Newton was a very smart man. As he worked on solving the problem of predicting planetary orbits, he saw that his solution wasn't going to work. To predict and understand planetary orbits requires calculus, and calculus is hard. Not hard as in "I am going to fail math," but hard as in "No matter what trick I play here, these equations have no solution that I can just write down." Newton saw this problem pretty early on, and found that given just two bodies (e.g., the Earth and the Moon), he could solve the equations and come up with orbital predictions—add in a third (or more), and solutions just vanished.

As it turns out, this is a pretty general issue in physics. Given two bodies that are interacting, the calculus is generally solvable; once that third body turns up, solutions vanish quicker than a kid's gratitude to Santa. Thus was born the three-body problem and many, many horrible physics jokes.

Fast forward to 1970 and a theoretical physicist, called Efimov, who was interested in how nucleons stuck together to form a nucleus. He discovered that under certain very restricted conditions, three nucleons could come together to form a resonant bound state—basically, the three nucleons would stick together. Furthermore, a large number of bound states existed in a series that showed a trait called self-similarity. Further investigation showed that if the particles were neutral and spinless, the number of resonant states would shoot up to infinity. Forty years later, experimentalists have finally caught up with Efimov.

As Efimov noted in his original paper, the conditions that produce these resonant states were both very general (as long as there was a resonant interaction, an Efimov state could be induced) and very restrictive—the range of the interaction force compared to some critical length scale had to fall within a certain range of values before the series of Efimov states would emerge. Some quick calculations showed that the states might exist in lighter nuclei, but the "series" for these nuclei would involve, at most, one state. As a result, the search for Efimov states was limited to looking for nuclear states that, according to the shell model of nuclear physics, shouldn't actually exist.

That all changed in the last two decades with the the development tools for the production of ultracold atomic states. Now we can make dilute gases that have temperatures of just a few nanoKelvin, and can control the interactions among individual atoms using an externally applied magnetic field. This phenomena, called a Feshbach resonance, basically transfers energy between the internal states of atoms and their interactions with other atoms, changing the interaction strength. As a result, inter-atom interactions can be changed from strongly attractive to strongly repulsive, where strong indicates a range of about three orders of magnitude.

Effectively, these clouds allow arbitrary control over inter-atom interactions—as a result, experimenters can produce conditions that allow Efimov states to exist. Furthermore, because of the range over which the interaction forces can be tuned, a number of Efimov states can be observed, allowing Efimov's predictions to be tested. A few experimentalists have already tried to do this, but this latest work, from Rice University, involves a systematic exploration of Efimov states.

The experiments were mainly performed with lithium atoms, cooled to near absolute zero. The cloud of cold atoms then has insufficient energy to allow any of the atoms to exit a trap that confines them. When the magnetic field strength is tuned so that Efimov states can form, their formation imparts energy to the atoms that's sufficient to kick them out of the trap. The experimenters were then able to map out the locations of Efimov states by observing which magnetic field strengths led to atoms leaking out of the trap. An elegant experiment, but technically quite challenging.

Efimov predicted that the separation between the states would scale by about 22.7. That is, if the first state occurred for an interaction strength of one, the next state would be at interaction strength 22.7, and the state after that would be at interaction strength 515. Experimentalists observed that the states occurred within ten percent of the values predicted. Most of the uncertainty was due to the fact that, towards the extremes of their observational range, they were getting very close to not satisfying the conditions under which we can calculate the location of Efimov states.

There was, excitingly, one exception to this set of data. This is a bit subtle, but the Feshbach resonance has a shape and features to it. These features are also expected to reoccur where the Efimov states reappear. And they do, but they are out by a factor of two. The scientists observe that this discrepancy appears to be universal—it occurred under a variety of different experimental conditions and for different atomic gases. Although this observation doesn't conclusively rule out experimental conditions as the cause, the physics community is quite excited to think that this might be real.

So what should we make of this? I liken the difference between this work and previous efforts to the difference between Abel Tasman and James Cook. Both were explorers and made fantastic discoveries, but James Cook was absolutely fastidious in his record keeping and is the guy who is rightly remembered for providing Europe with detailed maps of the South Pacific. And he got eaten by a group of angry Hawaiians, so who wouldn't want to be associated with a success like that?

ScienceExpress, 2009, DOI: 10.1126/science.1182840

Listing image by Argonne National Laboratory