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ID Date Author Type Category Subject
3076   Thu Jan 26 17:54:35 2023 aaronDailyProgressLab WorkPSOMA experiment plans for upcoming week

Shruti and I finished replacing gaskets and bolts on the remaining 3 CF flanges. The subsequent pumpdown is still proceeding slowly enough that I expect a leak (despite not yet performing a rate-of-rise test). The next step is to clean and reseat the large viton o-rings on the top and bottom of the chamber.

3075   Wed Jan 25 15:05:43 2023 aaronLab InfrastructureLab Workdry nitrogen arrived in lab

I received compressed dry nitrogen this afternoon. I connnected the regulator we had been using, and valved off the line going to the cryo cavs experiment (there was already a valve at the cryo cavs table). Despite the low-pressure-side gauge on the regulator having a 100 psi range, the regulator can only supply ~10 psi. This is awkward because I spec'ed the calibrated leak to fill at ~30 psi; it will still leak, but the rate will be lower. We could decide to swap regulators if it's taking too long to vent through the leak (I've seen the regulator on our He line supply 100 psi).

3074   Wed Jan 25 11:51:47 2023 aaronDailyProgressLab WorkPSOMA experiment plans for upcoming week

After Maty gave us a tutorial on CF flanges, JC and I

• vented the PSOMA chamber
• removed 3x CF35 flanges
• began installing new gaskets before realizing we didn't have the right socket size (1/4" worked finger tight but no further)
• Covered remaining open gaskets and blanks in UHV foil, then broke for lunch so JC can retrieve supplies from 40m

One of the CF flanges we removed had at least one bolt that galled well before it was fully seated in the plate nut; others had minor galling on some bolts. We put all the steel bolts, washers, and plate nuts in a bag labelled "BAD," and can either throw out the entire batch or just the ones with noticeable galling.

In the afternoon, we installed 3 out of 4 CF35 flanges and 2 out of 4 CF125 flanges. We'll finish tightening the remaining 3 flanges tomorrow.

3073   Wed Jan 25 10:34:19 2023 JcDailyProgressLab WorkPSOMA experiment plans for upcoming week

Aaron, Madeline, and I met up in CRYO to discuss what would be the best move to check the PSOMA chamber. Attachment 1 has the plans for the upcoming week and what we plan to do.

Attachment 1: CC43B4CE-A4E8-4760-B3E6-32EA827D6D2A.jpeg
3072   Tue Jan 24 11:44:46 2023 shrutiDailyProgressPSOMAhow much AM do we expect?

Here is a notebook that takes into account the change in the interference condition and phase-lock phase offset to estimate how much AM and PM we expect.

(More details coming soon...)

3071   Mon Jan 23 15:50:18 2023 aaronUpdateVacuumnitrogen line connected

We were supposed to receive dry, compressed N2 in cryo lab today... but it never arrived. I've asked JC to follow up with airgas (or whoever was supposed to deliver).

In the meantime, I found fittings to adapt the 1/4" VCR male flange on our calibrated leak to the 3/8" tubing that carries nitrogen to the PSOMA experiment (1/4" male VCR -> 1/4" female VCR coupling body -> 1/4" VCR to swagelok tubing adapter -> 1/4" gas line filter -> 1/4"-to-3/8" right angle connector). See photo for assembly. I borrowed the VCR connectors from Hutzler lab, and identified swagelok SS-4-WVCR-6-400-SC11 as the adapter we want to purchase.

Attachment 1: 266FD66A-1E3D-49FF-9CD5-3952619B8F5F.jpeg
3070   Sun Jan 22 21:23:09 2023 aaronNotesPSOMAproposed next measurements for PSOMA cavity

True

 Quote: I don't think it's necessary to have to do the whole matrix calculation again for breaking up blocks with no cross-coupling because each block is just a product of sub-blocks...

3069   Fri Jan 20 07:41:23 2023 Not aaronNotesPSOMAproposed next measurements for PSOMA cavity

I don't think it's necessary to have to do the whole matrix calculation again for breaking up blocks with no cross-coupling because each block is just a product of sub-blocks...

3068   Thu Jan 19 15:28:19 2023 aaronNotesPSOMAproposed next measurements for PSOMA cavity

### Additional notes on measuring $k$

To make this proposal more explicit... since it's easy to measure $v_1$, $v_2$, and the error signals in loop without additional calibration, we could estimate $k$ by exciting at $\gamma_1$ and measuring

$k=\frac{v_2}{v_1}*\frac{1-A_2B_2}{A_2B_1}=\frac{f_2}{f_1}*\frac{1-A_2B_2}{A_2B_1}$

I'm assuming we inject the excitation in such a way that $v_1,v_2$ can be identified with their respective nodes $2,5$. This seems like a reasonable measurement between ~1 kHz and ~100 kHz, but might be impossible at lower frequency near the cantilever resonance where it's hard to measure the loop transfer functions. I included the equivalent estimate based on $f_2/f_1$, but in practice we would measure the ratio of error signals and would need to add a node inside of $B_i$ to derive the appropriate transfer matrix.

## Including the error points in the transfer matrix

We could also excite at $\gamma_2$ or at the error points. Breaking $B_i$ into the plant $P_i$ and controller $C_i$ and labelling the new nodes $7,8$ corresponding to error signals $e_1, e_2$, we have a new open loop transfer matrix

$\textsl{T}=\begin{pmatrix} 0 & 0 & 0 & 0 & 0 & 0 & P_1 & 0\\ 0 & 0 & A_1 & 0 & X & 0 & 0 & 0\\ 1 & 0 & 0 & -1 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & P_2 \\ 0 & 0 & 0 & 0 & 0 & A_2 & 0 & 0\\ k & 0 & 0 & 1 & 0 & 0 & 0 & 0\\ 0 & C_1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & C_2 & 0 & 0 & 0 \end{pmatrix}$

The matrix $\vec{S}=(1-T)^{-1}$ is identical to the matrix above in the 6x6 upper-left quadrant, except with all references to $B_i\to C_iP_i$. The rest of the matrix is

$\vec{S}=\begin{pmatrix} *&*&*&*&*&*& P_1-A_2C_2P_1P_2 & A_2C_1P_1P_2X-A_1C_1P_1P_2 \\ *&*&*&*&*&*& P_1A_1-(1+k)P_1A_1A_2C_2P_2 +A_2kX & A_2P_2X-A_1P_2 \\ *&*&*&*&*&*& P_1-(1+k)A_2C_2P_1P_2 & (1+k)A_2C_1P_1P_2X - P_2 \\ *&*&*&*&*&*& kA_2C_2P_1P_2 & P_2-A_1C_1P_1P_2-kXA_2C_1P_1P_2 \\ *&*&*&*&*&*& kA_2P_1 & (1+k) A_1A_2C_1P_1P_2-A_2P_2 \\ *&*&*&*&*&*& k P_1 & P_2 - (1+k)A_1C_2P_1P_2 \\ A_1C_1-(1+k)A_1A_2C_1C_2P_2+kA_2C_1X & C_1-A_2C_1C_2P_2 & A_1C_1-A_1A_2C_1C_2P_2 & A_2C_1X-A_1C_1 & C_1X-A_1C_1C_2P_2 & A_2C_1X-A_1A_2C_1C_2P_2 & 1-A_2C_2P_2 & A_2C_1P_2X-A_1C_1P_2 \\ kA_2C_2 & kA_2C_1C_2P_1 & kA_1A_2C_1C_2P_1 & A_2C_2-(1+k)A_1A_2C_1C_2P_1 & C_2-A_1C_1C_2P_1 & A_2C_2-A_1A_2C_1C_2P_1 & kA_2C_2P_1 & 1-A_1C_1P_1-kXA_2C_1P_1 \end{pmatrix}$

It's not easy to FM the laser at low frequency using an EOM (requires phase modulation proportional to $1/f$), so let's assume we can't directly excite the laser frequency either before or after the beamsplitter. Instead, we can only sum into the control and error signals at $2,5,7,8$. Therefore, we only have access to columns 2, 5, 7, and 8 of $\vec{S}$. Likewise, we can directly measure only the control and error signals either before or after the injection point. This limits us to accessing rows 2, 5, 7, and 8 of $\vec{S}$.

(Note that we could consider measuring at node 3 using the driver's current mon, but since this is related to the control signal by a trivial transfer function I'm leaving it out).

This gives us a list of 4x4+1=17 transfer functions in the full system... the extra 1 is due to always being able to measure $\frac{1}{1-H}$ with the transfer function measured just after the injection point. The transfer functions in the table below are normalized by $\frac{\mathrm{excitation}}{1-H}$, and one could measure any ratio of these transfer functions just as easily (assuming both are coherent at the relevant frequencies).

 Injection point measure 2 measure 5 measure 7 measure 8 2 $1-A_2C_2P_2$ $kA_2C_1P_1$ $C_1-A_2C_1C_2P_2$ $kC_1C_2A_2P_1$ 5 $X-A_1C_2P_2$ $1-A_1C_1P_1$ $C_1X-A_1C_1C_2P_2$ $C_2-A_1C_1C_2P_1$ 7 $A_1P_1-(1+k)A_1A_2C_2P_1P_2 + kA_2X$ $kA_2P_1$ $1-A_2C_2P_2$ $kA_2C_2P_1$ 8 $A_2P_2X-A_1P_2$ $A_2P_2-A_1A_2C_1P_1P_2(1+k)$ $A_2C_1P_2X-A_1C_1P_2$ $1-A_1C_1P_1-kA_2C_1P_1X$

I'm having some trouble discerning which of these transfer functions are coherent at what frequencies, and I think we should just start trying them out in-lab.

**Note: I reproduced $\vec{S}$ in the 6x6 case, and I think there are a few minor typos above. Since there are several, someone should check again for final resolution, but there isn't a pattern to the differences so I suspect simple typos in the unwieldy matrix

• Row 3 column 1 should read $1-A_2B_2(1+k)$
• Row 3 column 2 should read $B_1-(1+k)A_1B_1B_2$
• Row 2 column 4 should read $A_2X-A_1$
• Row 3 column 4 should read $-1+(1+k)XA_2B_1$
• Row 6 column 4 should read $1-(1+k)A_1B_1$

### notes on signal injection

3067   Wed Jan 18 15:09:57 2023 aaronDailyProgressVacuumleak checking

The PSOMA chamber reached ~9e-5 torr overnight. I'm trying to identify and correct the leaks in the PSOMA chamber. Using the rate-of-rise test, I measured an O(1e-5 torr*L/s) source of gas in the chamber, based on ~1000 L chamber volume. The test seems to indicate an actual leak, because the rate of rise is steady or increasing after ~1 hour with the pump valved off. Attachment 1 shows the rate-of-rise test and subsequent pumpdown. Attachment 2 shows the leak rate during the test.

After replacing the CF flange I suspected of being leaky based on methanol spritz, the vacuum quickly pumped down to ~20e-5 torr. I'm leaving the system heated to ~80 C overnight to bake out water.

Attachment 1: pressure.pdf
Attachment 2: leak.pdf
3066   Tue Jan 17 17:26:30 2023 aaronDailyProgressVacuumvent and pumpdown to vacuum chamber

I replaced the gasket of the CF flange with broken bolt.

After a very slow roughing cycle (~1 hour with roughing pump only), the vacuum pressure reached a sufficiently low level that the turbo kicked on. Ultimately the vacuum pressure reached 25e-6 torr. (attachment 1 is the pumpdown curve)

The rate-of-rise test (valve off the pump only and watch the rate of pressure increase) suggests the presence of a real leak, not simply outgassing, because the rate of pressure increase remains approximately constant over time. The test is visible in the attachment where the pressure rises after bottoming out, then falls again to ~25 utorr. I stopped the test somewhat early to avoid the vacuum gauge switching over to Pirani readout, and to avoid needing to spin down the turbo before pumping down again.

