Once you have aligned the interferometer and obtained a clean interference pattern on the scope, use the cursor feature of the scope to measure the locations of the interference maxima (including an estimate on the uncertainty of these measured values) and record them in your lab notebook. You should also transfer a screenshot and the digitized data to the lab computer for inclusion in your out of lab assignment.

You will be expected to be able to articulate clearly and concisely how you performed this measurement, and how you estimated the uncertainties in the measured values.

Do not forget to measure and record the dimensions of the interferometer.

From this point forward you will want to focus on the first two doppler broadened features, the 87Rb(F=2) and 85Rb(F=3) transitions. For each of these two peaks you need to record and save a scope trace which has been zoomed in enough to see all 6 doppler free dips clearly. You should also use the cursor feature to carefully measure the locations of these dips, with estimated uncertainties.

You will need to spend some time adjusting the overlap and power of the probe and pump beam in order to see all 6 of the expected doppler free features on each of the doppler broadened peaks. The optimal beam powers for the 87Rb(F=2) and 85Rb(F=3) transitions are different enough that you will need to optimize and record them separately.

• Assuming the reader knows what thermal doppler broadening is, show your complete calculation of the expected line width due to thermal doppler broadening. (5 points)
  • Include proper units and sig figs for all numerical values.
  • For any measured quantities used in the calculation include a brief description of how the quantity was measured and how you estimated the uncertainty in the measurement.
  • Show all steps in the calculation as you would for a pset problem.
• Show how you performed the measurement of the doppler broadened line width. (10 points)
  • Include a publication quality annotated plot or figure illustrating what the signal looked like and the features you measured.
  • What were your measured quantities and how did you estimate their uncertainties.
  • Provide enough detail that someone familiar with the apparatus would be able to duplicate your measurement technique. Did you use the scope cursors, if so how. Did you perform a fit, if so what functional form did you use and why. Referring to your annotated figure should be helpful here.
• Present your line width vs temperature results. (10 points)
  • Show your measured values vs the theoretical expectation in an appropriate form. This could be a properly formatted table, or a plot. The choice is yours, but the result should make it easy for the reader to understand your results. Sig figs and units matter.
  • Include a publication quality plot that overlays the profiles of the doppler broadened peaks for all temperatures. This provides an excellent visual depiction of the broadening effect with temperature that compliments, but does not replace the numerical results.
  • Comment on whether or not your results are consistent with what you expect. You will not find precise agreement between your measured values and those calculated from theory, this is a plausibility test. I.e. you have been told that the width of these peaks is caused by thermal doppler broadening, the question is whether or not this statement is scientifically plausible. We strongly suggest that you discuss this point with an instructor before leaving the lab on day 2 in order to ensure your answer is reasonable.

• For each isotope present your DFSAS spectrum showing the six doppler free dips. (10 points)
  • Include a publication quality screen shot or plot of the spectrum that you used for measurements of the energy differences of the doppler free dips.
  • The figure should be annotated to identify which features are transitions and which are cross overs
• Describe how you performed your energy difference measurement. (10 points)
  • Make clear how you made the measurements. I.e. Did you use the scope cursor feature or some other method? How did you determine where to place the cursor and what limited how well you were able to make the measurement?
  • Did you make use of the cross-over features, if so how?
• For each isotope present your full data set. (10 points)
  • Include all measured values along with units and uncertainties.
  • Make clear which feature in the spectra each measurement corresponds to.
• Compare your experimental result with the literature values. (10 points)
  • Present your experimental results with their associated theoretical values.
  • Use the uncertainties in your measured values to assess the degree of agreement with the theoretical expectations. Keep in mind that you are not being graded on whether or not your values agree with theory. Your data are what they are, and it is your job to draw whatever conclusions you can from the data.

• Present your measurement of the natural line width for one Hyperfine transition. (5 points)
  • Include all measured values with associated uncertainties.
  • Briefly describe your procedure for obtaining your measured values and their uncertainties. Your annotated figure of the spectrum should be helpful here for making it clear what feature(s) you measured.
  • Show the full calculations of your measured natural line width and the theoretical expectation.
• Compare your measured natural line width with the theoretical line width. (5 points)
  • Compare your measured and theoretical values and make a statement on the degree of agreement between the two.
  • Keep in mind you are not expected to obtain some “correct” value. In fact there are instrumental factors such as the response time of the detectors and amplifiers which we are not considering. Obtaining a value within a factor of 2 of expectation would be reasonable.