deletions | additions       diff --git a/When_we_measure_the_transmission__.tex b/When_we_measure_the_transmission__.tex  index 046e32d..c99f0c0 100644  --- a/When_we_measure_the_transmission__.tex  +++ b/When_we_measure_the_transmission__.tex 
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When we measure the transmission of the probe beam with a photodiode, we get our negative Gaussian absorption curve, but we also get a small Lorentzian peak at the rest frequency of the transition (as seen in Fig.~\ref{fig:subDopplerEx}) because the probe beam is not being absorbed by the atoms at that frequency, since the pump beam has already excited all of the atoms in the zero velocity class. Since we have hyperfine structure, there are multiple transitions within the Doppler profile. The hyperfine structure appears as multiple Lorentzians. With the transitions we measure, we expect to see three hyperfine peaks due to three hyperfine states. However, due to crossovers, we actually see six peaks. An example of the six peaks can be seen in the graph of $5^{2}S_{1/2}$ F=2 ground state to the $5^{2}P_{3/2}$ F=1, F=2, and F=3 excited states of $^{87}$Rb shown in Fig.~\ref{fig:HyperfineFits}. Crossover peaks appear midway between each of the energy levels in the atom, therefore doubling the number of peaks. Crossovers appear midway between the energy levels because there are two different velocity classes interacting with both beams at the same time, but since the pump beam has a higher intensity, it excites the electrons instead of the probe exciting them. Crossovers can sometimes appear larger than the hyperfine peaks because there are two velocity classes contributing to a crossover peak, as opposed to one velocity class contributing to hyperfine peaks. (See \cite{Melissinos_2003} pp  244-245). \textbf{ARGH! You MUST actually insert a live citation here. It is NOT hard to do, and learning how to do so is an expectation for the course. }You already have been shown several examples of how to do it, and have been given an example using Melissinos as a reference. Why not do it?