectrum analyzer.

Attachment 1: 9A1686EF-FA76-4231-BE9E-C445E15C5044.jpeg
2982   Wed Aug 24 17:50:33 2022 ranaUpdateControl Systemlocking again

In the case that the free frequency deviations are too large, just decrease the asymmetry in the DFD cable lengths so that the linear range is ~100 MHz. Once you finish this calibration, you can restore it to nominal.

2981   Tue Aug 23 18:16:34 2022 aaronUpdateControl Systemlocking again

I don't have a beat note, but I can try it again tomorrow.

Update: Realized we've considered this before. We can use the beat note to measure the actuation gain (current-to-frequency), but can't do the calibration in one shot unless both lasers are locked to the cavity. With only one laser locked, the beat note's frequency deviations are larger than the linear range of the DFD, and too fast for our usual PLLs (marconi, Moku phasemeter, etc).

As an aside, using the Moku's internal oscillator for RF modulation in our PDH loops could let us lock both lasers to the cavity without notching out the unwanted sidebands at (f_mod1 - f_mod2), since we can choose an arbitrary modulation frequency.

 Quote: If you have the beat note, perhaps you can use the DFD and/or Moku Phase Tracker to measure the calibration of the servo control signal. Then we can put that calibration into the CDS system so that the control signal recorded in frames as a DQ signal is in units of kHz.

2980   Tue Aug 23 18:16:14 2022 aaronUpdateControl Systemlocking again

I found a reliable lock point for the cavity, and recorded a video (google drive link) of myself sweeping the TEC setpoint by about 1 kOhm with the cavity catching many lock points on the way down. I tried to measure the loop transfer functions, but couldn't easily make a measurement with high coherence. Nonetheless, I'll attach the noise curves, PDH calibration, and transfer functions with low coherence, and note some issues with the measurements today.

### What happened

1. Tried to improve the stability of the lock
1. I nulled the PDH offset by adjusting HWP1 and HWP2 as above, then blocking the cavity and changing the PDH error point offset until the error signal was nulled (loop disengaged, sweep off). This resulted in a 1.7 mV PDH offset.
2. Increased integrator saturation slightly (from 47.1 dB to 48 dB)
3. Tried adjusting other filter parameters to qualitatively improve lock, but didn't find anything better. Overall system was the same as this morning.
2. Tried to measure and calibrate the noise spectrum
1. Recorded 1 min of control and error signal data at 300 kHz sampling in the Moku laser lock box
2. Observed that the PDH error signal was a mess... there was a large, non-monotonic drift in the error signal roughly periodic at the sweep frequency (at any sweep frequency, in decades from 3 Hz to 30 kHz). The drift was about 100 mV pkpk, comparable to the PDH error signal
3. I attempted several things to clean up the PDH error signal, none of which changed much.
1. Adjusting the phase at the PDH mixer by first tuning the phase to minimize the PDH mixer output (with the cavity blocked), then increasing the phase by 90 degrees. This choice of phase maximizes the DC level out of the PDH mixer. I then adjusted the PDH setpoint to null the error signal, then unblocked the cavity. Not much change after this procedure.
2. Introduced a DC offset to the RF modulation signal going to the EOM. I was able to null the DC offset after the mixer without changing the PDH setpoint by adjusting the RF modulation offset to -273 mV. Qualitatively better lock, but the PDH error signal still had a large drift.
3. I noticed that holding the patch fiber in my hand rotated the polarization of the launched beam (the REFL_MON level increased severalfold). The last patch fiber just before the beam leaves the fiber box wasn't properly secured and was touching the laser diode's heat sink, so I re-laid it and taped it down.
4. Tried adding a PBS after HWP1 to fix the polarization into the cavity at "S". This PBS was already on the table, and mounted such that the P polarized light is directed upwards. I used HWP1 to maximize power transmitted through the PBS (about 1.7 mW). However, as before the transmitted beam was misaligned into the cavity and I couldn't observe flashing (tried changing the orientation of the HWP with the kinematic mount, no luck). I didn't want to lose our "good enough" alignment, so I removed the PBS. I left HWP1 at its new setting, which should be closer to true "S" polarization than my previous method.
4. After removing the PBS, I noticed that the PDH error signal was somewhat larger and the periodic drift was reduced. However, this was only true if I allowed enough power incident on REFL for REFL_MON to be about 1-2 V. See attachments for some examples.
3. Found a qualitatively stable loop configuration (mentioned in the video above), and recorded the control and error signals for 1 min at 1 MHz. Settings were (also in attachment)
• 1.920 MHz lowpass filter
• 83.041001 degree LO phase shift, 33.59 MHz LO
• 0 V PDH setpoint, control signal offset, RF modulation offset
• Control filter is inverted, integrator gain is 1 at 2.383 kHz, integrator saturation is +47.2 dB
• Could acquire lock anywhere between TEC setpoint 7 kOhms and 9 kOhms, but I measured around 8.2 kOhms
• Current driver settings unchanged
• Moku input/output stages introduce extra 20 dB attenuation for RF input to ch1; 14 dB gain for control signal out of output ch 1
4. Tried to measure some loop transfer functions by injecting at the control point, but couldn't maintain both lock and coherence (excitations in sections from 3 Hz to 3 MHz, excitation amplitudes 1 mVpp to 20 mVpp). Observed REFL_MON and TRANS_MON flashing, and error signal exceeding 10% of PDH range.
5. Noted that REFL_MON had 20% dips when the cavity was flashing (relative to 'cavity unlocked,' not relative to the maximum attained REFL_MON level when the cavity loses lock)