I sprayed methanol on all flanges and wasn't able to identify a single limiting leak. However, there are some candidate CF flanges:

• between the 4-way cross and valve 3
• On the Cf35 flange 135 degrees clockwise from the hinge.

I'm leaving the system pumping overnight to see if it reaches a lower ultimate pressure.

Attachment 1: Screenshot_from_2023-01-17_17-31-02.png
3065   Tue Jan 17 11:47:42 2023 aaronNotesPSOMAproposed next measurements for PSOMA cavity

Here are some comments on the proposed measurements. Intended to let me understand fully, no fault assumed.

### A. Loop coupling by modulation: $k$

• Currently, we can't lock both loops with $X=0$ (or maintain lock while $X$ is turned down to 0). This might be possible once we're in vacuum, which would be my suggestion for attempting this measurement.
• I think measuring $6\to 1$ and $3\to 4$ requires the following additional calibrations, based on my understanding that $6$ is the North laser frequency, $3$ is the South laser frequency, $1$ is a weighted combination of frequencies 'seen' by the PDH plant, and $4$ is the difference frequency between the N and S lasers.
• Transfer function from AF drive voltage to N laser frequency ($3$)
• Transfer function from AF drive voltage to S laser frequency ($6$)
• Transfer function from $f_2$ to PLL error signal (which is inside block $B_2$)
• Transfer function from $f_1$ to PDH error signal (which is inside block $B_1$). To avoid circular reasoning, I think this transfer function is identical whether measured with the PLL on or off, so we could eliminate the term in $f_1$ involving $k$

### C. Full Loop Gain, H

Requires same calibration transfer functions as used in (A) to calibrate (6) and (1). I don't understand why the modulation at the N EOM should be converted to voltage at current driver input. Doesn't 6 correspond to frequency of the N laser, so we want to refer to N laser frequency?

### D. Signal Transfer Function

What are $E_S$ and $E_N$?

Since the current driver is a sub-block of $A_i$, wouldn't the equations instead apply to transfer functions when monitoring the control signal for either PLL or PDH? I may be misunderstanding whether $6$ and $3$ appear before or after the EOM.

Just as an aside, the only alternative I know to measuring the various loop transfer functions above is to pick off the beam just before the cavity and directly measure amplitude and phase fluctuations on the pickoff using BHD (or whatever). I'm not sure where we'd get the clean (unaffected by unwanted loop couplings) LO for such a pickoff measurement.

Since it seems pretty straightforward to measure all of the blocks independently, maybe the following computationally complicated measurement would actually be experimentally simpler:

1. Measure the individual blocks as in (B)
2. Measure transfer function from signal injection point to all available mon ports (minimally both PDH and PLL error and control points). This can be done in one shot of a swept sine.
3. Fit k using the full matrix, which should be overdetermined.

We could do some meta-analysis of how much information each monitor point contributes (as a function of frequency), and eventually simplify the measurement. But since we wouldn't need to worry about calibrating and comparing multiple excitation points, this might minimize calibration uncertainty.

This could also be expanded to directly measure the optomechanical transfer function, as in the other log entries in this thread.

Draft   Tue Jan 17 10:58:52 2023 shrutiNotesPSOMAMeasuring amplifier gain and noise figure

## 1. Measuring IO relations

### 1. Injecting AM and PM

The phase offset in the PLL sets both the signal quadrature (relative to the pump) and also the interference condition between the two lasers in the current setup. We always apply phase modulation at the north EOM...

Assume, $\phi_{offset}=0$, is when the modulation is AM wrt the pump.

### 2. Measuring AM and PM

- By measuring the DC port of the 1811 REFL PD directly, the AM can be measured (I think?)

- PM can be measured in the PDH error signal

## 2. Estimating PSOMA gain

### A. As ratios derived from the IO relations:

$\begin{pmatrix} b_1[\Omega] \\ b_2[\Omega] \end{pmatrix} = \exp(-i 2 \eta_{cav}) \begin{pmatrix} 1 & 0 \\ - K[\Omega] & 1 \end{pmatrix} \begin{pmatrix} a_1[\Omega]\\ a_2[\Omega] \end{pmatrix}$

1) The ratio of PM measured in the PDH error signal when AM is injected to PM measured when PM is injected

[ Considering the change in power with the change in interference condition ]

## 3. Spurious couplings

1) Residual amplitude modulation

In principle, when AM is injected, and gain=0, this signal should not be detectable in the PDH error signal unless there is some residual amplitude modulation in the north EOM.

3063   Tue Jan 17 09:22:18 2023 shrutiNotesPSOMAproposed next measurements for PSOMA cavity

## 1. Description

The two loops with feedforward that currently make PSOMA controls using two lasers are shown in Attachment 1.

The south laser is the pump and is locked to the cavity using PDH locking. The north laser is the probe/signal simulator and is locked to the south laser with a phase-locked loop. In practice, the beat between the two lasers is locked to a local oscillator at $f_{offset}$ (150 or 300 MHz was used) and an additional modulation at $f_{offset}$ is applied, one of whose sidebands is resonant with the cavity. The signal is an audiofrequency sideband of the cavity resonance. There is an additional feedforward $X$ from the PDH to the PLL to allow the phaselock to follow the PDH loop when the cavity is very noisy.

The two lasers are mixed on a 50/50 BS and the PLL uses the beat in the AS port and symmetric port with (mostly) constructively interfering light is sent to the cavity.  Since the frequency noise measured around the cavity sees the north laser/path frequency noise only when the additional modulation is applied, the two loops' error signals depend on the north and south paths as:

$\begin{pmatrix} f_1 \\ f_2 \end{pmatrix} = \begin{pmatrix} 1 & k\\ -1 & 1 \end{pmatrix} \begin{pmatrix} f_1' \\ f_2' \end{pmatrix}$

where $f_1'$ is the frequency noise of the south laser and $f_2'$  is that of the north laser.

$M = \begin{pmatrix} 1 & k\\ -1 & 1 \end{pmatrix}$ is shown in the bottom-center of Attachments 1 and 2.

$f_1$ is the error signal seen by the PDH loop (in frequency units). For the PLL, the error signal is proportional to $\Delta\phi = 2\pi\frac{f_2' - f_1'}{s} = \frac{2 \pi f_2}{s}$ in the Laplace domain.

$\\ f_1' = A_1 v_1\\ v_1 = B_1 f_1\\ f_2' = A_2 v_2\\ v_2 = B_2 f_2$

Explicitly,

$f_1' = f_{south} - f_{cavity} \\ f_2' = f_{north} - f_{south} - f_{offset}$

Also, $v_1, v_2$ are the control signals of the PDH and PLL loops respectively.

## 2. Loop calculations

For the nodes as numbered in Attachment 2, the open-loop transfer matrix is

$\mathcal{T} = \begin{pmatrix} 0 & B_1 & 0 & 0 & 0 & 0 \\ 0 & 0 & A_1 & 0 & X & 0 \\ 1 & 0 & 0 & -1 & 0 & 0 \\ 0 & 0 & 0 & 0 & B_2 & 0 \\ 0 & 0 & 0 & 0 & 0 & A_2 \\ k & 0 & 0 & 1 & 0 & 0 \\ \end{pmatrix}$

[convention: row index-> column index for both S and T]

In closed loop, the full set of relations are $\mathcal{S} = \left( 1- \mathcal{T} \right)^{-1}$

$\mathcal{S} = \left(\frac{1}{1-k X A_2 B_1 + (1+k) A_1 A_2 B_1 B_2 - A_1 B_1 - A_2 B_2} \right) \\ \times \begin{pmatrix} 1-A_2 B_2 & B_1-A_2 B_1 B_2 & A_1 B_1-A_1 A_2 B_1 B_2 & X A_2 B_1-A_1 B_1 & -A_1 B_1 B_2+X B_1 & X A_2 B_1-A_1 A_2 B_1 B_2 \\ A_1+kX A_2 - (1+k)A_1A_2B_2 & 1-A_2 B_2 & A_1-A_1 A_2 B_2 & A_1-X A_2 & -A_1 B_2+X & -A_1 A_2 B_2+X A_2 \\ 1 - (1+k)A_1A_2 & B_1 -(1+k)A_1A_2B_2 & -k X A_2 B_1-A_2 B_2+1 & -1 +(1+k)XA_1B_2& X B_1-B_2 & X A_2 B_1-A_2 B_2 \\ kA_2 B_2 & kA_2 B_1 B_2 & kA_1 A_2 B_1 B_2 & -k X A_2 B_1-A_1 B_1+1 & B_2-A_1 B_1 B_2 & A_2 B_2-A_1 A_2 B_1 B_2 \\ kA_2 & kA_2 B_1 & kA_1 A_2 B_1 & A_2 - (1+k)A_1A_2B_1 & 1-A_1 B_1 & A_2-A_1 A_2 B_1 \\ k & k B_1 & k A_1 B_1 & 1 - (1+k)A_2B_2 & kX B_1+B_2 - (1+k)A_1B_1B_2 & 1-A_1 B_1 \\ \end{pmatrix}$

## 3. Measurements for calibration

### A. Loop coupling by modulation: $k$

With the feedforward turned off, $X=0$, while both loops are on, this can be measured  as  $\frac{6\rightarrow 1}{3 \rightarrow 4}$

Experimentally, this would mean measuring two transfer functions, the first by modulating the north EOM (the secondary AF sideband) and measuring the PDH error signal, and the second, by modulating the south EOM and measuring the PLL error signal in frequency units.

### B. Individual blocks

$X$ is just the constant factor (=0.5) specified in the Moku cross-coupling matrix, but can be easily measured between the PDH control signal and the North laser HF MON (by dividing out the voltage->current conversion of the north current driver).

Since both loops can be individually locked at the same servo settings, the A's and B's can be measured separately in each loop.

### C. Full loop gain, $H$

The full/overall loop-suppression = $1 / (1 - H)$, where

$H = k X A_2 B_1 - (1+k) A_1 A_2 B_1 B_2 + A_1 B_1 + A_2 B_2$.

This factor can be measured directly (with or without feedforward) , once $k$ is known.

$H(s) = 1 - \frac{k}{(6 \rightarrow 1)(s)}$

where 6->1 is the measured by modulating the north EOM (but converting it to voltage units at the current driver input) and measuring the PDH error signal.

### D. Signal transfer functions

When a signal, $\eta(s)$, is injected as the secondary audio sideband in the north EOM and both laser driver current monitors are measured, the following transfer functions are obtained:

For the south monitor,

$\frac{I_{S}}{\eta}(s) = \left( \frac{E_N}{E_S}\right) \left( \frac{k A_1 B_1}{1 - H}\right) = \frac{k A_1(s) B_1(s)}{1 - H(s)}$

$E_S = 1$ since the south EOM does not change affect the frequency between the south laser and the cavity. If $\eta(s)$ is calibrated to units of frequency of the north laser, $E_N = 1$.

For the north monitor,

$\frac{I_{N}}{\eta}(s) = \left( \frac{1}{L_N (s)}\right) \left( \frac{1 - A_1(s) B_1(s)}{1 - H(s)}\right)$

$L_N$ is the transfer function of the north laser in units of Hz/A.

