We have seen detuning change more than we expect, such as elog 2512 and elog 2537. In elog 2512, we expect detuning change less than ~15Hz, but we observed detuning change of ~50Hz. In elog 2537, according to the alignment change calculated in elog2540, we expect detuning change of ~3Hz, but we observed detuning change of ~10Hz.

To understand in more detail why this can happen, we take into account the errors of other degradation parameters (shortly DP) (squeezing level, RTL, mode matching, optical losses, phase noise, locking accuracy) and use Monte-carlo estimation to see how the fit result changes. In this entry, I used data of one curve from elog2512, but the same calculation can be applied to other data. The code used in this entry is based on Eleonora's code.

From least square curve fit, the expectation and standard deviation are estimated by giving fixed DPs. The result is angle 11.22+/-0.13,  detuning 105.09+/-0.54.

The Monte-carlo estimation gives expectation and std based on random chosen of DPs within normrnd(mean,std). The means of DP are chosen as the same with least square curve fit, while std is chosen as indicated in PRL paper. This means that, for one calculation, 8 DPs are chosen randomly while cavity detuning and homodyne angle are left free, then matlab uses least square method to give a fit of the FDS measurement and gives center values of detuning and homodyne angle. After calculating for 1000 times, we have 1000 center values for [cavity detuning, homodyne angle], which took 1.5 hours. This result is plotted as two histgrams as the attached figrue.This gives result of angle 11.22 +/- 0.35, detuning 105.04 +/- 1.18.

We can see basically the fitting error becomes about two times larger.