More progress on anti-hydrogen

To put it mildly, this blog has been rather quiet, but I hope that this post signals a return to semi-regular blogging. Let me first quickly sum up the news in high energy physics since December: a standard model-like Higgs is looking more and more likely at about 125 GeV, and low-energy supersymmetry is looking less and less likely, as the models which are still consistent with the data are getting uglier. With that out of the way, let me turn to the subject of today's post…

In the second ever entry in this blog, I discussed the ALPHA experiment at CERN, which is designed to trap and study anti-hydrogen. As a birthday present to me yesterday, a new paper from the collaboration was published online by Nature. Last year they managed to trap anti-hydrogen for several minutes at a time, and they are now beginning to study its energy levels, which is the whole point of the experiment. Theory says that these should be exactly the same as for hydrogen, and any deviation from this would be very big news indeed.

My understanding of the experiment is as follows. They use inhomogeneous magnetic fields to trap the atoms. The magnetic moment of an anti-hydrogen atom in its ground state is dominated by the spin of the positron, and the experiment traps those atoms in which the positron has one polarisation; the others escape. Once the atoms are trapped, the team irradiates them with microwaves, tuned to a frequency which should induce a spin-flip in some of the atoms, resulting in them escaping the trap and annihilating in the surrounding material. They have of course performed control experiments in which the microwaves are off-resonance.

The measurements are somewhat complicated by the external field required to trap the atoms. The interesting quantity is the hyperfine splitting between the two energy levels in which the spin of the positron is aligned or anti-aligned with that of the anti-proton, but the atoms' energy is dominated by their interaction with the external field. As such, the hyperfine splitting can only be measured indirectly. Let's look at this a bit more closely.

Denote the possible ($s$-wave) states of an anti-hydrogen atom by $\vert\uparrow \Uparrow\rangle, \vert\uparrow \Downarrow\rangle, \vert\downarrow \Uparrow\rangle, \vert\downarrow \Downarrow\rangle$, where the thin arrow represents the spin state of the positron, and the thick arrow that of the anti-proton. In the absence of an external field, $\vert\uparrow \Uparrow\rangle$ and $\vert\downarrow \Downarrow\rangle$ have precisely the same energy, but this is slightly higher than the energy of $\vert\uparrow \Downarrow\rangle$ and $\vert\downarrow \Uparrow\rangle$, due to the different interaction between the magnetic moments of the anti-proton and the positron; this is the hyperfine splitting. The ALPHA team introduce an external magnetic field such that the states $\vert\downarrow \Uparrow\rangle, \vert\downarrow \Downarrow\rangle$ get trapped, but have a higher energy than $\vert\uparrow \Uparrow\rangle, \vert\uparrow \Downarrow\rangle$, which do not get trapped (a picture would be handy, but taking it from Nature would violate copyright, and I'm too lazy to make one myself).

So there are two types of transition the team can induce: $\vert\downarrow \Uparrow\rangle \to \vert\uparrow \Uparrow\rangle$, and $\vert\downarrow \Downarrow\rangle \to \vert\uparrow \Downarrow\rangle$. The difference in the transition energies allows them to measure the hyperfine splitting. They are not yet claiming an accurate measurement; they say only that they find a resonance in the region expected, and that they expect to make a precise measurement in the future.

The press release version is here.