Before pointing out all faults and reasons why these measurements are not immediately possible in the lab, please consider
1. These are what directly follow from the calculations as what occurred to me as the easiest way to measure those quantities theoretically when I couldn’t think of a more practical method. For e.g., X=0 cannot be possible while acquiring lock, but maybe it could be slowly decreased when the setup is stabilized. Please let me know if you do think of a better way to measure k.
2. Of course, from where we actually end up injecting the signal there may be an additional calibration of the drivers, etc that may be necessary which I can easily add. But I have taken into account the units whenever I thought was necessary.

Attachment 1: Controls_physical.pdf
Attachment 2: Controls_block.pdf
3062   Fri Jan 13 16:22:43 2023 aaronDailyProgressVacuumvent and pumpdown to vacuum chamber

Spritzing methanol around the CF flanges securing valves 2 and 3 reduced the vacuum pressure by ~3 ntorr (10%). I'll keep an eye on these flanges as we test the rest of the chamber.

I proceeded to vent the chamber, roughly following the steps to reach chamber isolated, vent ready, and vented in the elog above... with the exception that valve 2 remained closed at all times and I abridged steps related to venting with dry nitrogen (I'm just using room air at 1 atm).

### Venting with room air

1. Close valve 1.
2. turn off the pump
• Since the chamber is isolated close to atm by valve 2, I tried to open the chamber to inspect its o-ring. I unlatched the clamps on top of the chamber, but some residual vacuum inside the chamber prevented the lid from opening. However, after the vacuum gauge reached ~1e-5 torr, the lid swung open rapidly on its own. Apparently the hydraulic hinge pulls with sufficient force to open the chamber on its own, and a hand is required to prevent the lid from opening too quickly. It is easy to close and open the chamber, but going forward the chamber should not be left closed but unclamped. To avoid dust settling, I closed and clamped the chamber lid. The o-ring looks clean.
• With valves 1, 2, and 3 closed, the pressure at the gauge increases ~1utorr/min. Since the chamber has a much larger volume than the hose around the gauge, this might actually be acceptable. If the chamber reaches ~10s mtorr in O(day), we'll be leak checking.
3. Open valve 3
4. Open valve 1
5. Open up-to-air valve
6. Open valve 2

I opened the chamber lid and wiped the o-ring and mating surface with a dry lint-free cloth. The o-ring already has some vacuum grease applied. Then, I pumped down the chamber.

### Pumpdown

1. Close valve 3 and up-to-air valve. Valves 1 and 2 are open.
2. Turn on pumping station
• The vacuum pressure stayed close to atmosphere, indicating a screaming leak (almost just an open port, except there isn't one).
• When I closed valve 2, the pumpdown continued as normal, so it's a problem on one of the chamber flanges.

I turned off the pump and re-tightened the CF flanges. I had been tightening the flanges on the chamber to a torque specification, but this time I tightened until the metal surfaces of the flange completely touched.

On one of the CF35 flanges, the bolt broke off in the nut desite a visible gap present between the CF surfaces. Maybe I need to use a lubricant with these bolts? Since I now need to garb up and completely open at least one flange, I'm going to push this leak hunt to next time.

Attachment 1 shows the pressure during the above. The linear plot focuses on the leak rate with valves 1, 2, and 3 closed.

Attachment 1: Screenshot_from_2023-01-13_17-17-25.png
3061   Fri Jan 13 14:47:56 2023 aaronLab InfrastructureGeneraloptimal height of PSOMA optics table

[shruti, aaron]

Shruti and I checked out the ergonomics of the PSOMA cryostat and table. We determined that we should acquire new legs for the optics table that are 8.25-8.5" shorter than the current legs. The distance from the floor to the bottom of the rail around the enclosure is 28.25", and the table is 12" thick. The current legs are 22.25", and have a protrusion for the floating attachment to the table which ends ~24" from the ground.

We want the new legs to attach to the bottom of the optics table (28.25"-12") = 16.25" from the ground. Up to ~1" longer legs would be fine.

This would put the top surface of the optics table ~28.25" from the ground. This height is comfortable for both Shruti and I to work on from a standing position with no stool or bending over, and it would be comfortable to reach over the 19.5" tall cryostat especially with assistance from a stool or short platform.

3060   Thu Jan 12 17:30:04 2023 aaronDailyProgressVacuumPSOMA vacuum closed, pumping down (hose only)

The PSOMA vacuum chamber is closed. The attachments describe the current system.

1. A sketch of the system is in attachment 1
2. Attachment 2 shows valve 2, valve 3, the calibrated leak, and the up-to-air valve
3. Attachment 3 is the pumpdown curve from this afternoon. I'm pumping overnight only up to the vacuum gauge (so valve 1 is open but valves 2 and 3 are closed). I tried to grab the pumpdown curve from dataviewer, but somehow the data aren't being saved to frames? I can hold however much data in the ndscope buffer, but not retrieve dataviewer reports no data found (also "no data output" and "bad file descriptor"). Anyway, when I left after around 1 hour of pumping the pressure is ~0.25 utorr.
• Update: Chris restarted a process and restored our access (elog pending). After ~24 hours of pumping, the pressure between the pump and closed valves 2/3 (so up to but not including the chamber) is <3e-8 torr! Pumpdown in attachment 3.

It would be helpful if someone could review and discuss these proposed procedures for operating this vacuum system.

## Vacuum procedures

### Pumpdown

1. Start with valves 1 and 2 open and 3 closed, so the chamber is open to the pump but the venting path is closed.
2. Turn on pumping station. Call this state at vacuum

### Isolating the vacuum chamber

1. Start "at vacuum"
2. Close valve 1
3. Turn off the pump. Call this state chamber isolated

We could consider adding a second gauge on the opposite side of the chamber, in which case valve 2 could be closed here instead of 1. This would allow continuous monitoring of both the chamber pressure and pressure in the line between the pump and chamber.

### Preparing for vent

1. Start at chamber isolated with the pump speed at 0 rpm
2. Close valve 2
3. Open the up-to-air valve
4. Flush dry nitrogen into the venting path through the calibrated leak by supplying 200 kPa from the gas cylinder
5. Close the up-to-air valve
6. Open valve 3. The leak is now filling the line between closed valves 1 and 3 with nitrogen, with the pressure in this line monitored by the gauge.
7. Once the vacuum gauge reading is greater than the pressure in the rough vacuum line, turn off the supply of nitrogen at the gas cylinder.
8. Open valve 1.
9. Turn on the pumping station.
10. Once the pressure equilibrates (pumping rate is equal to leak rate with no nitrogen supplied from the cylinder), the system is vent ready

### Venting

2. Open valve 2
3. Increase pressure in the dry nitrogen line to 200 kPa
4. Close valve 1. The system is now venting at the leak rate, and the vacuum gauge is monitoring the chamber pressure.
5. Turn off the pumping station
6. Once the system approaches atmospheric pressure, expose the up-to-air valve to atmosphere. The system is vented
• Note that to expose the system only to dry nitrogen, I'll need to add an additional relief valve. The calibrated leak cannot flow enough nitrogen into 1 atm.

I should make a state diagram of these processes.

Attachment 1: Screen_Shot_2023-01-12_at_18.39.22.png
Attachment 2: 2AC90352-B687-4431-88DA-C56DF2B3DD22.jpeg
Attachment 3: Screenshot_from_2023-01-13_14-57-24.png
3059   Thu Jan 12 16:29:10 2023 aaronLab InfrastructureDAQnds errors

I'm having trouble with nds...

• I can caget the expected value of slow channels defined in epics (eg X1:OMA-ERC_PRESSURE_UTORR reads ~atmosphere), but nds (ndscope, dataviewer) reports these channels as reading 0
• nds (specifically ndscope) and epics agree on the value of slow channels defined by rtcds such as X1:OMA-ERC_REFL_MON_OUTPUT
• nds (specifically ndscope) reports the expected value of fast channels defined by rtcds such as X1:OMA-ERC_REFL_MON_OUT, but also reports a "Low level daq error occurred [1]: Unspecified error". Epics (as expected) can't find these fast channels.

I tried restarting the epics services on cominaux, restarting rtcds using the rtreset script on cymac1, and rebooting all of cominaux, cymac1, and spirou workstation. systemctl on cominaux reports the usually services are running on that machine, and I don't know what to do based on the status screens on sitemap (attached).

Attachment 1: Screenshot_from_2023-01-12_16-28-16.png
3058   Thu Jan 12 11:51:19 2023 KojiLab InfrastructureGeneralHow to move the large engine hoist through the narrow door

How to move the large engine hoist through the narrow door

3057   Wed Jan 11 16:52:13 2023 aaronDailyProgressVacuumclosed some CF flanges

I continued closing the PSOMA chamber, and will post a sketch of the vacuum system comorrow when all the bolts are tightened.

3056   Tue Jan 10 16:29:03 2023 aaronDailyProgressPSOMAproposed next measurements for PSOMA cavity

### tldr: need some input on measuring the fields before the cavity

We saw some promising signals, but need to say definitively what is happening in our amplifier cavity. We want to observe the dynamics of our plant (cavity), and preferably while minimally resorting to detailed modeling of the coupled PDH and PLL loops. So what measurements should we make? I'm writing this up following discussion with Chris to help clarify for myself.

Ignoring intracavity noises, the fields reflected from the cavity are

$\begin{pmatrix}b_1\\b_2\end{pmatrix} = e^{2i\eta}\begin{pmatrix} 1 & 0 \\ \kappa & 1\end{pmatrix} \begin{pmatrix} a_1\\a_2\end{pmatrix}$

Where the quadratures are amplitude (1) and phase (2), $\eta$ is a frequency dependent phase due to the cavity pole, and $\kappa$ is the ponderomotive coupling. To full characterize the optomechanical transfer function, we want to measure the transfer function from excitation to each of $a_1, a_2, b_1, b_2$. I think measuring all of these transfer functions using the same excitation point lets us characterize the cavity transfer function no matter how complicated our controller is (even if the controller itself involves many coupled loops), because the above equation must hold in steady state. We could even measure them simultaneously with a single excitation.

The DC MON on REFL is sensitive to $b_1$, while the cavity pole lets us measure $b_2$  after demodulating at the PDH sideband frequency (the usual PDH technique). Likewise, the BEAT PD is sensitive around DC to $a_1$, and is sensitive to $a_\mathrm{probe,2}$ by demodulating at the PDH sideband frequency. The last claim is justified because the acoustic signal sidebands around the probe are not (directly) present on the pump laser or its RF sidebands.

Formally, the Beat PD sees a slightly different field than the cavity, but the transfer function measurements might be mappable between $a$ and $\tilde{a}$. As long as $a_\mathrm{probe,2}\approx a_2$ and either the pump or probe dominates in the amplitude quadrature, measuring phase fluctuations at BEAT PD is equivalent to measuring the fields just before the cavity.

$\begin{pmatrix} a_1\\a_2\end{pmatrix} = \begin{pmatrix}a_\mathrm{pump,1} \\ a_\mathrm{pump,2}\end{pmatrix} + \begin{pmatrix}a_\mathrm{probe,1} \\ a_\mathrm{probe,2}\end{pmatrix}$

$\begin{pmatrix} \tilde{a}_1\\\tilde{a}_2\end{pmatrix} = \begin{pmatrix} a_\mathrm{pump,1}\\a_\mathrm{pump,2}\end{pmatrix} - \begin{pmatrix}a_\mathrm{probe,1}\\a_\mathrm{probe,2} \end{pmatrix}$

However, in practice I'm not sure we can monitor only BEAT PD. The PDH loop will inject any signal in $b_2$ back to $a_2$ by driving the pump frequency. Therefore, we probably cannot approximate $a_\mathrm{probe,2}\approx a_2$, especially in the limit of amplitude-quadrature signal injection (meaning direct coupling of signal to $a_\mathrm{probe,2}$ is small) with high ponderomotive gain (meaning $b_2$ can be much larger than $a_2$); furthermore, the PLL drives $\tilde{a}_2\to 0$, so we would expect $a_\mathrm{pump,2}\approx a_\mathrm{probe,2}$. In other words, we might be able to use the BEAT PD to estimate fields entering the cavity, but only if we measure some transfer functions of the coupled PDH-PLL loop.

