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Post_processing.rst

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4. Post-Processing the acquired data

Theory

The Rabi frequency is proportional to the square root of the Intensity. Let's write this relation as \Omega = A \sqrt{I}. Let's assume we know \Omega for a RF amplitude V_0, and write this Rabi frequency \Omega_0. Using our setup, we measure I_0 = I(V_0), and deduce A = \frac{\Omega_0}{I_0}. Therefore we now have \Omega^2(V) = \frac{\Omega^2_0}{I^2_0} I(V). V is obtained from \Omega^2 as V(\Omega) = I^{-1}(\frac{I^2_0}{\Omega^2_0} \Omega^2).

Implementation

The core of the problem is about building the inverse function of the intensity I^{-1}, that takes an intensity and outputs a voltage. From the output of the previous simulation, we have two arrays of data associating intensities i to voltage a. The function looks like a bijection, and it also makes sense to plot the voltage a function of the intensity i. This disrete V(I) set of points can be interpolated using :py:func:`scipy.interpolate.interp1d`, building the wanted V = I^{-1}(I) curve. Note that lots of points are necessary in the zones where the I(V) is almost constant (for small amplitudes for example).

To find the RF amplitude associated to a Rabi frequency, you then just have to call the interpolated function just built with parameter \frac{I^2_0}{\Omega^2_0} \Omega^2(V)