On Friday, I took some ADF sweeps of the FC and tried to measure frequency dependent squeezing on the homodyne. The FC detuning was fixed at around 1kHz throughout the measurment.
A bit about the ADF sweeps. I made a total of 8 sweeps, 4 sweeps with the filter cavity turned on and 4 calibration sweeps with FC2 misaligned. The 4 sweeps are upper(+ve) and lower (-ve) ADF measurements taken at squeezing and anti-squeezing. The measurement is the same as the one described in the ADF paper.
While trying to interpret the data, I realized that the squeezing and anti-squeezing data sets were not exactly at 0 and 90 degrees so it was not trivial to directly compute m_p and m_q from the measurements. Instead, I tried to fit the individual ADF sweeps. This required knowledge of the ADF Transmission gain G which is the ratio of the ADF-LO RMS while anti-squeezing to squeezing. This was measured to be around 3.23 for Friday's data.
There were a total of 8 functions that could be fit to obtain FC characterization data. The 4 ADF sweeps each have real and imaginary parts that can be fit separately. During the analysis, I opted to fit the real part of the upper ADF while squeezing and see if the fit parameters work for all of the other traces too. The parameters in the fit were squeezing angle, FC detuning, input mirror transmissivity T_in, round trip loss and mode-matching into the filter cavity. FC length noise is largely degenerate with round trip loss so i did not include it in the model. curve_fit did not seem happy with the large number of fit parameters, indicating that some parameters needed to be fixed. I first fixed the input mirror transmissivity to 1000ppm, a value measured at CIT. But that ended up giving negative values for round trip loss indicating that T_in might actually be lower. Lee mentioned that the optic vendor's quote for this value was lower (around 909ppm). After fixing T_in to that value, the fit parameters made more sense with a round trip loss of 36.4 ppm and a mode matching efficiency of ~97%. It is useful to note that the ringdown measurments made on Thursday cannot allow T_in to be greater than ~950ppm either (anything greater would also lead to negative loss). The fit params seem to reasonably agree with the other 7 traces that were used for estimating FC paramters.
SQZ Spectra:
After estimating these parameters, I tried to see if they make sense with the actual FDS spectra measured on friday and things seem to make sense.