We may need to pick off some light just before the cavity instead (easy enough), or fully characterize the coupled control loops (probably worth it to avoid loss in an eventual sub-SQL demonstration). We also would need to measure the phase of the pickoff using BHD, since we want to know the contributions to $a_2$ of both the pump and the probe and suspect that the pump contribution may dominate. I'm not sure where to pick off a BHD LO -- both pump and probe current drivers are controllers in either the PDH or PLL, so neither laser has a clean carrier free from any injected signal.

Alternatively, can we excite below the PLL UGF then assume $a_\mathrm{pump,2}\approx a_\mathrm{probe,2}$ and simply measure $a_\mathrm{probe,2}$ at the pickoff before the cavity and demodulating at PDH sideband frequency?

## next steps

To summarize a few possible approaches

1. Keep the same measurement setup (attachment 1), and assume $a_\mathrm{pump,2}\approx a_\mathrm{probe,2}$ and $a_\mathrm{probe,1}>>a_\mathrm{pump,1}$ to map measurements at BEAT PD to fields entering the cavity
2. Pick off just before the cavity and measure using a single RF PD. This lifts the assumption that $a_\mathrm{probe,1}>>a_\mathrm{pump,1}$ by directly measuring $a_1$, but still requires $a_\mathrm{pump,2}\approx a_\mathrm{probe,2}$ due to the incomplete measure of only the probe component of $a_2$
3. Pick off just before the cavity and measure phase with a BHD (or another method?). This would provide a direct measurement of both $a_1$ and $a_2$. I'm not sure where we'd get a clean LO for this measurement.

In either (1) or (2) above, we might lift the assumptions about pump and probe fields by making appropriate (and unkown to me) measurements of the PDH-PLL transfer function.

Attachment 1: 39CA7615-6C69-4816-81C7-D2CB92A27AEA.jpeg
3055   Thu Dec 22 14:30:08 2022 aaronDailyProgressVacuumclosed some CF flanges

I closed the 6.25" CF flanges on the PSOMA chamber with blanks, though I didn't completely seal the copper gaskets (I left two bolts finger tight on each flange).

On three of the flanges, I used Kapton tape to secure the outer edge of the copper gasket to the flange so I could easily install the blank without dropping the gasket. I wasn't satisfied with the result since I suspect at least some of flanges have a small piece of Kapton tape between the gasket and the groove. The tape is well outside the knife edge, but I'm concerned it will prevent the copper from fully forming into the groove. I'm going to remove and reseat these flanges.

I also started re-shelving some optics from the cryo-cantilevers experiment to make room for the chamber on the PSOMA table.

Attachments

1. vacuum workstation
2. The flanges are covered with an outer layer of foil, followed by cardboard, followed by an inner layer of foil. This is the inner layer of foil
3. prepping the blank and gasket before installation. I wiped the knife edges and gasket with a lint free cloth
4. After installing the blank. Bolts are finger tight
5. Cryo cantilevers optics "before"
Attachment 1: E04D8FF9-A1E2-4950-8441-6EB4826ECC9B.jpeg
Attachment 2: C4804B3C-C72B-4D79-84DD-2F363EEBD154.jpeg
Attachment 3: 96621ED3-587E-4BFC-B051-0F1EF60592CC.jpeg
Attachment 4: ED779D82-85F1-4D77-8487-EEE14651F0CC.jpeg
Attachment 5: 3B6E57F5-DCFA-4B7F-9080-3A81A4919C56.jpeg
3054   Wed Dec 21 17:26:24 2022 aaronDailyProgressPSOMAhow much AM do we expect?

I'm trying to understand the changes in DC power on BEAT MON and TRANS MON channels when the resonant probe field is tuned to constructively or destructively interfere with the pump. In particular, the change in DC power are larger than I would expect based on the sideband amplitude in the beat note spectrum.

Here are some observations. In all cases, I assume that minimizing power on BEAT mon (maximizing power on TRANS mon) implies the pump and probe are in-phase.

 Channel State Value Beat mon (DC) resonant probe in-phase with pump, PDH servo off, -15 dBm RF @ 150 MHz on probe EOM -3.08 V Beat mon (DC) resonant probe 90 deg detuned from pump, PDH servo off, -15 dBm RF @ 150 MHz on probe EOM -3.16 V Beat mon (DC) resonant probe 180 deg detuned from pump, PDH servo off, -15 dBm RF @ 150 MHz on probe EOM -3.25 V Beat @ 150 MHz PLL locked at 150 MHz, PDH servo off, -15 dBm RF @ 100 MHz on probe EOM -27 dBm Beat @ 50 MHz PLL locked at 150 MHz, PDH servo off, -15 dBm RF @ 100 MHz on probe EOM -54 dBm Beat mon (DC) Pump laser on, probe laser off -1.88 V Beat mon (DC) Probe laser on, Pump laser off -1.22 V Beat mon (DC) Both lasers off (dark current) 45 mV

The beat note at the PLL LO frequency is proportional to $\sqrt{P_\mathrm{pump}P_\mathrm{probe, 0}}$, while the probe's sideband is proportional to $\sqrt{P_\mathrm{pump}P_\mathrm{probe, 1}}$. Therefore, the ratio of field amplitudes for the probe's carrier and first sideband is

$\frac{\sqrt{P_\mathrm{pump}P_\mathrm{probe,0}}}{\sqrt{P_\mathrm{pump}P_\mathrm{probe,1}}}=\frac{E_\mathrm{probe,0}}{E_\mathrm{probe,1}}=27 \mathrm{dB}\approx 500$.

When one of the sidebands is made homodyne with the pump by driving the probe EOM at the PLL LO frequency, the probe's sideband field interferes with the pump with some detuning set by the relative phase ($\phi$) of the PLL LO and EOM drive tone. Beat mon voltage is proportional to the incident power at DC, which is

$P_\mathrm{beat}(0\mathrm{Hz})\approx (E_\mathrm{pump}+E_\mathrm{probe,1}\cos(\phi))^2+P_\mathrm{probe,0}+P_\mathrm{probe,1}$

Since the pump and probe lasers have approximately the same power, I'd expect the sideband to cause up to a ~1/250 fractional change in power at the pump carrier frequency. Even doing the calculation more carefully finds that the ratio of Beat mon levels when the pump and probe are constructively / destructively interfering should be

$\frac{P_\mathrm{beat}^\mathrm{\phi=0}(0 \mathrm{Hz})}{P_\mathrm{beat}^\mathrm{\phi=\pi}(0 \mathrm{Hz})}\approx 1.0039$

$\frac{P_\mathrm{beat}^\mathrm{\phi=0}(0 \mathrm{Hz})}{P_\mathrm{beat}^\mathrm{\phi=\pi}(0 \mathrm{Hz})}\approx1.054$

I still can't explain this discrepancy. When I made an analogous measurement with the cavity locked and comparing TRANS mon levels instead of Beat mon, I saw a similar discrepancy. I was driving the probe EOM with -10 dBm, and I saw ~10% difference between \phi=0 and \phi=\pi. The measurement above confirmed for me that the scaling is approximately linear and not a result of unexpected coupling between the PLL and PDH loops. It's great that I can see a lot of interference between my pump and probe, but disconcerting that I can't explain the effect. Have I missed something in this calculation or measurement?

## idea for the measurement...

While making this measurement I was able to drive the probe EOM with up to 3 dBm RF power and maintain PLL lock and even (noisy) PDH lock. I also drove the probe EOM at the PLL LO frequency detuned by <kHz and saw low frequency beating on Beat mon. If the PDH can remain locked with a frequency-detuned probe, this might let us make a lock-in measurement of the gain rather than controlling the pump-probe phase.

## Update

Chris found my error -- electronic voltage is proportional to optical power, so beat note power on the spectrum analyzer is proportional to $P_1P_2$ not $\sqrt{P_1P_2}$. Everything above is consistent with this modification.

3053   Tue Dec 20 17:48:48 2022 aaronDailyProgressPSOMAsaw some signal in amplifier output, but system not fully understood

I saw a signature of amplification, but I can't explain everything I observed so don't want to attribute it definitively to ponderomotive effects.

Attachments 1 and 2 show the PDH control signal in the top display (measured at pump's HF mon) and the MON of the beat note PD (amplitude fluctuations into the cavity) on the bottom display. In attachment 1, I've tuned the pump-probe phase to minimize the signal in the amplitude quadrature entering the cavity. Attachment 2 adds 90 degrees to the pump-probe phase, so the signal should be maximally in the amplitude quadrature (up to drifts during the measurent time).

When the signal is in the phase quadrature, it couples directly to the "output" of the amplifier since the PDH servo compensates phase fluctuations on the pump laser. When the signal is in the amplitude quadrature, it should only couple to the "output" of the amplifier if the cavity reflection transfer function rotates amplitude into phase (due to ponderomotive effects, or possibly due to the cavity sitting off-resonance).

The attachments show that the signal peak at the amplifier output is 2 dB higher when injected in the amplitude quadrature compared to the phase quadrature.

It's a bit premature to claim this is a ponderomotive effect because there are a number of unexplained features...

• I still can't explain the changes I see in HF mon. When the signal is close to fully in phase, the TRANS MON signal is either maximized or minimized, and the case with signal in amplitude quadrature has TRANS MON halfway between these extrema. However the span is too large (roughly 10% change between max and min).
• Here's a possible explanation: I was using the upper sideband at ~300 MHz to estimate the size of the lower sideband at DC. However, my EOM only has a 150 MHz bandwidth! So the 300 MHz peak could experience >>3 dB rolloff. Will check again with a lower PLL frequency.
• I think the signal strengths at amplifier input are identical whether rotated into phase or amplitude, since the power in the sidebands are identical. However, I need to think through at least once whether this works out in dimensionless units.
• Cavity detuning could cause amplitude-to-phase coupling
• The pump-probe phase drifts. I observed that if I integrated longer than ~5 min, the peak height started to drift with each new average.
• What is the extra feature in the PDH control spectrum in attachment 2? If it's residual phase noise from the PLL, why doesn't it appear in either input spectrum?
3052   Mon Dec 19 11:03:32 2022 aaronDailyProgressLasersignal injection, loop tuning

I was remiss in my eloging, but here's the update from last week...

tldr: I saw my AM signal before the amplifier above the noise floor, but wasn't able to see the optomechanically-induced PM signal after the amplifier. Then, I messed around with the PLL loop shape longer than I should.

## Setup

I removed the amplitude modulator from the pump path to get us back to ~1 W circulating pump power. I also changed the PLL LO frequency (offset between the pump and signal lasers) to 150 MHz, the bandwidth of our fiber EOM. The loop seemed to work fine at 300 MHz offset, but if the EOM response is falling off there could be some unnecessary phase delay, and 150 MHz seems far enough from the cavity resonance and PDH sidebands.

I tried two signal injection schemes. In both cases, the Moku and Marconi are locked to the same 10 MHz timing signal.

### Audio signal phase modulates the probe after the PLL

1. Phase lock the pump and probe lasers 150 MHz apart. The LO for the PLL is generated internally by the Moku, and has a user-adjustable DC phase.
2. Use the Marconi and a fiber EOM to phase modulate the probe at the same frequency as the PLL's LO, generating a sideband at the pump frequency and phase-locked to the pump. The relative phase of the Marconi and Moku LO sets the phase of the homodyne probe sideband.
3. Phase modulate the Marconi LO to generate audio sidebands on the homodyne probe. The audio sidebands are AM when the probe is out of phase with the pump.

