Physicists have long sorted all elementary particles into two tidy bins: bosons (force carriers like photons) and fermions (matter builders like electrons, protons, and neutrons). It was a neat system, like a filing cabinet with only two folders. But nature, it turns out, is a hoarder, and it's been hiding a third category in lower dimensions.
Since the 1970s, scientists predicted the existence of anyons - particles that are neither bosons nor fermions but something in between. In 2020, researchers finally observed these rule-breakers at the edge of supercooled, strongly magnetized, one-atom-thick (two-dimensional) semiconductors. Now, scientists from the Okinawa Institute of Science and Technology (OIST) and the University of Oklahoma have pushed the concept into even weirder territory: one-dimensional systems.
In two papers published in Physical Review A, the team identified a 1D system that can host anyons and outlined their theoretical behavior. Recent advances in controlling individual particles inside ultracold atomic systems could make these ideas testable in actual lab experiments - not just thought experiments involving chalkboards and furrowed brows.
“Every particle in our universe seems to fit strictly into two categories: bosonic or fermionic. Why are there no others?” asks Professor Thomas Busch of the Quantum Systems Unit at OIST. “With these works, we've now opened the door to improving our understanding of the fundamental properties of the quantum world, and it's very exciting to see where theoretical and experimental physics take us from here.”
The distinction between bosons and fermions comes from what happens when two identical particles swap places. In three dimensions, experiments show only two outcomes: either the system stays the same (bosons) or it flips sign (fermions). No other options. This behavior ties into quantum physics' most maddening principle: indistinguishability. Unlike marbles - which you can paint different colors to keep track of - identical quantum particles like electrons cannot be individually labeled if all their quantum properties match. Swapping them produces a state that is physically indistinguishable from the original.
Raúl Hidalgo-Sacoto, a PhD student in the OIST unit, explains: “Because this exchange is equivalent to doing nothing, the mathematical statistics governing the event, known as the exchange factor, must obey a simple rule: the square of the exchange factor must be equal to 1. The only two numbers that satisfy this rule are +1 and -1. That's why all particles must be, respectively, bosons, for which the factor is 1, or fermions, for which the factor is -1.”
These two families behave very differently. Bosons naturally group together and act collectively - lasers, where photons of the same wavelength move in sync, are a classic example, as are Bose-Einstein Condensates. Fermions resist sharing the same state, which is one reason the periodic table has so many elements. (Thanks, fermions, for the variety.)
So why can lower dimensions produce something different? In lower-dimensional systems, particles have fewer possible paths when they exchange places. Their trajectories become braided together through space and time, and unlike in three dimensions, those paths cannot simply be untangled afterward. As a result, the exchanged state is no longer equivalent to the original one.
Hidalgo-Sacoto continues: “In lower dimensions, this exchange is no longer topologically equivalent to doing nothing. To satisfy the law of indistinguishability, we need exchange factors over a continuous range to account for the exchange, dependent on the exact twists and turns of the paths.” That opens the door to anyons, whose exchange factors can take values beyond just +1 or -1. They are neither purely bosons nor purely fermions - they're quantum nonconformists.
In the newly published studies, the researchers demonstrated that the boson-fermion divide remains broken even in one-dimensional systems. They also discovered something especially interesting: the exchange factor in 1D systems can be directly tuned. In one dimension, particles cannot move around each other to swap places - they must pass directly through one another. This changes the exchange behavior in a fundamental way compared with higher dimensions.
The studies show that the exchange factor in these systems is linked to the strength of the particles' short-range interactions. That means scientists could potentially fine-tune the exchange statistics experimentally, creating opportunities to explore a wide range of new quantum phenomena.
“We've identified not only the possibility of existence of one-dimensional anyons, but we've also shown how their exchange statistics can be mapped, and, excitingly, how their nature can be observed through their momentum distribution,” summarizes Prof. Busch. “The experimental setups necessary for making these observations already exist. We're thrilled to see what future discoveries are made in this area, and what it can tell us about the fundamental physics of our universe.”
Materials provided by Okinawa Institute of Science and Technology (OIST) Graduate University. Note: Content may be edited for style and length.