Make sure that the students grasp the concepts covered in the RESEARCH section of the experiment wiki page.

Guide them through the process of developing a sensible optical plan for both the spectroscopy and calibration parts. When they come to lab on day 1 they should have a diagram of their optical layout. Focus on conceptual understanding of what the different optical components do and how they combine to create the beam paths we need. Do not worry about covering details of how to operate the laser, or the physics of how waveplates work as this will likely just get lost in information overload.

You should make clear that one of the learning objectives is gaining hands on experience working with and aligning beam optics. They should not expect to come into the lab and successfully build their optical layout on the first try. They will almost certainly have to at least partially disassemble their first attempt or two and rebuild before they get a functioning setup. This is simply the only way to learn how to work with laser optics. Emphasize that their lives will be significantly easier if they work systematically front to back along the optical path, making certain that they have the optic they are working on completely aligned and locked down before moving on to the next component.

A good goal for the first day in lab is to get the spectroscopy part of the layout build well enough that they can turn on the laser and see both doppler broadened peaks and at least 3 hyperfine features in the 87Rb(F=2) peak. If they are working on optimizing to see all six peaks they are doing well.

If they do not get this far they still have plenty of time to get things sorted out and should not feel like they are behind.

Day two in lab should focus on finding all six hyperfine dips, capturing the spectra on the scope and then building the interferometer and taking a calibration spectrum.

With the assistance of the lab staff it is almost guaranteed that they will reach this point by the end of the second day.

In their analysis the students should have been able to identify at least 5 of the 6 hyperfine dips, determine the calibration factor and measure the energy of the splitting.

Most of the obvious uncertainties are related to the bit resolution associated with reading data off of the scope trace. Poorly chosen scope scales can make these uncertainties worse if they are too zoomed out. Uncertainty in the lengths of the two arms of the interferometer as measured with a tape measure will put a limit on how well the calibration is known.

Other sources of bias in the data, which students can be reasonably expected to investigate or account for include:

• Linearity of the laser frequency sweep calibration.
• Deriving a time to frequency difference calibration from too large a portion of the laser sweep. Most of the spectral features will span only a small portion of the full sweep and the non-linearity mentioned above can cause problems.
• Building an interferometer where the two arms are too close to the same length. They really need to get the largest possible difference between the two arms in order to get at least one interference cycle over the part of the sweep where their spectroscopy measurements were taken.
• The hyperfine dips are superimposed on the shape of the doppler broadened peak which can bias their locations. A more precise measurement can be made if the doppler broadened part of the spectrum can be subtracted off leaving only the dips. This can be done in the lab by building a layout which allows simultaneous measurement of the spectra both with and without the pump beam. There are a couple of reasonably ways to achieve this.

If students did not get adequate data from the first two days, likely due to alignment or power optimization issues, they can spend time as required on the third day to improve the basic part of the measurement.

Additional measurements which students can be expected to make include:

• Verifying that the width of the doppler broadened peaks is consistent with a gas at room temperature. Consistent with meaning within 50% is good enough.
• Measuring the line width of the doppler free features and seeing how close they can get to the natural linewidth. Note that there is no correct answer here, but then can reasonably be expected to get within a factor of two where the difference is likely due to effects like power broadening.
• Building an optical setup which allows the doppler broadened part of the spectrum to be removed.
• Using polarization optics to allow for simultaneous measurements of hyperfine spectra, doppler broadened spectra and interferometer calibration. This is a more challenging extension which should be offered to more motivated students, but should not be presented as required.