### Audio signal phase modulates the probein the PLL

1. Phase lock the pump and probe lasers 150 MHz apart, with the LO for the PLL provided by the Marconi.
2. Phase modulate the Marconi LO to generate audio sidebands around the probe.
3. Use the Moku to generate a pure tone at the PLL LO's carrier frequency, and modulate the probe laser at the EOM with this tone. For example, if the PLL LO is 150 MHz with some audio sidebands, the Moku drives the EOM with a pure 150 MHz tone.

In both cases, the signal can appear as either PM or AM on the pump according to the relative phase of the LOs used for the PLL and for driving the EOM.

I didn't actually notice that one of these methods generated more AM around the pump, but I didn't make a careful enough comparison. I expected that modulating the probe after the PLL would lead to the PLL suppressing the signal. Will have to re-measure and re-think this.

### Is our signal injection working at all?

To find out, I'm looking at REFL and BEAT MONs on the SR785 spectrum analyzer. I was able to produce AM sidebands above the noise floor between 40 Hz and 10 kHz, and could change the height of these AM sidebands by roughly tuning the relative phase of pump and homodyne probe.

With both the PLL and PDH servos locked, I can change the transmitted light level by changing the relative phase of the pump and homodyne probe. This makes sense: when the pump is in-phase with the pump, it just looks like more carrier power to the cavity. However, the magnitude of the changes in transmission power is larger than I expect (O(10%) changes in transmitted power, but I think the homodyne probe field amplitude is only 1% that of the pump).

### I couldn't find our signal after the amplifier

Assuming the signal is AM, it would only appear in the PDH loop after being rotated to PM by pushing on the cavity mirror. Below the UGF of the PDH servo, I would expect to see a signal peak in the PDH control spectrum as the loop compensates. I couldn't find this peak in the pump laser's HF mon when the cavity was locked. I tried integrating the spectrum for O(5-10 minutes), as well as using a lock-in amplifier with similar integration times.

## Thursday

Messed around with the PLL, and tried to understand the open questions.

## Friday

I tuned up the PLL servo for several hours by measuring the PLL open loop transfer function then adjusting a two-stage PID filter (with up to 4 integrators and 2 derivatives total) a) increase gain below the UGF in the region with significant residual error, b) increase the UGF frequency, c) increase the phase margin at the UGF, and d) increase the gain margin where the phase margin vanishes. I made and unmade many marginal improvements, and found a few heuristics about our PLL.

We can push the UGF above 150 kHz and maintain lock, but the intrinsic phase delays in the loop limit the stability of this loop. For example, I could get a marginally stable loop with UGF above 200 kHz by adding a second derivative, but since this reduces the gain rolloff above the UGF I still get gain peaking wherever the phase margin vanishes.

There is some

3051   Tue Dec 13 10:58:12 2022 aaronDailyProgressOpticstest of intensity modulator S/N 6800-03

I checked the general function of the intensity modulator. The internal PD port responds to input laser power (reads ~10 mV with S laser off, ~865 mV with S laser on). I'm using the beat note PD to monitor transmitted laser power, and checked that the changing the DC bias level with a function generator can change the DC output of the beat note PD from 0 V to ~325 mV.

I created a couple of new cds filters to monitor and control the intensity modulator

• X1:OMA-PUMP_AM_MON, whose input monitors the internal PD of the MXAN
• X1:OMA-PUMP_AM_BIAS, whose output goes to the DC bias port of the MXAN

I make'd and installed the new x1oma model, and ran rtreset to restart the front ends. Rather than wait for Chris' cronjob to run this week, I ran "./mdl2adl.sh" from /opt/rtcds/tst/x1/scripts/mdl2adl directory on cominaux to generate updated medm screens. Note that running the script only on the x1oma model (as in "./mdl2adl.sh x1oma") threw an error.

I used a function generator to sweep the DC bias level with a +- 10 V triangle wave, and monitored the DC power level on the beat note PD and internal PD of the modulator (ndscope traces in attachment 1, all y-axis units in counts). The internal PD is supposed to monitor a 90:10 or 99:1 tap fiber on the transmission side, so I'm surprised to see a nonlinear output.

Attachment 1: Screenshot_from_2022-12-13_15-20-24.png
3050   Tue Dec 13 10:06:19 2022 aaronDailyProgressVacuumvacuum testing

I've left the system under vacuum for about a week. On early Sunday morning ~4am (nobody was in the lab), the pressure apparently dropped to 1e-7 torr for several minutes then increased to ~600 utorr. Each step change was in about a minute. The pump is still operating as normal, and I wasn't able to find a leak by spritzing methanol around the flanges. The vacuum pressure over the last 7 days is attached.

Attachment 1: Screenshot_from_2022-12-13_10-05-46.png
3049   Fri Dec 9 17:24:48 2022 aaronDailyProgressOpticsamplitude modulator in pump path

I added the MXAN-LN-10 amplitude modulator to the pump (S laser) fiber path, just after its EOM. I do see the expected ~3dB of insertion loss due to the AOM (though I should measure this more carefully). I was able to lock the cavity with no trouble with the new modulator in the path (no modulation applied). I'll measure the modulator's transfer functions and Mach-Zehnder DC tuning next time.

I connected the RF ports of the modulator to the front panel with LM-200 SMA cables. While I had the box open, I swapped out some lossier SMA cables for LM-200 cables: between the beat note PD RF port and the front panel, and between the S EOM RF port and the front panel. The cables were not of the same length, so I expect the PDH phase will have changed.

Due to space constraints, I mounted the amplitude modulator on top of the S EOM, separated by the breakout breadboard and a heat sink as shown in attached photos. I used rubber to soften the clamp, and placed another small heat sink between the rubber and the amplitude modulator. I didn't use any conductive interface between the heat sinks and the modulators.

Attachments

1. Fiber setup before modification

2. fiber setup after modification

3. Clamp

4. heat sink

5. breakout PCB is supported not dangling

Attachment 2: B0307390-69BB-4442-868E-41BFEAFA2B90.jpeg
Attachment 3: B87F0703-5F13-404A-BCCD-E0E62CFAC14B.jpeg
Attachment 4: C2146338-F2E0-40EA-BBDF-F1F3C0B19866.jpeg
Attachment 5: 44B069F8-E331-4A5D-B27F-260CC0C51096.jpeg
3048   Thu Dec 8 17:26:44 2022 aaronDailyProgressElectronicssma breakout for fiber amplitude modulator

I'd like to add the MXAN-LN-10 fiber-based amplitude modulator to our pump path to allow us to amplitude modulate our pump independent of our PLL-and-probe-laser scheme for signal injection. Since we aren't yet using a Mach-Zehnder to reject pump RIN, we won't really be taking a hit from the perspective of SNR, and it would be nice to test the optomechanical response of the cavity independent of the PLL and transfer functions involving the probe laser.

Zach had been using wire clips to tune the DC electrodes of our MXAN. Since this is a semi-permanent installation, I made a PCB board to connect the electrode pins to SMA connectors. The result is attached.

I'm not sure whether our model actually has an internal photodiode, but I included a connector for pins 3 and 4 anyway. I checked that the electrical connections work and there isn't unexpected shorting. I also found some heat sinks that I can place under the MXAN, since the body of the modulator won't press directly on the optical breadboard.

Attachment 2: 5FF5A44D-7A26-4E1C-9A4D-4F5C10529196.jpeg
3047   Thu Dec 8 09:45:56 2022 aaronDailyProgressVacuumvacuum testing

### minor observation about the vacuum pressure

For about 9 hours after turning off the heater and removing insulating foil, the vacuum pressure was below 1e-7 torr. Then, the pressure increased to several 1e-7 torr, where it has remained. Not sure why this order of magnitude increase in vacuum pressure.

The vacuum pressure minute trend for the last day is in attachment 1, and the raw data for the hour or so where the pressure was rising is in attachment 2.

### possible explanation?

This vacuum handbook from Agilent that I return to often notes that at high vacuum, most of the remaining gas in the system is adsorbed on the walls rather than residing in the volume. Slide 7 notes that at 1e-9 torr, there are 500,000 molecules on the surface for every one in the volume, and it takes 2200 seconds for a monolayer to form (with both of these numbers inversely proportional to vacuum pressure in the molecular flow regime). Maybe for the first ~9 hours after the heater was turned off, the vacuum pressure was determined by (pumping speed + adsorption to the walls) - (desorption from the walls + permeation through KF flanges + backflow + outgassing + etc), with the adsorption rate limited by the surface area of the vacuum system. If there's some relation between number of monolayers and adsorption/desorption rate, at some point the number of monolayers could limit the net adsorption rate and lead to a higher equilibrium pressure.

At a pressure of ~4e-8 torr, the walls would form 1 monolayer of gas in about a minute. So in 9 hours, ~500 monolayers would form. I'd sort of expect the adsorption/desorption rate to equilibrate with just 1 monolayer of gas, so maybe I need another explanation.

Attachment 1: Screenshot_from_2022-12-08_10-16-47.png
Attachment 2: Screenshot_from_2022-12-08_10-17-25.png
3046   Wed Dec 7 18:25:05 2022 aaronDailyProgressNoise Budgetupdated noise budget

I tuned up the PDH servo by widening the region with positive phase above 100 kHz and setting the PI corner near the cavity pole. I measured the plant transfer function from 10 kHz to 100 kHz and found that the phase is -45 degrees relative to ~DC near 37 kHz; the recent PDH sweep implied cavity pole ~39 kHz, so this is reasonable.

I measured the transfer functions and noise spectra (at error and control points) for the S laser locked to the (higher finesse) cavity. I kept the N laser off during these measurements, so it's the same 1-loop system we worked with in September. The cavity pole is now lower, ~37 kHz, and the UGF is ~115 kHz.

I plotted the results, but wasn't completely satisfied that I caught all factors of few in the units from the HP spectrum analyzer, so I'll update with attachments when I do so.

Update: The results are attached.

1. Transfer function measurements. Below 100 kHz taken with SR785, above 100 kHz taken with HP spectrum analyzer. In the future maybe I'll divide out the 'actuator' transfer function (HF mon to laser frequency) and instead plot just the plant (cavity transfer function). THe UGF is 116 kHz, and phase margin is 62 degrees.
2. Noise spectra. These are consistent with the UGF ~116 kHz. There is a 14 dB discrepency between the spectra measured at error mon and HF mon, probably due to my accidentally taking data with the Moku +14 dB output gain stage on for some of the measurements... but I couldn't figure out where the mistake was made, so I left it uncorrected. I suspect the control mon is the correctly calibrated curve.
3. Stage 1 control filter
4. stage 2 control filter

I pushed this updated noise spectrum to the gitlab, and debugged the pipeline so the results are again available on this webpage.

Attachment 1: LoopTFs.pdf
Attachment 2: AllSpectra_HzrtHz_20221207.pdf
Attachment 3: 0339DB09-10BA-4506-9368-1B36D5715105.png
Attachment 4: 07D4744E-1903-4B22-883E-B5B082014652.png
3045   Wed Dec 7 11:59:54 2022 aaronDailyProgressVacuumvacuum testing

I turned off the heater and let the system return to room temperature. The pressure settled between 2-6e-8 torr (attachment 1  shows pressure decreasing for a couple hours after turning off the heater). This far exceeds our requirement for this vacuum system.

Attachment 1: Screenshot_from_2022-12-07_12-02-46.png
3044   Tue Dec 6 11:56:36 2022 aaronDailyProgressVacuumvacuum testing

The pressure did reach 6e-6 torr, but then jumped to ~mtorr for after less than an hour.

