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 Tue Jun 4 00:17:15 2019, gautam, Update, BHD, Preliminary BHD calculations Thu Jun 6 18:49:22 2019, gautam, Update, BHD, Preliminary BHD calculations Wed Jul 3 11:47:36 2019, gautam, Update, BHD, PRC filtering Wed Jul 31 09:41:12 2019, gautam, Update, BHD, OMC cavity geometry Wed Jul 31 17:57:35 2019, Koji, Update, BHD, OMC cavity geometry Fri Aug 23 10:01:14 2019, gautam, Update, BHD, OMC cavity geometry - some more modeling Tue Aug 6 15:52:06 2019, gautam, Update, BHD, Preliminary BHD calculations
Message ID: 14652     Entry time: Tue Jun 4 00:17:15 2019     Reply to this: 14658
 Author: gautam Type: Update Category: BHD Subject: Preliminary BHD calculations

​Summary:

Attachment #1 shows the RIN and phase noise requirements for the 40m BHD for measuring Ponderomotive squeezing.

Some details:

1. The interferometer topology is not systematically optimized - I just picked values which are likely close to what we will eventually choose. Namely, $P_{\mathrm{PRM}} = 8\,\mathrm{W}$$\phi_{\mathrm{SRC}} = 0.275 ^{\circ}$$\zeta_{\mathrm{homodyne}} = 88 ^{\circ}$$\mathcal{L}_{\mathrm{rt}}^{\mathrm{arm}} = 30\, \mathrm{ppm}$$G_{\mathrm{PRC}}\approx 40$. Nevertheless, I think these requirements will not change by more than 30% for changes to the interferometer config.
2. The requirements are evaluated using the following criterion: assuming that the dominant noises are (i) coil driver at mid-frequencies and (ii) quantum noise at high frequencies, what do the RIN and phase noise on the LO have to be such that the equivalent displacement noise is a factor of 10 below? I opted for a safety factor of 10, this can be relaxed.
3. An unknown is how much contrast defect light we will end up having due to the mismatch between arms. I assumed a few representative values.
4. The calculations were done analytically. This paper provides a good summary of the relations - although my RIN requirement is more stringent because of the safety factor of 10, and phase noise requirement is less stringent (despite the same safety factor) because we plan to read out at nearly the amplitude quadrature.
5. Since we are discussing the possibility of delivering the LO field using a fiber-coupled pickoff of the laser prior to RF sidebands being added, these requirements do not benefit from passive filtering from the cavity transfer functions. Consequently, the requirements are pretty challenging I think.

Conclusions:

1. The RIN requirement looks very challenging - we will need a shot noise limited ISS with 100 mW DC sensing light, and will likely have to relax the safety factor depending on how much contrast defect light we end up having. This actually sets some requirement on the amount of filtering we need from the OMC (next step).
2. The phase noise requirement also looks very challenging - I need to look up what is possible with the double-pass through fiber technique.

Next steps:

1. Evaluate the pointing stability requirement on the LO field (IFO output is filtered by the OMC).
2. We still need to think of a control scheme for the LO phase - likely, I think we will need a suspended optic between the fiber collimator delivering the light to the BHD setup with some kind of length actuation capability.
3. Numerical validation of this analytic study. I believe Finesse is still missing some capabilities that allow us to calculate these couplings, but I'll ask the experts to be sure.
4. Build up the requirements on the OMC cavity:
• Backscatter requirement (related = OFI isolation requirement, relative length noise between SRM and OMC, OFI and SRM). Does the OFI also have to be suspended?
• Filtering requirement
• Pointing stability requirement
• Length noise requirement
 Attachment 1: LOreqs.pdf  26 kB  Uploaded Tue Jun 4 01:32:38 2019
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