Michael and Yuhang

We took FDS with filter cavity GR control about two weeks ago. The measurement contains 12 effective data with 6 for detuning around 200Hz and 6 for detuning around 70Hz. The data below around 70Hz is contaminated by back scattered noise. To have some margin from back scattered noise, we start fit from 100Hz.

The mcmc code needs a good enough initial value and corresponding range. We start with a least square fit with detuning, homodyne angles free and other parameters fixed. The fit result was used as initial value for mcmc code. The least square fit results are attached as figure 1 and 2.

We used the result of least square for mcmc and set four parameters to be free, including homodyne angle, detuning, optical losses, generated squeezing level. The result is attached as figure 3 and 4. The FDS with 200Hz detuning has more information about the squeezing quadrature rotation. Therefore, the error of fitting result is more precise. But the FDS with 70Hz detuning has less information, which makes the fit result has larger error on detuning.

The mcmc result gives more stabilized detuning, which means data favors a more stable detuning. The least square mothod gives larger detuning change may just comes from the fact that we are fixing other parameters but leave only two free.