I could not identify leaks by spritzing methanol around all flanges, but after going up to atmosphere noticed one KF flange was somewhat loose.

I noticed that the gauge reports >1000 torr at atmospheric pressure. After spinning down the turbo and venting to atmosphere, I calibrated the atmosphere reading by shorting pin 7 of the gauge to its negative supply. Even after the atmosphere calibration, the gauge read >900 torr, so I introduced an offset voltage on my calc channel to send the gauge's pressure reading at atmosphere to 10 V (the nominal gauge output at atmosphere). The -0.082 V 'ad hoc' offset decreases the absolute pressure reading by 25% at any given pressure.There is a Vacuum gauge manual available online

I then pumped down to several utorr and again shorted pin 7 to the negative supply to provide a 'vacuum' reading for the pirani. I only somewhat trust the absolute pressure readings (maybe to 25%), but presumably the pumpdown curves can now be consistently compared going forward.

After tightening the KF flanges and calibrating the gauge, I pumped down again and maintained at < 1 utorr for over 1 hour. I tried tightening the CF flange, but in doing so caused a leak that limited vacuum pressure to ~600 utorr (one of the KF flanges was torqued while tightening the CF bolts, and I'm not sure whether the leak is at the CF or one of the KF flanges since methanol reveals no leaks at any flange). I vented back up to atmosphere, cleaned the effected KF flanges, and replaced the copper gasket and resealed the CF flange. Then, I pumped down again.

The latest pumpdown curve is in attachment 1. I wrapped the cross in heat strap and foil, and when the pressure reached ~utorr turned the heater on to equilibrate at 85 C.

Attachment 1: Screenshot_from_2022-12-06_17-35-24.png
3043   Mon Dec 5 18:18:22 2022 aaronDailyProgressVacuumvacuum testing

With the Edwards WRG-S gauge borrowed from QIL, I'm continuing with planned tests of the PSOMA chamber.

I don't have a controller for this gauge, so I cut off an RJ45 cable and added BNC connectors to the appropriate wires for +18V power supply and pressure signal output.

I'm testing the gauge by pumping on a minimal system: right angle valve -> KF40 and KF16 cross -> [KF16 blank, up to air valve, KF40-to-DN40CF adapter] -> WRG-S with DN40CF connection. Pumpdown curve is attached, I'll leave it pumping overnight to see how low the pressure gets.

Attachment 1: Screenshot_from_2022-12-05_18-18-01.png
3042   Mon Dec 5 18:00:13 2022 aaronLab InfrastructureElectronicsoverdrawn Sorensen on +18V supply

On Friday, I noticed that the PSOMA S laser diode had suddenly reduced power (we've been seeing 1.7 mW at the beam launch, and suddenly I was getting only 0.5 mW). I was close to wrapping up, and was able to recover full power by hopping to a different hysterisis curve with TEC set to ~10 kOhm. Lee also pointed out that he wasn't seeing as much laser power as expected out of the cryo cavs diodes.

However, today I'm seeing odd behavior in the Acromag channels (such at X1:AUX-ACROXT_AI_1, which is the analog input channel for PSOMA vacuum pressure). The channels alternate between reading 0 and reading the correct value, for 10s of seconds at a time in either state.

On investigating the acromag chassis' power supply, I found that the +18 V rail is only supplying ~11 V. This could explain the sudden loss in laser power -- the current driver is probably supplying less current than it would with full voltage supplied. Probably turning on the cryo cavs lasers (plus whatever else we've plugged in since they were last used) drew too much current.

I increased the current limit on that Sorensen, and the DC current increased from 3.5 mA to 3.8 mA. The acromag-related channels are now fully functioning.

3041   Thu Dec 1 11:07:34 2022 aaronDailyProgressPSOMAcleaning cavity optics

I'm measuring the beam properties at a few more locations

 Distance from front of fiber launch x-axis beam diameter (13.5% clip) y-axis beam diameter (13.5% clip) ellipticity 9 mm 856.7 um 883.4 um 1.03 188 mm 1078.1 um 1083.9 um 1.01 232 mm 1142.9 um 1145.8 um 1.00 252 mm 1183.5 um 1184.3 um 1.00 268 mm 1218.2 um 1216.5 um 1.00 296 mm 1267.7 um 1259.9 um 0.99 313 mm 1296.3 um 1286.8 um 0.99

These measurements and the alamode fit for the beam profile are in attachment 1. The x data best fit waist radius is 405.6 um at -103 mm from the front plane of the fiber launch. The y data best fit are 421.3 um at -103 mm.

Attachment 2 shows the >0.99% mode matching solution least sensitive to errors in modematching lens position. It uses a 500 mm FL lens at 0.3023 m from the launch plane, and a 850 mm FL lens 0.4608 m from the launch plane. The target beam waist is larger than yesterday's plot because I looked up the quote for our coastline concave lens, and found it has a 1m ROC (not a 1m FL).

After these changes, I am seeing a bit more transmitted power. Power measurements suggest 72% mode matching and 450 ppm loss. I added a second stage ID filter to give some extra gain between 10 Hz and 100 Hz to suppress the cantilever motion. The PDH servo filters are in attachment 3 and 4. I measured the open loop transfer function to determine that the UGF is between 100 kHz and 125 kHz, which helped in choosing the derivative corner and saturation. When adjusting mode matching lenses, I increased the servo gain by 6dB and tuned the output HWP to adjust the amount of light sent to REFL PD; this allowed me to lock on the 00 mode most of the time just by roughly placing the lenses such that the beam spot maintains the same position on REFL camera.

I'm not convinced my mode matching solution is any better than the previous one, or perhaps the lenses are misplaced. The reflected beam still looks like a 1st order Laguerre-Gauss mode. I'm still placing the first mode matching lens at a 30-45 degree angle to correct astygmatism. THe reflected beam is the top monitor in attachment 5. Since there seems to be >1W of circulating power, I'll move on to signal injection tomorrow, but it would be good to know how to diagnose and correct this mode mismatch.

Attachment 1: 221201_alaPSOMA_fit.pdf
Attachment 2: 221201_alaPSOMA_MM.pdf
Attachment 3: B3046E97-3811-419D-9886-24EAFF8FE138.png
Attachment 4: F223FF47-81F4-4D3E-8E7F-4AC41941BBC5.png
Attachment 5: B7BE18D5-4A78-4B77-9D99-312547CD02E7.jpeg
3040   Wed Nov 30 12:50:26 2022 aaronDailyProgressPSOMAcleaning cavity optics

Thanks Koji! Shruti also suggested that WinCamD might be Si-based... I was looking at their TEL Phosphor response curve! I'm using the InGaAs camera on the Beam'R2-DD now.

I recorded the following beam parameters, with no lenses in the beam path. I left one steering mirror and the input HWP in the beam path. I need to check out the manual to understand some of these measurements... I think it's something like the camera scans a slit along two orthogonal directions (parameterized by 'theta'), and uses this to measure the beam power along the slices defined by the slit.

 parameter Value 8 mm from front surface of fiber launch Value 308 mm from front surface of fiber launch Ellipticity 1.03 1.00 Beam width at 13.5% clip, x-axis 854.4 um 1284.0 um Beam width at 50% clip, x-axis 459.3 um 800.7 um Beam width at 13.5% clip, y-axis 883.7 um 1281.8 um Beam width at 50% clip, y-axis 501.8 um 771.3 um

I measured the distance from the front surface of the beam launch to the HR surface of MC1 to be 523 mm. MC1 to MC2 is 230 mm. MC2 to MC3 is 230 mm. And MC3 to MC1 is 53 mm.

I found some mode matching solutions with a la mode (eg attached), and will implement one tomorrow.

Attachment 1: alaPSOMA.pdf
3039   Wed Nov 30 11:39:24 2022 KojiDailyProgressPSOMAWincamD/Beam'R2 (Re: cleaning cavity optics)

Regarding WincamD:
WincamD is a silicon-based CCD camera (I believe). And may not have sufficient sensitivity at 1550nm.

Instead, use Beam'R2, which you probably brought back together with the WincamD combo. It has Silicon PD and exInGaAs PD and the exInGaAs can measure the beam profile even at the wavelength of 2um. So, your success is promised. You just need to make sure to use the exInGaAs side.

3038   Tue Nov 29 13:57:59 2022 aaronDailyProgressPSOMAcleaning cavity optics

[shruti, aaron]

We adjusted MC3 by 1 full knob turn clockwise in yaw, and recorded the following power measurements after realigning the incoming beam to the cavity. These imply ~65% mode matching and 460 ppm loss.

 REFL voltage (locked) 167 mV REFL voltage (unlocked) 470mV Transmission power 0.57 mW Incident power 1.79 mW

I also retrieved the beam profiling cameras from OMC lab, and am using WinCamD to profile our beam and improve mode matching... but wasn't able to find the beam in about an hour of searching with the camera in a couple locations on the input path, using different ND filters, gain/exposure settings, etc. The camera responds to ambient light, but maybe I'm missing something.

3037   Mon Nov 28 18:46:57 2022 aaronDailyProgressPSOMAcleaning cavity optics

I tuned MC1's yaw knob 1/2 turn clockwise, which should move the cavity axis closer to center on MC1 and MC3. I didn't get a stable enough lock to characterize the cavity with the box off, but it seemed to have moved the beam closer to center as expected (based on where the razor blade cuts off the cavity) and may have decreased the cavity pole (based on where I needed to put the PI corner to get more stable locks).

3036   Fri Nov 25 16:59:01 2022 ranaDailyProgressPSOMAcleaning cavity optics

that's great news! I guess it makes sense to move things into the vacuum, since the table HEPA situation is not great yet.

We would really like to be able to close the sliding doors without a gap and install a switch to adjust the speed of the HEPAs. We should strategize something with JC.

3035   Wed Nov 23 14:08:57 2022 aaronDailyProgressPSOMAcleaning cavity optics

### Cleaning MC1 and MC3

Today I'm removing the dust from the PSOMA cavity optics by drag wiping their HR surfaces in-situ.

I prepared the environment by wiping down surfaces inside the enclosure with kimwipes and 70% isopropanol. With both HEPA FFU on "high," I first wiped the surfaces that go inside the box covering the cavity (optics table, optomechanics, interior and exterior of the plastic box) and covered the cavity with the box. Then I wiped the other surfaces inside the enclosure (optics table, optomechanics, vacuum chambers, oscilloscope, cables, TV monitors, cables, interior and exterior surfaces of enclosure walls, etc).

Per Koji's drag wiping tutorial and advice, here's my procedure for cleaning the optics:

1. Garb up in the usual clean room attire (hair net, hood, coat, mask, gloves)
2. Prepare a work area on (IPA-wiped) UHV foil with necessary ingredients. See attachment.
• 100% isopropanol decanted into a small bottle. Flush the bottle with isopropanol first to remove any dust since last time.
• 99.5% acetone decanted into a small bottle. Flush the bottle with acetone first.
• Syringes and tips for acetone and IPA delivery. Flush the syringes with their corresponding solvent before use.
• Package of lens tissues
• tweezers, wiped down in IPA (not sure will be needed)
• small scissors for cutting lens tissue, wiped down with IPA
3. Remove box covering cavity. Wipe down gloved hands with 70% IPA.
4. Remove apparent dust by drag wiping with IPA
5. Remove solvents (eg from fingerprints) by drag wiping with acetone
6. Remove possible watermarks due to acetone cleaning by drag wiping again with IPA
7. Inspect and photograph optics. Use a red laser pointer to illuminate optic, and search for diffuse scatter away from normal incidence using a camera with manual exposure control.
• There's probably a red laser pointer in the lab (not sure where), and there's a HeNe on the optics table... but as soon as I finished cleaning the optics, I could see that the TRANS MON signal is several times higher! I took some normal incidence photos with my phone, but need to come back to check the diffuse scatter.
8. Replace box covering cavity

Our pure IPA and acetone supplies were opened more than 2 years ago, so Koji lent me two newer bottles for today.