Notes, issues

• The Moku laser lock box using its internal oscillator as LO only exposes the control signal for further summing or measurement, not the error signal; to measure or inject an excitation at the error point, I'd have to reconfigure the instruments.
• Need to check whether the RFPD is saturating again. I only got stable locks and a clean(ish) PDH error signal with REFL_MON well above 500 mV, but Rana and I observed saturation there earlier.
• I noticed that the sampling rate of the Moku laser lock box lowpass filter is only 78.125 MHz... but I've been using the same LO frequency as our OCXO, 33.59 MHz. Feels dangerously close to the Nyquist frequency. Might briefly try out a lower modulation frequency, at risk of changing Shruti's mode spectrum calculations.

Attachments

1. Nulling error signal with DC offset on RF modulation. The O(1 Hz) breathing on the error signal is approximately in time with the noise from Rocket Lake hard drive bay, but that could be incidental.
2. PDH error signal sweep representative of what I was getting before adjusting the polarization with PBS and increasing power incident on REFL PD.
3. PDH error signal sweep with a strange choice of RF modulation offset and PDH setpoint (1 V and 0 V respectively; 1 V is the maximum allowed RF modulation offset, and wasn't quite enough to null the error signal offset at that time). I only include it because it's the cleanest error signal I saw.
4. PDH error signal for the "final" system as described in (3) above. Swept at 314 Hz.
5. PDH error signal for the "final" system as described in (3) above. Swept at 3.14 kHz. Surely I should be able to explain the difference between attachment 4 and 5?
6. Moku multi-instrument setup for measuring transfer functions. The frequency response instrument has unity gain, and currently just passes (A-B, aka control - excitation) to its output.

I thought I recorded noise spectra over almost a minute for the "final" system, but alas only about 400 us saved. Anyway, can't calibrate it yet. Next time.

Set the HEPA FFUs on "High" before leaving

Attachment 1: IMG_0025.PNG
Attachment 2: MokuLaserLockBoxData_20220823_155142_Screenshot.png
Attachment 3: MokuLaserLockBoxData_20220823_162218_PDHsweep_1620mVREFLDC_Screenshot.png
Attachment 4: IMG_0033.PNG
Attachment 5: MokuLaserLockBoxData_20220823_163127_PDHscan_goodLock_Screenshot.png
Attachment 6: IMG_0038.PNG
2979   Tue Aug 23 11:55:31 2022 ranaUpdateControl Systemlocking again

If you have the beat note, perhaps you can use the DFD and/or Moku Phase Tracker to measure the calibration of the servo control signal. Then we can put that calibration into the CDS system so that the control signal recorded in frames as a DQ signal is in units of kHz.

