Today in the lab of atomic spectra we built a setup for observing the hyperfine structure of cesium. It is a big deal for atomic clocks as they use this transition to “tick”. It is also a very very tiny and fine effect (as its name suggests) so it’s pretty exciting that we can see it with such simple setup.
First, here is a brief description of atomic structure notation. The source of the text and picture is http://webphysics.davidson.edu/Alumni/JoCowan/honors/section1/THEORY.htm
The electrostatic attraction between the electron and the nucleus could be described by the principal quantum number, n. The combination of l and s gives an electron’s total angular momentum, J. Magnetic coupling between the electron’s orbit and spin causes an energy splitting between levels with different J called the fine structure. The fine structure is split again into the hyperfine structure denoted by the letter F. The hyperfine structure is due to a magnetic coupling between the electron’s total angular momentum, J, and the nuclear spin, I.
In order to observe the hyperfine structure, i. e. the two distinct energy levels at F=3 and F=4, and to measure the frequency difference between them, we carried out the following experiment.
The concept is to set the laser generation exactly at the wavelengths of absorption of cesium (they are two known peaks around 895 nm). For this we use an IR laser diode and we can modulate its wavelength by changing the temperature and the supplying (triangular) current. We are thus “scanning” the laser. In order to ensure the scan is smooth – that is, the laser doesn’t “jump” from one mode to another, we add an interferometer Fabri-Perot (IFP) which also serves as an etalon for the frequencies.
So we have the laser diode, connected to a thermoregulator and powered with triangular current, which is monitored on the oscilloscope screen. The beamsplitter sends the laser beam through the interferometer and the output is detected by a photodiode, hooked to the oscilloscope. The other part of the beam is reflected by a mirror in such manner that it passes through a glass case with cesium inside. The output is again recorded with a photodiode and displayed on the oscilloscope screen.
Finally, at the right adjustment of the scan, we get our lovely hyperfine structure:
The only thing left is to process the data we recorded with the oscilloscope and plot it. Now, to find out what is the frequency difference, we’ll need two things: the FSR (free spectral range) of the interferometer and the number of peaks of the IFP signal between the two cesium split levels. The FSR = c/4L, where L is the length of the IFP and in our case 0,2 m. Thus, the FSR is 375 MHz.
As you see above, I have counted the number of peaks and they are 22. So for our final result, we multiply them and get frequency difference of 8,25 GHz which is close enough to the real one of ~9 GHz, considering how imprecisely the experiment was made and the fact that our IFP was pretty bad. Well, it is possible that I messed up somewhere, I’ll find out in a week. :-)