I completed the steps above, drag wiping at least 3x in each of steps 4-6. There is still a visible streak on the left side of MC1 (close to the beam spot) that wasn't affected by wiping with either solvent. Both MC1 and MC3 still have some visible dust, and MC1 still looks a bit hazy.

### Cavity losses significantly reduced

As soon as I finished cleaning the optics, I saw several times stronger flashes in TRANS PD. I needed to reduce the PDH servo gain to lock to the 00 mode, and reshape the high frequency response a bit to avoid oscillation. The TRANS PD is saturating, so I reduced its gain setting (from 70 dB to 50 dB).

 incident power (measured with power meter) 1.45 mW transmitted power (power meter) 0.67 mW REFL mon mean (unlocked) 310 mV REFL mon mean (locked) 74 mV

Based on the above power measurements, the mode matching is 54% and intracavity loss is 575 ppm. Rana points out that these power measurements aren't very reliable, because they depend on our mediocre estimates of mirror transmissivities. Still, we can see a factor of >20 increase in transmitted light implying ~1 W circulating in the cavity. The implied cavity finesse based on power measurements is 2600, and the linewidth would be 230 kHz. The cavity pole based on power measurements is ~58 kHz. The cavity should now be overcoupled.

The new PDH slope based on attachment [] is -4 MHz/V. The implied cavity linewidth is 150 kHz, and finesse is F~3900. I'm a bit wary of this measurement, because based on REFL levels I'd expect a PDH slope closer to -6 MHz/V. Sweeping the laser current more slowly resulted in the error signal being dominated by cantilever motion at 40 Hz; sweeping laser current more rapidly resulted in ringing near the peaks of the error signal. The implied cavity pole based on PDH sweep is ~39 kHz.

### attachments

1. drag wiping materials
2. MC1 after cleaning
3. MC3 after cleaning
4. changes to PDH servo controller
5. PDH error signal sweep
6. beam spots for REFL (top) and TRANS (bottom) with cavity locked. The REFL camera seems to indicate some remaining mode mismatch.
Attachment 1: 2811C2DE-B896-4E15-A27B-6A1C8D94655C.jpeg
Attachment 2: 3A17904B-8CB7-4BD4-9D72-D8D7EE54A9D7.jpeg
Attachment 3: 9F1EE930-C827-4049-8641-0736422265F6.jpeg
Attachment 4: 79ECCC0A-4DDF-4A00-A5D7-BE22677DC2E4.png
Attachment 5: D0179575-0DA4-46A3-9E1A-3E12201F4EBA.png
Attachment 6: 50EBA08E-42DC-494B-87A4-B92B98234DAB.jpeg
3034   Tue Nov 22 15:27:23 2022 ChrisComputingControl Systemscreens from simulink

I set up a script to autogenerate medm screens from simulink models in /opt/rtcds/tst/x1/scripts/mdl2adl, and added it to the crontab on cominaux to run on a weekly schedule. Screens are available from a link button on the sitemap (see attachments).

Attachment 1: sitemap.png
Attachment 2: x1oma_ERC.png
3033   Tue Nov 22 15:15:45 2022 aaronDailyProgressPSOMAinvestigating cavity losses

We think we're seeing ~5000 ppm intracavity losses, which is limiting the power buildup in our cavity to about 5% of the lossless case.

I removed the box covering our cavity to investigate the source of these losses.

There is dust visible by eye across all three optics. MC2 (the cantilever) is clear across most of its front surface; MC1 (curved mirror) is the most uniformly coated with dust. I used a white LED flashlight for the attached photos.

With the cavity locked, I moved a razor blade (by hand) in front of each of the cavity mirrors. I identified that the beam is far left of center (closer to the edge than the center of the optic) on MC1 and MC3, but only slightly right of center of MC2. The beam is close to centered in pitch on all three mirrors .

Attachments

1. Dust on MC1
2. Dust on MC3
3. Dust on MC2

Attachment 1: 7E766D83-7FA4-47C3-840B-0D2BFECD80E0.jpeg
Attachment 2: 4B9C5DF2-ED97-474C-8BBF-9637CEF781E9.jpeg
Attachment 3: IMG_3689.jpg
3032   Tue Nov 22 11:51:46 2022 aaronDailyProgressVacuuminitial pumpdown of PSOMA chamber

I wiped down all o-rings and KF flanges with isopropyl alcohol and lint-free tekwipes, then closed up and am once again pumping down on just a single 4-way cross.

turbo -> right angle valve -> 4-way cross -> [up-to-air valve, vacuum pressure gauge, KF40 blank]

I noted some black particulate on the steel mesh filter just before the turbo pump. It looks like it could be silicon flakes? Attachments show the same flakes on a KF16 blank.

Update: After the group meeting, JC and I took the 4-way cross with up-to-air valve, gauge, and KF40 blank over to "camel" (formerly TCS) lab where we tried pumping down with their pumping station. We were still unable to reach below 6 mtorr, so concluded that the turbo pump is not to blame.

Next, we removed the MKS 748B gauge and used instead the combination gauge that had been in use for the photodiode testbed cryostat. The pressure was immediately able to reach below 1e-5 torr (the limit of this gauge). It seems the MKS 748B gauge we were using was either faulty (not providing an accurate pressure reading below ~6 mtorr) or actively leaking. I'll find a different combination gauge not currently use and continue testing the PSOMA vacuum system until a new gauge arrives.

I returned the "camel" lab pumping station and photodiode testbed to its previous state, and returned the 4-way cross and accessories to cryo lab.

----

Attachment #3 is the photo of pressure gauge reaching 'The pressure was immediately able to reach below 1e-5 torr (the limit of this gauge)'.

Attachment 1: CA5CF62E-3717-422B-8EDD-5B767311938F.jpeg
Attachment 2: E23472C1-4DB1-4655-8C9A-B6FACBB5438B.jpeg
Attachment 3: Screen_Shot_2022-11-23_at_11.00.54_AM.png
3031   Mon Nov 21 11:00:57 2022 aaronDailyProgressPSOMAmore mode matching

### we're locking to the carrier, not the sideband

It's been suggested that we might be locking to a sideband, rather than the main carrier. I've just confirmed that the RF sidebands for PDH are at 33.59 MHz, and on the beat note spectrum are -30 to -33 dB below the carrier. If we were locking to one of these sidebands, we would expect to see 0.1% (or worse) mode matching efficiency. However, this morning the REFL dips indicate at least 20% modematching efficiency (136 mV dips on REFL mon when the 00 mode is flashing, relative to 669 mV average REFL power away from resonance, and 2-3 mV from room lights and dark current with the beam blocked).

I also flipped the sign of the loop to double check, and saw a dimmer transmitted beam after increasing loop gain to acquire lock. This indicates that the original sign was selecting for the carrier.

We think our cavity is overcoupled and close to critically coupled, based on 1300 ppm MC1 transmissivity and 500 ppm MC2 transmissivity. MC3 has <50 ppm transmissivity, and hopefully our intracavity losses are less than 700 ppm (but we haven't measured this). If we are somewhat over- or under- coupled we don't expect REFL to approach (0W + sideband power + dark current and ambient light power) even for the perfectly matched beam.

### Mode matching or cavity losses degraded slightly since Friday

I didn't note the REFL dips after improving modematching and alignment on Friday, but based on the ratio of TRANS/BEAT PD power the mode matching transmission gain is 3x lower this morning than the last measurement on Friday.

X1:OMA-ERC_MM_OUTPUT (trans mon / beat mon) is at 1.2 today, compared to 3.9 on Friday. It would be good to calibrate this channel to be a ratio of power on TRANS and BEAT PDs, rather than a ratio of their raw voltages.

The ratio of TRANS to BEAT power with the North laser off is affected by mode matching efficiency, cavity losses, and relative changes in loss on the paths to BEAT PD and TRANS PD. Mode matching should be the most sensitive to temperature changes in the lab that could occur over the weekend, but cavity losses or losses in the free space path to the cavity could also change especially if we are close to clipping. While realigning, I also noticed that the z-adjustable stage I've been using for MM2 can push on the mount for SM2 if care is not taken.

### What is the mode matching efficiency today anyway?

Here's a table of measurements and calculations from this morning. I'm not putting REFL in power units because the reflected beam is attenuated to avoid saturating the PD, so only relative changes in the MON voltage matter.

 REFL (unlocked) 669 mV REFL dips (unlocked, delta relative to resonance) 136 mV transmitted power (from power meter) 27 uW Circulating power based on 500 ppm MC2 transmission 54 mW incident power (from power meter) 1.6 mW Measured $G_\mathrm{refl}$ based on REFL dips 0.80 Measured $G_\mathrm{trans}$ based on incident and transmitted power 0.017

For the equations below, $r_n$ is the field reflectivity of the nth cavity mirror, $l$ is the intracavity power loss, $p$ is the mode matching efficiency (power matched to 00 / total power), and the right arrow indicates the value for perfect mode matching (p=1) to the critically coupled cavity (assuming $l\approx 750$ ppm to impose critical coupling)

$G_\mathrm{refl}=\left| \frac{E_\mathrm{refl}}{E_\mathrm{inc}}\right |^2=\left|\frac{-r_1+r_2r_3\sqrt{1-l}}{1-r_1r_2r_3\sqrt{1-l}} \right|^2p+\left|r_1\right|^2 (1-p)\to 0$

$G_\mathrm{opt}=\left|\frac{E_\mathrm{circ}}{E_\mathrm{inc}}\right|^2=\left|\frac{t_1}{1-r_1r_2r_3\sqrt{1-l}} \right|^2p\to 770$

$G_\mathrm{trans}=\left|\frac{E_\mathrm{trans}}{E_\mathrm{inc}}\right|^2=\left| \frac{t_1t_2}{1-r_1r_2r_3\sqrt{1-l}} \right|^2p\to 0.38$

If we assume some value for intracavity loss, we can use either the refl or trans gain to estimate mode matching efficiency... or since we have two measurements and two unkowns, we can use the refl and trans gains together to estimate both intracavity loss and mode matching efficiency.

I did just that with scipy.optimize.fsolve (see "scripts/Cavity gain measurements.ipynb"). Based on the above equations and measurements of reflected and transmitted gains, the best fit mode matching efficiency is 34% with an intracavity loss of 5300 ppm. Wow, are we really this undercoupled due to loss in the cavity? The cavity finesse would only be about 880 with the loss this high, based on

$\mathcal{F} = \frac{\pi}{1-r_1r_2r_3\sqrt{1-l}}$

### PDH slope

I swept the HF drive for the S laser with a 2 Vpp, 314 Hz triangle wave and recorded attachment 1, which shows the pk-to-pk PDH voltage and frequency spacing. The PDH slope for the resonant carrier is 10.5 MHz / V.

The cavity length is about 50 cm, implying the FSR is ~600 MHz. The separation in frequency of the PDH carrier peaks is ~750 kHz, which would imply a finesse of ~800, consistent with the estimate above based on reflected and transmitted power. If the finesse is 880, an FSR of 600 MHz would imply 680 kHz linewidth.

