Thu Apr 25 15:47:54 2019, Anjali, Update, Frequency noise measurement, Homodyne v Heterodyne

Message ID: 14576
Entry time: Thu Apr 25 15:47:54 2019
In reply to: 14573

Author:

Anjali

Type:

Update

Category:

Frequency noise measurement

Subject:

Homodyne v Heterodyne

My understanding is that the main advantage in going to the heterodyne scheme is that we can extract the frequecy noise information without worrying about locking to the linear region of MZI. Arctan of the ratio of the inphase and quadrature component will give us phase as a function of time, with a frequency offset. We need to to correct for this frequency offset. Then the frequency noise can be deduced. But still the frequency noise value extracted would have the contribution from both the frequency noise of the laser as well as from fiber length fluctuation. I have not understood the method of giving temperature feedback to the NPRO.I would like to discuss the same.

The functional form used for the curve labeled as theory is 5x10^{4}/f. The power spectral density (V^{2}/Hz) of the the data in attachment #1 is found using the pwelch function in Matlab and square root of the same gives y axis in V/rtHz. From the experimental data, we get the value of V_{max} and V_{min}. To ride from V_{max} to V_{min} , the corrsponding phase change is pi. From this information, V/rad can be calculated. This value is then multiplied with 2*pi*time dealy to get the quantity in V/Hz. Dividing V/rtHz value with V/Hz value gives y axis in Hz/rtHz. The calculated value of shot noise and dark current noise are way below (of the order of 10^{-4 }Hz/rtHz) in this frequency range.

I forgor to take the picture of the setup at that time. Now Andrew has taken the fiber beam splitter back for his experiment. Attachment #1 shows the current view of the setup. The data from the previous trial is saved in /users/anjali/MZ/MZdata_20190417.hdf5

Quote:

If I understand correctly, the Mach-Zehnder readout port power is only a function of the differential phase accumulated between the two interfering light beams. In the homodyne setup, this phase difference can come about because of either fiber length change OR laser frequency change. We cannot directly separate the two effects. Can you help me understand what advantage, if any, the heterodyne setup offers in this regard? Or is the point of going to heterodyne mainly for the feedback control, as there is presumably some easy way to combine the I and Q outputs of the heterodyne measurement to always produce an error signal that is a linear function of the differential phase, as opposed to the sin^2 in the free-running homodyne setup? What is the scheme for doing this operation in a high bandwidth way (i.e. what is supposed to happen to the demodulated outputs in Attachment #3 of your elog)? What is the advantage of the heterodyne scheme over applying temperature feedback to the NPRO with 0.5 Hz tracking bandwidth so that we always stay in the linear regime of the homodyne readout?

Also, what is the functional form of the curve labelled "Theory" in Attachment #2? How did you convert from voltage units in Attachment #1 to frequency units in Attachment #2? Does it make sense that you're apparently measuring laser frequency noise above 10 Hz? i.e. where do the "Dark Current Noise" and "Shot Noise" traces for the experiment lie relative to the blue curve in Attachment #2? Can you point to where the data is stored, and also add a photo of the setup?