Sensitivity calculations for a RF heterodyne system

[JaySardesai444]

Thank you for making this tool, it's been very helpful!

I'm currently trying to extract a measurement of sensitivity (units of nV/cm/sqrt(Hz)) from the RF heterodyne response graph. It is my understanding that susceptibility is a good measure of transmittance/absorbance [REF] due to it's effect on scattering. I'm aiming to measure sensitivity so I can compare two-photon Rydberg EIT sensors to values in the literature, which also seem to use this metric [Haoquan Fan et al 2015 J. Phys. B: At. Mol. Opt. Phys. 48 202001]. I'd also like to compare this metric to the Standard Quantum Limit (SQL) for the minimum detectable field (from the same paper).

where N_{at} is the number of atoms participating in the measurement, and T_{2} is the dephasing time of the coherent EIT process. The integration time over which the measurement takes place has been set to 1s here.

Bandwidth may also be a useful measurement to help calculate sensitivity here, but I'm not sure.

All of this is a really roundabout way of asking the question: Is the sensitivity a metric that can be extracted from the response curve? (such as that in the RF heterodyne example)

[dihm]

The response curve is a necessary part, but there is more to it. Sensitivity is a short hand for saying what input field is required such that SNR=1 (where SNR is in variance, power units). Rydiqule can numerically calculate how the signal changes as a function of some input. Rydiqule does not tell you what the appropriate noise model is.

I'd actually recommend looking at the Calculating SNR notebook, or more precisely the calculate_snr function. Basic idea is to calculate the change in response as you change some input parameter by a small amount (ie assume response is linear, calculate derivative, extrapolate to SNR=1 point). If you are clever in setting up the problem, you can even avoid the time-solver and just work in steady-state for certain problems, which is much faster.

[JaySardesai444]

Thank you! My current method involved measuring the IBW of the rf heterodyne system, and estimating sensitivity as the min electric field/sqrt(bandwidth). I'll try this method, it seems to be more accurate. Interestingly, as I'm unable to input an initial condition when using doppler broadening, for large rabi frequencies (rf_rabi > 150 Mrad/s), I get a curve like this:

instead of my usual bandwidth graph

which is concerning. I'll try and see what the problem is, though it's likely just a foolish mistake on my part.

Thank you again for all your help!