I was listening to a podcast recently that delved into timekeeping and atomic clocks, and was surprised that they got a couple of details wrong. I haven’t done a post explaining how atomic clocks work, because that’s something easily found on the intertubes, and so I’m not particularly motivated to recreate Wikipedia or HowStuffWorks.

But someone was wrong on the internet, and the basis of that “wrongness” has some physics behind it. The claim was made in explaining clocks that when electrons absorb energy they jump up a level, and then radiate it when they jump back down. And while that’s true, it’s not the basis for a Cesium or Rubidium clock. The thing is that you don’t want the atom to radiate on its own if you are going to make a clock out of it. Transitions between atomic states are not infinitely narrow, i.e. there is an uncertainty in the energy of the emitted photon. This is known as the linewidth of the transition, and for a good clock you want a really narrow transition so that you know what the frequency is. While there are several factors that can increase that linewidth, the fundamental width is due to the Heisenberg Uncertainty relation between energy (or frequency) and time.

The uncertainty of the frequency and the lifetime of the transition are inversely related, and \(Delta omega Delta t = 1 \) (that should be greater than or equals, but latex is choking on that for some reason)

In order to get a narrow transition, you want a long-lived state. So you don’t want something that radiates readily on its own, and atomic clocks don’t. Cesium and Rubidium devices are passive: you shine radiation on them, and then read out whether or not your radiation was on resonance by looking at which state the atoms are in. Active masers do radiate, but as the acronym tells us, the radiation is stimulated, rather than being spontaneous. (Left on its own, the lifetime of the Hydrogen atom state is about 10 million years) The search for long-lived states becomes even more important for optical clocks, since the larger energy differences tend to lead to shorter lifetimes. What is generally done is to search for so-called forbidden transitions, in which the strong coupling of electric dipole transitions aren’t present, and you are left with other types of transitions or ones that must couple through other states and end up taking much longer.