deletions | additions       diff --git a/section_Introduction_It_is_common__.tex b/section_Introduction_It_is_common__.tex  index f3360d5..22f8412 100644  --- a/section_Introduction_It_is_common__.tex  +++ b/section_Introduction_It_is_common__.tex 
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If we had a cell at zero temperature, and the rubidium was still a gas, as the frequency of the laser is scanned, the transmission through the vapor cell would produce Lorentzian dip. Off resonance the transmission should be $100\%$. As the laser frequency passes through the resonance, the laser transmission drops. The resulting Lorentzian shaped dip is a direct result of the Heisenberg uncertainty principle. The inverse of the full width half maximum of the Lorentzian profile (in angular frequency space) is the average lifetime of the excited state. As the temperature increases from zero kelvin, the peak will broaden about this central frequency. Doppler broadening, described below, is actually a convolution between the zero temperature Lorentzian profile and the Maxwell Boltzmann Gaussian shaped velocity profile. In the Doppler spectroscopy experiment, we fit to a negative Gaussian profile because there are six different Lorentzian shaped profiles that are simultaneously Doppler broadened. (An example of a fit to a negative Gaussian is shown in Fig.~\ref{fig:NegativeGaussian}. This data will be thoroughly discussed in the Results section.) The resultant complicated Voight profile is extremely difficult to fit. We therefore expect the fitted temperature to be larger than room temperature since we ignore this convolution. This is what we find, see Discussion.   \textbf{It is a good idea to insert an explanation of Doppler spectroscopy (as you did above), since your readers are unlikely to already know what it is. But in addition, you also need to include some references to relevant papers ---- such as ones you yourself read and consulted in preparation for this experiment? --- where your reader can learn more, or where they can find where the technique was first used. I have randomly chosen a paper to cite by using Authorea's search CrossRef function (searching on the term ``Doppler Spectroscopy of Rb''), but you should replace it with one you actually used. }  To understand Doppler broadening, consider a vapor cell at room temperature. Since the atoms have some temperature, they are moving at some velocity whose distribution (ignoring the natural Lorentzian profile) can be exactly described by the Maxwell Boltzmann distribution. When an atom is moving towards or away from the laser beam, it sees photons of a higher or lower frequency as being the correct frequency to excite the electrons—so, different frequencies of light interact with different velocity classes of atoms. In the atom frame of reference, only photons with the correct frequency are absorbed, but in the lab frame of reference, the Doppler shift added to the frequency of the laser is the frequency of light that the atoms absorb. We measure in the lab frame, so we see a broadened curve.   An atom with zero velocity, which is in what is referred to as the zero velocity class, is the one which will absorb light at the exact frequency of the transition in the lab frame. This atom is either not moving, or is moving perpendicular to the laser beam. To be exact, the atom's velocity in the direction of the laser beam has to be within the Lorenztian profile of the transition.