Five-body recombination, in which five identical atoms form a tetramer molecule and a single free atom, could be the largest contributor to loss from ultracold atom traps at specific “Efimov resonances”, according to calculations done by physicists in the US. The process, which is less well understood than three- and four-body recombination, could be useful for building molecules, and potentially for modelling nuclear fusion.
A collision involving trapped atoms can be either elastic – in which the internal states of the atoms and their total kinetic energy remain unchanged – or inelastic, in which there is an interchange between the kinetic energy of the system and the internal energy states of the colliding atoms.
Most collisions in a dilute quantum gas involve only two atoms, and when physicists were first studying Bose-Einstein condensates (the ultralow-temperature state of some atomic gases), they suppressed inelastic two-body collisions, keeping the atoms in the desired state and preserving the condensate. A relatively small number of collisions, however, involve three or more bodies colliding simultaneously.
“They couldn’t turn off three body [inelastic collisions], and that turned out to be the main reason atoms leaked out of the condensate,” says theoretical physicist Chris Greene of Purdue University in the US.
Something remarkable
While attempting to understand inelastic three-body collisions, Greene and colleagues made the connection to work done in the 1970s by the Soviet theoretician Vitaly Efimov. He showed that at specific “resonances” of the scattering length, quantum mechanics allowed two colliding particles that could otherwise not form a bound state to do so in the presence of a third particle. While Efimov first considered the scattering of nucleons (protons and neutrons) or alpha particles, the effect applies to atoms and other quantum particles.
In the case of trapped atoms, the bound dimer and free atom are then ejected from the trap by the energy released from the binding event. “There were signatures of this famous Efimov effect that had never been seen experimentally,” Greene says. This was confirmed in 2005 by experiments from Rudolf Grimm’s group at the University of Innsbruck in Austria.
Hundreds of scientific papers have now been written about three-body recombination. Greene and colleagues subsequently predicted resonances at which four-body Efimov recombination could occur, producing a trimer. These were observed almost immediately by Grimm and colleagues. “Five was just too hard for us to do at the time, and only now are we able to go that next step,” says Greene.
Principal loss channel
In the new work, Greene and colleague Michael Higgins modelled collisions between identical caesium atoms in an optical trap. At specific resonances, five-body recombination – in which four atoms combine to produce a tetramer and a free particle – is not only enhanced but becomes the principal loss channel. The researchers believe these resonances should be experimentally observable using today’s laser box traps, which hold atomic gases in a square-well potential.
“For most ultracold experiments, researchers will be avoiding loss as much as possible – they would stay away from these resonances,” says Greene; “But for those of us in the few-body community interested in how atoms bind and resonate and how to describe complicated rearrangement, it’s really interesting to look at these points where the loss becomes resonant and very strong.” This is one technique that can be used to create new molecules, for example.
In future, Greene hopes to apply the model to nucleons themselves. “There have been very few people in the few-body theory community willing to tackle a five-particle collision – the Schrödinger equation has so many dimensions,” he says.
Fusion reactions
He hopes it may be possible to apply the researchers’ toolkit to nuclear reactions. “The famous one is the deuterium/tritium fusion reaction. When they collide they can form an alpha particle and a neutron and release a ton of energy, and that’s the basis of fusion reactors…There’s only one theory in the world from the nuclear community, and it’s such an important reaction I think it needs to be checked,” he says.
The researchers also wish to study the possibility of even larger bound states. However, they foresee a problem because the scattering length of the ground state resonance gets shorter and shorter with each additional particle. “Eventually the scattering length will no longer be the dominant length scale in the problem, and we think between five and six is about where that border line occurs,” Greene says. Nevertheless, higher-lying, more loosely-bound six-body Efimov resonances could potentially be visible at longer scattering lengths.
The research is described in Proceedings of the National Academy of Sciences.
Theoretical physicist Ravi Rau of Louisiana State University in the US is impressed by Greene and Higgins’ work. “For quite some time Chris Greene and a succession of his students and post-docs have been extending the three-body work that they did, using the same techniques, to four and now five particles,” he says. “Each step is much more complicated, and that he could use this technique to extend it to five bosons is what I see as significant.” Rau says, however, that “there is a vast gulf” between five atoms and the number treated by statistical mechanics, so new theoretical approaches may be required to bridge the gap.
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