The frequency discriminant for the PDH error signal is $D\equiv \frac{-8\sqrt{P_\mathrm{carrier}P_\mathrm{sideband}}}{\delta \nu}$ for linewidth $\delta \nu$. Therefore, if our linewidth is 750 kHz, carrier power is 1.6 mW, and sideband power 1.6 nW, the discriminant is 1.7e-11 W/Hz. Our NewFocus 1811 PD has 1 A/W responsivity and 4e4 V/A transimpedance gain, so nominal discriminant becomes 6.8e-7 V/Hz.

However, there are some unaccounted for losses: we only send ~half the reflected light to the cavity (based on 1 V/mW at DC) to avoid saturation; the Moku has -20 dB attenuation on its input stage; and +10 dB digital gain before the point where we monitor the PDH error signal. Accounting for these factors, the expected discriminant becomes ~9e-8 V/Hz, or 10 MHz / V PDH slope. This is consistent with my measurement from sweeping the HF drive.

Attachment 1: 9434209F-2BCC-482B-8069-E82FC95D4B28.png
3030   Fri Nov 18 13:33:47 2022 aaronDailyProgressPSOMAmore mode matching

Since I expect we still have a factor ~10 available in cavity gain, I'm playing with the mode matching again.

I aligned the cavity and placed an iris between the input PBS and MC1. The second alignment reference is the REFL camera (and to some extent REFL PD).

By moving the mode matching lenses MM1 and MM2 along the beam axis and realigning where I found the strongest transmission flashes, I was able to roughly double mode matching efficiency. Transmission is up to 6 V on TRANS PD (70 uW on the power meter).

To estimate mode matching efficiency, I made a new channel in CDS called "X1:OMA-ERC_MM" that is the ratio of (TRANS MON voltage) / (BEAT MON voltage). The beat note PD is in fiber, so can be used to normalize for total power (assuming the probe laser is off or has constant power).

I noted that when I close the iris before MC1, the beam on REFL camera starts to clip even before ERC_MM is affected. This indicates that the edges of the beam aren't coupling into the cavity -- the beam should be more tightly focused. Moved MM1/MM2 to make that happen. Noted that the REFL beam is clipping on the output PBS mount, but doesn't affect the mode matching. Also, the MM2 lens needs to be at an angle to correct for some asymmetry in the beam after MM1.

Here's where I ended up after clamping MM1 and MM2:

 TRANS PD 7.42 V 1.6 uW Power meter in front of TRANS camera 86 uW TRANS MON / BEAT MON (ratio of uncalibrated voltages) 3.9 Incident power 1.4 mW

The circulating power is ~200 mW (based on the power meter measurement and 500 ppm MC2 transmissivity). The optical gain is ~140... still lower than expected, but by a factor of a few (<10).

3029   Thu Nov 17 12:18:22 2022 aaronDailyProgressPSOMA

I adjusted the PDH servo's input offset, which let the slow temperature loop drive the S laser current drive to 0 at DC without losing lock.

### mode matching

With the cavity locked and the slow temperature servo on, I adjusted the input steering mirrors to improve cavity mode matching. Because the slow control loop is on, the current and laser power are nearly constant during alignment. Transmission increased from 850 mV to 1.28 V at the transmon PD, indicating a 50% improvement in mode matching. The transmission beam is visibly brighter on the camera.

I also rotated the input half-waveplate 8 degrees to maximize transmitted power. There is a PBS before the cavity, so only S polarization reaches the cavity and this rotation should simply change the amount of S polarized light transmitted through the PBS. To make sure the increased cavity transmission is not due to changing the plant gain by increasing light incident on REFL PD, I also rotated the output HWP and observed no change in transmitted power for small rotations. Adjusting the input polarization further improved mode matching by 7% (1.22 V transmitted to 1.31 V transmitted).

The TRANS PD is a PDA20CS with response ~1 A/W at 1550nm; with the gain knob at 70 dB, we read out 4.75 MV/A. Therefore, ~1 V on TRANSMON implies about 0.2 uW cavity transmission. Since we measured the cantilever mirror transmission (MC2) to be ~500 ppm, this implies ~0.4 mW circulating in the cavity and the pickoff BS in transmission is 90-10, this implies ~4 mW circulating in the cavity. This seems too low -- we want a large cavity gain, and should have it based on the cavity finesse ~9000 and having measured the curved mirror (MC1) to have 1300 ppm transmission for S-polarized light. We have 2-3 mW incident on the cavity, which means we're seeing cavity gain ~2 (we expect more like G=1000 based on those transmissivities and no loss).

I noted the following

 TRANS MON (cavity locked) 1.32 V 0.3 uW REFL MON (locked) 1.20 V 1.20 mW REFL MON (unlocked) 1.36 V 1.36 mW REFL MON dips (unlocked) 152 mV 152 uW

[aaron, chris]

### Chasing down clipping

I pointed out to Chris that the circulating power in the cavity seems way too low He noticed that I hadn't accounted for the 90-10 pickoff BS in transmission, and we used the power meter to measure 11 uW transmitted through the cavity (compared to 0.3 uw reported by the TRANS PD). I'm not sure why the TRANS PD isn't reporting as much power as the power meter, but the power meter measurement implies ~20 mW circulating in the cavity (based on 500 ppm MC2 transmission).

This still is less circulating power than we expect. To check the mode matching, we took the camera from cryo cavs experiment's transmission path and placed it in the REFL path for the PSOMA cavity. We found one clean ghost beam and a much brighter main beam that was severely clipped from below. We used a shard of broken silicon wafer to pickoff the beam just before and after the cavity's plastic box, and thought the beam looked OK entering the cavity but definitely clipped exiting the cavity.

We removed the plastic box, and were able to identify that the beam was clipping on the PBS the selects for 'S' polarized light entering the cavity. We centered an iris between the PBS and MC1, and centered the REFL beam on both the REFL PD and the camera to provide two alignment references. We then gave the PBS a height-adjustable mount and were able to avoid clipping. The REFL beam looks much cleaner, and the cavity transmission when locked is slightly higher than before even without fixing up the mode matching.

While we have such a convenient alignment reference, I adjusted the MM2 lens (the beam was all the way on the right side of the lens) such that the REFL beam with cavity blocked is round.

With these alignment and mode matching improvements, I'm seeing 3-4x higher cavity transmission, indicating ~60-80 mW circulating in the cavity. I measured ~1 mW incident on the cavity with the power meter, so the cavity gain is 60-80. Still a factor of 10 lower than expected, but getting closer.

The beam spots with cavity locked are attached. The bottom monitor is TRANS, top monitor is REFL.

Attachment 1: A20051C6-C674-4D3D-8ACA-506332704403.jpeg
3028   Thu Nov 17 11:11:02 2022 shrutiDailyProgressPSOMAturning on the experiment

The temperature had railed to a bad region with very low power overnight. We had left everything locked and fans on.

While trying to get everything locked, the slow temperature caused oscillations in and out of lock. Turning off the fans and adjusting the gains helped this a little but it was easier to get everything locked for a long time without the slow temperature control.

Transmission is 850 mV, down from ~1V yesterday.

3027   Wed Nov 16 10:32:09 2022 shrutiDailyProgressPSOMAsignal injection

[shruti, aaron]

## I. Reacquired lock after fixing the mode-matching.

1. PDH lock acquisition

• Transmission: 1 V (PD gain 70 dB) when locked
• Reflection: 970 mV when locked, 1.1 V when unlocked

• Refl RF rms: 10 mV (with -20 dB at input)

South temperature setting was ~7.4 kOhm

2. PLL lock acquisition

With the north laser temperature setting at ~6.9 kOhm, the beat between the two lasers was roughly at 300 MHz.

3. Simultaneous locking

With the south laser locked and the feedforward of the PDH control signal to the north laser with a gain of 1/2, the beat remained roughly stable at 300 MHz.

Took some effort and tuning of the PLL servo transfer function but we were able to lock the PLL with the PDH and feedforward on.

## II. Generated signal sidebands around cavity resonance and measured its in-loop transfer function

### 1) Tested whether a 300 MHz sideband can be injected while maintaining the lock

With both the PDH and PLL locked, we sent a 300 MHz modulation to the North EOM, and the locks remained stable. This was from the same Moku oscillator used for phase-locking.

It was not easy to acquire a simultaneous lock with the 300 MHz modulation applied to the north EOM (as expected).

### 2) Measured the signal transfer function with both loops engaged

We phase-locked the clocks of both the Moku and a Marconi using the 10 MHz external oscillator from the RF distribution board. On a spectrum analyzer, we saw that the peaks of a 300 MHz oscillation from the two coincided to within a kHz (I think even better, since our spectrum analyzer RBW was <1kHz during this measurement (measurement span was O(khz)).

We used the Marconi to drive the north EOM first at 299 MHz. While the PDH loop was unlocked and the PLL locked, we saw that the beat between the two lasers was at 300 MHz and there was a sideband at 1 MHz. Then adding a phase-modulation to the Marconi at 20 kHz resulted in sidebands around this 1 MHz peak [Attachment 2]. We noted that with a -20 dBm RF carrier phase modulated with 0.02 rad deviation, the acoustic sidebands appeared with -111 dBm compared to -35 dBm for the direct beat note (so these sidebands are 70-80 dB weaker than the direct beat note, depending on our choice of modulation depths).

Mini aside: we also separately tested that the response of the Marconi with PM (not FM) was more or less flat up to its limit of 20 kHz.

With both the PDH and PLL loops engaged, we drove the Marconi's EXT MOD IN using the DAQ and measured the in-loop response at the PDH and PLL control points ('SLD_HF_MON' and  'NLD_HF_MON' respectively in Attachment 1). This was the first time we were able to get a high coherence transfer function of the secondary sidebands that is the "signal" [Attachment 1]

### Weirdness in the offsets

The PDH lock does not seem to like to operate when the mean output control voltage being 0. We tried adjusting the temperature to slowly move the voltage from some high voltage (~$\pm$ 50 mV) to 0 and the loop would lose lock almost instantly when this number was brought below something like $\pm$5 mV. Adjusting the input offset also does not seem to work. The slow control also causes issues when it reaches a point where the control signal comes close to 0.

I think we eventually got this to work by adjusting the control filter. The next day I also ran into this problem after improving mode matching with N laser off then turning 'on' the N laser again. I needed to check for high gain near the cantilever resonance, no loop oscillation at high frequency, and no saturation at the REFL PD. With these conditions, I could set-and-forget the PDH input offset within a few mV of zero.

For the transfer functions mentioned above and in attachment 1, the slow temperature servo was on and holding the S laser current control close to 0 V.

### side quest -- slow temperature control for S laser

[aaron]

I realized that the N and S current mon cables were swapped. Once that was corrected, the HF mon channel actually corresponds to the control signal that we read out from the analog HF mon port of the laser current drive boxes. The Cathode mon channel has a fixed voltage when the laser is on (good, the anode is being modulated). And, the LF mon reads out a value proportional to the analog knob setting. All is well.

I changed the slow temperature script to drive SLD_HF_MON_OUT16 to zero. The ERC_LOCKED channel I defined in x1oma was a binary input EPICS channel, which is not set by the FE. Instead, I'm using the channel SLD_PDH_LOCKED, which is a an EPICS calc record defined on cominaux in SoftIOC/CRYO.db and compares the TRANS_MON level with ERC_THRESH.

With those changes, the slow temperature control successfully keeps the cavity locked for long times (many minutes). With the PLL also locked, the N laser can follow the S laser also for minutes.

Attachment 1: Screenshot_from_2022-11-16_17-25-38.png
Attachment 2: A34327A5-BCCE-4DB2-BD14-94B9EE637C01.jpeg
Attachment 3: 1BF7007C-8E20-4CB3-B333-D2483B5F0782.jpeg
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