Laser-Cooled Atoms: Ytterbium

Element: Ytterbium (Yb)

Atomic Number: 70

Mass: Seven "stable" isotopes, from 168 to 176 amu. Two of those are nominally radioactive, with half-lives vastly in excess of the age of the universe.

Laser cooling wavelength: 399 nm and 556 nm.

Doppler cooling limit: 690 μK in the UV and 4.4 μK in the green.

Chemical classification: A rare earth/ lanthanide, one of the hard to distinguish metals in the little island that floats off toward the bottom of the usual presentation of the periodic table, because it's too hard to wedge them in between barium and hafnium. Yet another greyish metal.

Other properties of interest: Like strontium, ytterbium has a singlet ground state, with no angular momentum, but it does have hyperfine structure, so it's possible to do some Sisyphus cooling. It's got seven isotopes, including both bosons and fermions, and people have cooled both sorts to quantum degeneracy.

History: Ytterbium is a relative latecomer to the laser cooling world, probably because of the slightly annoying UV laser-cooling line-- you need to use a collection of expensive lasers to make it work, so it wasn't trapped until 1999. It probably wouldn't be worth the bother if not for the fact that it has a pair of states that can serve as the basis for an atomic clock, at 578 nm. Ytterbium is attractive as a clock system because of the relatively friendly wavelength of the clock transition, and the fact that it's pretty heavy, and thus slow-moving.

Both ytterbium ions and neutral atoms have been used in clock experiments, with a really impressive recent experiment managing a clock with instability at the 10-18 level, which is mind-boggling. You can do a bunch of exotic physics tests with it because of the big mass and the possibility of ultra-precise clock measurements. The artsy image in the center above is from Trey Porto's group at JQI where they're looking at mixtures of ytterbium and rubidium, which also have some fun potential uses.

Random fun things: I don't actually know all that much about ytterbium, outside the context of cool AMO physics papers. It's been used by Norval Fortson's group, so I assume it must be incredibly noxious in some manner (I had dinner with a bunch of people from that group once; every substance they've ever worked with has horrible properties-- highly corrosive, or toxic, or foul-smelling), but I don't know the details.

Art: The cartoon version of ytterbium is a reading Swede. The Comic Book Periodic Table comes up empty, alas. Very little love for the lanthanides in comics.

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Two of those are nominally radioactive, with half-lives vastly in excess of the age of the universe.

You mentioned this a coupla times now.

How does one actually measure the rate of decay, when it's so low?

You just need to collect a whole lot of atoms.

If you have a half-life of 10,000,000,000 years, that's the time it takes for half of the sample to decay away, or (roughly) for you to have a 50% chance of seeing one particular atom decay. If you have 10,000,000,000 atoms in your sample, though, you've got (roughly) a 50% chance of seeing one of them decay in one year. Increase that to 4,000,000,000,000 atoms, and you've got good chance of seeing one decay per day, and so on.

Sili, I don't know of an analytical way to predict a half life (although I'm not a physicist, so there may be one), but in the absence of that, the way you'd do it is, get a very large number of atoms, and wait. Even though the half life is very long, with a large enough sample, you'll get enough decay events to extrapolate a half life.

The decay equation for the number of atoms remaining, n, after time t, from an original sample with n0 atoms and half life T, is

n(t) = n0 * (1/2)^(t/T)

With some fancy differentiation, we find that the rate of change in the number of atoms is

dn/dt = n0/T * ln(1/2) * (1/2)^(t/T)

where ln is the natural logarithm. So, if we plug in T = 15 billion years, and n0 = 6.02 x 10^23 (1 mole of atoms, about 173 grams), and t = 0 to find the rate of decay now, we find that we'll have 2.8 x 10^13 atoms of ytterbium decaying per year, or about 900,000 per second. That should be plenty to detect and get good statistics from.

I should note that "vastly in excess of the age of the universe" means 130 trillion to 160 quadrillion year half lives. So 1 mole samples of those isotopes would decay at an initial rate of between 100 atoms/second and 1 atom every 2 minutes.

Thanks. That's what I get for not doing the maths.


Love the 'YAGM' phrase. Yb metal isn't too bad. The ions are great dopants for NIR lasers.