In order to determine the amount of broadening in the absorption spectrum due to the Doppler effect, we measured the amount of light absorbed by the sample over a range of wavelengths. We kept the rubidium sample at room temperature to eliminate significant effects due to collisional, lifetime, and resonance broadening. The following graph displays the amount of light absorbed by the Rubidium sample versus the wavelength of light emitted by the laser. The actual wavelengths on the graph are inaccurate, however the difference between the wavelengths are pretty reliable. This is because we knew how much the stepper was stepping (approximately 27.25 femtometers) but only knew roughly where it started stepping. We measured the starting point using ocean optics and the resolution of this system was close to 2 nm.
We analyzed this graph using origin in order to get an accurate estimate of the Full Width Half Maximum of this absorption spectrum. After fitting our data to a gaussian we found that FWHM= w/.849 (Origin 6.1 Help Menu). So, the FWHM of this spectrum is 13.34 picometers. The calculated FWHM of the spectra due to Doppler broadening is 1.03 picometers. So, we are off by a factor of 13. Because the broadening was so much bigger than we thought it would be, we tried to find possible sources of error. The laser we were using to excite the rubidium atoms has a Δf of 3-15 GHz. At 780 nm, this means the Δλ of the laser is about 10.14 picometers. So, the broadening of the above spectrum was actually due to the length of the laser line width instead of the Doppler broadening of the sample.
In order to measure any sort of broadening due to the sample, the broadening needs to be greater than 10.14 picometers. So, we decided to heat the sample up. Our thinking was that if the sample was hot, then the pressure would go up. If the pressure went up then our sample would experience pressure broadening. If this broadening was greater than the breadth of the laser line width then we would get “good data.” That is the breadth of our spectra would be due to the sample rather than the laser. So, using heat tape and a thermocouple, we raised the temperature of our sample. These are three of the nine sets of data we obtained.
When the sample was heated to 33˚C above room temperature FWHM=10.76 pm
When the sample was heated to 48.5˚C above room temperature FWHM=10.72 pm
When the sample was heated to 65˚C above room temperature FWHM=7.33 pm
The broadening we observed when we heated the sample to 326˚K and 341.5˚K was comparable to the width of the laser line. When we heated the sample to 360˚K, the broadening actually decreased. This may be merely due to the lack of a good fit to the data and the lack of a enough data points. Unfortunately, when we heated the sample, the intensity of light measured by the detector went down. This was because the rubidium atoms stuck to the walls of the cell and prevented light from leaving. If this had not been a problem, I am confident that all three temperatures would have had line widths comparable to the laser line. Therefore, we can conclude that the broadening we see is merely due to the laser and not the sample. Why did we not observe the expected pressure broadening? After all, we increased the pressure by several orders of magnitude. The reason we did not see this broadening was because resonance broadening and lifetime broadening affects the emission spectra of the rubidium cell and not the absorption spectra. Because we were measuring only the absorption spectra we, of course, saw none of this broadening. If we had increased the pressure of our rubidium cell even more we would have been able to see changes in the absorption spectra due to collisional broadening. Because this broadening affects the actual energy levels in the atom, then both absorption and emission spectra would have been broadened. Unfortunately at our temperatures, the collisional broadening mechanism was not large enough to “overcome” the line width of the laser we were using. At the highest temperature, the laser line width wouldn't have been noticable at all (increased by 1*10^-20)
There are several things we can conclude from all of our work. First, the line width of our laser is somewhere around 10 pm when emitting light with a wavelength of about 780 nm. Second, the Doppler broadening of our rubidium cell is less than 10 pm. This affirms our prediction that the Doppler broadening is approximately 1 pm. Third, both collisional and resonance broadening do not significantly affect the absorption spectrum of the rubidium cell at relatively low pressures.