2978   Tue Aug 23 11:09:21 2022 aaronUpdateControl Systemlocking again

At Rana's direction, I switched back to using Moku's laser lock instrument as the PDH control servo (we're hoping to eventually implement a digital resonant gain filter to damp the 40 Hz cantilever mode). The system is now as in attachment 1.

I adjusted the halfwave plate WP1 to minimize transmitted power through MC1. Then, I adjusted the halfwaveplate WP2 such that the DC level on REFL is about 500 mV. Then, I closed the enclosure doors and turned off the HEPA FFUs.

Attachment 2 shows the state of the Moku laser lock box. The Moku's aux modulator (which is phase-locked to its internal LO) is set to 50 mVpp at 33.59 MHz. The scan is off, lowpass filter is 1.920 MHz, and the controller is inverted. I found that a 90 degrees phase shift on the LO produced a reasonably strong PDH error signal at testpoint A.

Without changing the laser current driver settings (coarse: 4.88, fine: 5.00) and with the control loop disengaged after the "Fast controller" filter, I adjusted the TEC setpoint until I saw flashes on the REFL and TRANS monitor channels on an oscilloscope and on the transmission CCD camera (around 8.128 Ohms). I then engaged the control loop (exactly as in attachment 2), and adjusted the "Fast controller" filter until the cavity locked for O(10s) without interruption. Attachment 3 shows the final settings on the control filter: an integrator with G=1 at 2.383 kHz, and saturates at +46 dB. Below the filter in attachment 3 are the error (probe A, red) and control (probe B, blue) signals with the cavity locked.

Notes:

•  I originally was attempting to lock with the TEC setpoint lower, around 7.1, but found that when the control signal saturated the current changed enough for the laser to fall off its hysterisis curve; at the final TEC setting, the laser is on a single branch of its hysterisis curve no matter how the control signal adjusts the laser current.
• I've seen the cavity locked more stably. If I tap the table, the cantilever is sufficiently excited to lose lock (cavity flashes at 40 Hz until the cantilever motion decays)
• Before locking, I tried to observe the beat note between N and S Rio lasers on an HP 4395A. I mixed the 10% pickoff of the N laser and 10% pickoff of the S laser (after the S EOM) on a 50-50 fiber BS, sent to an FC1611. I then scanned the N laser TEC setpoint through one round trip of its hysterisis curve at several laser current settings between 100 mA and 128 mA. However, I never found the beat note. The spectrum analyzer was at full span (500 MHz), with a 1 MHz BW, which put its noise floor around -60 dBm. I probably could have tried this longer, but might find a faster spectrum analyzer instead.

I'll measure transfer functions, estimate the noise budget, and try to improve the stability this afternoon.

Attachment 1: 99B4F752-376A-4234-8D58-DDBC730F2F31.jpeg
Attachment 2: 3075F9EA-1342-40A1-846A-1CB44FD80872.png
Attachment 3: B85BE9A6-4BD6-4949-9745-A1567EB03249.png
Attachment 4: 63D452A8-54FE-4036-9896-60BBD5770314.png
2977   Mon Aug 22 15:14:07 2022 JCLab InfrastructureGeneralNew bolts on panel door handles and HEPA filter

[Aaron, JC]

There was an issue of the metal screws from the handles scratching the plastic panels from the sliding doors. To fix this, I ordered some Nylon nuts and bolts from McMaster as replacements. The previous screws were 1" in length as the new ones are 0.75".

Along with this, Aaron and I also decided to mount the 2nd hepa filter. The procedure went smoth and we decided to put tape over the remaining gap around the edges of both filters.