“There’s a process in strongly interacting physics where fundamental particles like electrons can come together and behave as if they were a fraction of an electron,” said Davis, a graduate student in Foster’s research group. The process is called fractalization and, as Davis states, “It’s a really exotic, fundamental process that shows up theoretically in many places. It may have something to do with high-temperature superconductivity, and it could be useful for building quantum computers. But it’s very hard to understand and even harder to measure.”

Quantum materials include high-temperature superconductors, one of the most puzzling mysteries in physics, and materials that exhibit topological phases, which earned its discoverers the 2016 Nobel Prize in physics. Materials that exhibit these phases are, so far, the only place physicists have unambiguously measured fractionalization via an exotic electronic state called the fractional quantum Hall effect. In this state, flat two-dimensional materials conduct electricity only along their one-dimensional edges.

Of course, these only represent a 2D example. Foster says, “It’s clear that fractionalization is occurring there because if you measure the conductance of these edge states they behave as though they’re made of particles that behave like one-third of an electron. There are no real particles carrying one-third of the electric charge,” he said. “It’s just the effect of all the electrons moving together in a such a way that if you create a local excitation, it will behave like an electron with one-third of a charge.”

Foster and Davis said the main motivation for describing their ultracold atomic test was to be able to observe fractionalization in a system that is very different from the fractional quantum Hall example. The team says their main goal is to observe these physics in at least one other context in a completely unambiguous way.

Their proposed experiment calls for laser-cooling atoms to act as stand-ins for electrons that have lasers oppose the motion of atoms, progressively slowing them and resulting in colder and colder temperatures. The cold atoms are trapped by other lasers that form optical waveguides which are one-dimensional channels where atoms can move left or right but cannot go around one another. The quantum behavior of the atoms in these one-dimensional guides mimics the behavior of electrons in 1D wires, resulting in a new perspective.

While the individual elements of the experiment have been developed, Foster says, “…we don’t believe they’ve been put together in a single experimental setup. That’s where we need the help of experimentalists who are experts in laser-cooling.”

Foster and Davis propose creating a set of parallel 1D waveguides that are all in the same two-dimensional plane to observe fractionalization in an ultracold system. A few additional atoms would then populate the 1D guides near the center of the experiment. “So we’ll start with the 1D ‘wires,’ or guides, and the initial density in the middle, and then we’ll drop some of the lasers and allow the atoms to interact between the wires in a kind of 2D mesh,” Foster said. “We can very accurately describe the 1D system, where strong interactions cause the atoms to behave in a correlated way. Because the whole system is quantum mechanical and coherent, those correlations should get imprinted on the 2D system.

“Our probe is letting go of that extra bump of density and watching what it does,” he said. “If the atoms in the 1D guides are not interacting, then the bump will just spread out between the wires. But, if there was initial fractionalization due to correlated effects in the wires, what we can confidently calculate is that the density will do something completely different. It will go the other direction, flying down the wires.”

Foster said he’s interested in discussing the feasibility of the test with ultracold atomic experimentalists. “We know it can take years to build and perfect some of the experimental setups for these kinds of experiments,” While it may take years for researchers to build, test, and perfect these experimental setups, Foster is hopeful. “As theorists, we know the ingredients we need, but we don’t know the ones that will be most challenging to implement or if it may be easier to modify some setups as opposed to others. That’s where we’ll need the help of our experimental colleagues.”