The hyperfine structure of cesium

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

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:

Screen Capture

Green signal is the current, yellow is the interferometer signal and blue is cesium signal with the energy level splitting

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. 🙂



  1. Great experiment, also very well structured writing! I wonder in what range could the laser diode’s temperature drift be, maybe the accuracy requirements on the temperature regulator could be quite high to achieve a sub-nm accuracy. I notice the output of the interferometer photodiode has a quite low amplitude (sub-100mV peak-peak) as compared to the Cs sample diode (4V), does the interferometer have such a low transmission coefficient, or maybe it is that there was an amplifier attached to one of the diodes? In any case the last is probably not relevant to the accuracy of the measurement.

    It is very possible that all of my writing above is complete nonsense 🙂

    And this is really fun!


    1. It isn’t nonsense, you’re pretty observant 🙂

      The laser diode changes its wavelength by 0,3 nm/K, the temperature is controlled by a Peltier element and stabilized with a thermistor. Laser diodes can “scan” their wavelength enormously, in this case in an interval of approx. 15 nm (within their recommended working temperature). The only ones that are better at this are dye lasers (and some other kind I forgot), but laser diodes are way cheaper and more compact. Also, there are some temperature values that cannot be achieved as the transition is not continuous, but instead the laser modes change in a discrete manner.

      As for the output amplitudes, I think they are indeed as seen. Our interferometer has a bad reflection coefficient and we had some trouble in order to make sure the beam passes through and ends up in the photodiode. Even the spot seen on the test card (because we humans do not see infrared, of course) was almost unsee-able, whereas in any other part of the beam it was ok. But we worked with what we got, we’re even not supposed to do our exercises in this lab 😀

      Glad you liked it, and it is fun, really!

      Liked by 1 person

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