Summary:

Craig and I have been trying to put together a Simulink diagram of the proposed alternative calibration scheme. Each time I talk the idea over with someone, I convince myself it makes sense, but then I try and explain it to someone else and get more confused. Probably I am not even thinking about this in the right way. So I am putting what I have here for comments/suggestions.

What's the general idea?

Suppose the PSL is locked to the MC cavity, and the AUX laser is locked to the arm cavity (with sufficiently high BW). Then by driving a line in the arm cavity length, and beating the PSL and AUX lasers, we can determine how much we are modulating the arm cavity length in metres by reading out the beat frequency between the two lasers, provided the arm cavity length is precisely known.

So we need:

1. Both lasers to be stabilized to be able to sense the line we are driving
2. A high bandwidth PDH loop for locking the AUX laser to the arm cavity such that the AUX laser frequency is able to track the line we are driving
3. An accurate and precise way to read out the beat frequency (the proposal here is to use an FPGA based readout)
4. An accurate measurement of the arm length (I think we know the arm lengths to <0.1% so this shouldn't dominate any systematic error).

To be able to sense a 1kHz line being driven at 1e-16 m amplitude, I estimate we need a beat note stability of ~1mHz/rtHz at 1kHz.

Requirements and what we have currently:

• The PSL is locked to the mode-cleaner, and the arm cavity is locked to the PSL. The former PDH loop is high BW, and so we expect the stabilized PSL to have frequency noise of ~1mHz/rtHz at about 1kHz (to be measured and confirmed)
• The AUX laser is locked to the arm cavity with a medium-BW (~10kHz UGF) PDH servo. From past out-of-loop ALS beat measurements, I estimate the expected frequency noise of the AUX laser at 1kHz to be ~1Hz/rtHz with the current PDH setup
• Rana suggested we "borrow" the stability of the PSL by locking the AUX laser and PSL in a high bandwidth PLL - if we want this loop to have ~300kHz BW, then we need to use an EOM as an actuator. The attached Simulink diagram (schematic representation only, though I think I have measurements of many of those transfer functions/gains anyways) shows the topology I had in mind. Perhaps I did not understand this correctly, but if we have such a loop with high gain at 1kHz, and the error signal being the beat between PSL and AUX, won't it squish the modulation we are applying @1kHz?
• Is it feasible to instead add a parallel path to the end PDH loop with an EOM as an actuator (similar to what we do for the IMC locking)? Ideally, what we want is an end PDH loop which squishes the free-running NPRO noise to ~1mHz/rtHz at 1kHz instead of the 1Hz/rtHz we have currently. This loop would then also have negligible tracking error at 1kHz. Then, we could have a low bandwidth PLL offloading onto the temperature of the crystal to keep the beat between the two lasers hovering around the PSL frequency.

Hardware:

On the hardware side of things, we need:

• Broadband EOM
• FSS box to drive the EOM (Rana mentioned there is a spare available in the Cryo lab)

Koji and I briefly looked through the fiber inventory we have yesterday. We have some couplers (one mounted) and short (5m) patch fibers. But I think the fiber infrastructure we have in place currently is adequate - we have the AUX light brought to the PSL table, and there is a spare fiber running the other way if we want to bring the PSL IR to the end as well.

I need to also think about where we can stick the EOM in given physical constraints on the EX table and the beam diameter/aperture of EOM...