ROUGH DRAFT authorea.com/90970

# Defining energy levels in Rubidium 87 and 85 using Doppler and Doppler-Free Spectroscopy: 2nd draft

Abstract

We performed both Doppler and subDoppler spectroscopy on the $$5^{2}S_{1/2}$$$$5^{2}P_{3/2}$$ transition of rubidium 85 ($$^{85}$$Rb) and rubidium 87 ($$^{87}$$Rb). We fit the Doppler spectroscopy curves to Maxwell Boltzmann velocity distributions to determine the temperature of the cell. We also fit the subDoppler spectroscopy curves to extract the transition energies and hyperfine structure of the $$5^{2}S_{1/2}$$ F=2 ground state to the $$5^{2}P_{3/2}$$ F=1, F=2, and F=3 excited states of $$^{85}$$Rb, the $$5^{2}S_{1/2}$$ F=3 ground state to the $$5^{2}P_{3/2}$$ F=2, F=3, and F=4 excited states of $$^{85}$$Rb, the $$5^{2}S_{1/2}$$ F=1 ground state to the $$5^{2}P_{3/2}$$ F=0, F=1, and F=2 excited states of $$^{87}$$Rb, and the $$5^{2}S_{1/2}$$ F=2 ground state to the $$5^{2}P_{3/2}$$ F=1, F=2, and F=3 excited states of $$^{87}$$Rb. The calculated difference between the transition from the F=2 excited state of the $$5^{2}S_{1/2}$$ state of rubidium 87 to the $$5^{2}P_{3/2}$$ state and the transition from the F=3 excited state of the $$5^{2}S_{1/2}$$ state of rubidium 85 to the $$5^{2}P_{3/2}$$ state, was found to be $$1.062 x 10^{9}$$ Hz $$\pm$$ $$1.6 x 10^{7}$$ Hz, compared to the value from (Daniel Adam Steck 2001) of $$1.22039 x 10^{9}$$ Hz $$\pm$$ $$2 x 10^{4}$$ Hz. Our results for Doppler Spectroscopy were not quite consistent with theory within uncertainty, but there are many possible reasons for this slight discrepancy. The uncertainty in the Doppler profile fitting is most likely due to an incomplete model of the transmission curve. While we modeled the as a Maxwell Boltzmann Gaussian distribution, the actual curve is a convolution between the six Lorentzian line profiles and the Gaussian distribution. The uncertainty in the hyperfine fitting is likely mainly due to the fact that we modeled our frequency scan as linear but it is not actually linear.