Document mask and clustering feature extraction

[alecandido]

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✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.86%. Comparing base (6988e24) to head (143f875).

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##           stabilize-extract-feature    #1324      +/-   ##
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src/qibocal/protocols/utils.py	93.05% <100.00%> (-0.02%)	⬇️

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[lballerio]

@alecandido in the new commit I tested the signal detection for ResonatorPunchout without using the mask...as you can see we see the signal in the two distinct regimes (high and low amplitudes), but still we cannot find the intermediate regime where the interaction is slowing switching on.
Why don't we save indeed the two clusters separately?

[alecandido]

@lballerio as mentioned, the case of the "punchout" (aka power shift) is quite different from the flux dependencies.

Indeed, we do not have (or at least apply) a global model for the behavior of the lower-dimensional feature. Even in the flux-dependencies, we do not have a model for the full 2-dimensional behavior. But once we extract the 1-dimensional feature, we can model it all.

However, for the power shift, our assumption is just that we have two different regimes, with two different resonance frequencies. And they should be steady, in a certain range.
I.e. from a certain point on, it does not matter how much power you give (until you break it), the resonator will be in the "high power" regime, with a fixed frequency. Same for the low-power, until your signal is killed by SNR.

So, our intended fit will consist of two vertical lines[*], once we have identified the two regimes. We are not modelling what is happening in the middle. And there is not much incentive to do that, since we will not consume this information: for us, this experiment is mostly useful to identify the bare and dressed frequency. Thus, the $\omega_r$ frequency of the resonator, and the dispersive shift $\chi$.

It's perfectly fine, and advised, to process the two clusters separately. Given that we are able to actually separate them in advance, automatically.

[*]: In that case, we may even have a 2D model, in a restricted area, since for each cut they should be fixed resonance shapes. Lorentzians, if you are lucky enough. But there are not many guarantees about the parameters which are not strictly related to the resonator itself, e.g. as the baseline.