Both Doppler free absorption spectroscopy and Doppler Spectroscopy were successfully used to characterize energy levels seen in \(^{85}Rb\) and \(^{87}Rb\). Furthermore Doppler free absorption spectroscopy was successfully used to capture the hyperfine structure seen in these two isotopes of Rubidium. Transmission data as measured from the oscilloscope was fitted to multiple Lorentzians. From the four plots of transmission data and their corresponding fits shown in Figure \ref{fig:HyperfineFits}, the values of \(\tilde{\chi}_\nu^2\) ranged from \(0.08\) to \(0.17\). While values of \(\tilde{\chi}_\nu^2 \ll 1\) can indicate a disagreement between our proposed model and the data, we inferred that it was instead a problem with our calculated uncertainties as small values of \(\tilde{\chi}_\nu^2\) can also be an indicator of underestimated uncertainties. Actually, just the opposite. Chi-sq gets smaller as the uncertainty gets larger. Our frequency scan was also determined to be non linear, although we had modeled it to be linear. With this uncertainty we could roughly relate wavelength to oscilloscope time for Doppler spectroscopy. For Doppler Free spectroscopy the variations in the frequency scan were too great to make the same correlation.
Hyperfine structure could not be resolved by Doppler spectroscopy, but we were able to calculate average temperature of the atoms. We expected the temperature of the atoms to be around \(T=300 K\) (room temperature), however most of our temperature values were consistently higher than the expected value. We attributed this to our decision to fit our data using a Maxwell-Boltzmann distribution instead of the more accurate Gaussian/Lorentzian combination, and not error in our experiment.
Future experiments could have a way of monitoring frequency scan so that we can be sure it is linear. Then we will be able to covert oscilloscope time into a transmission frequency, which can then be compared to known values.