Physicists have traditionally sorted all elementary particles in our three-dimensional universe into two categories: bosons and fermions. Bosons mostly include particles that carry forces, such as photons, while fermions make up ordinary matter, including electrons, protons, and neutrons.
That simple division starts to break down in lower dimensional systems. Since the 1970s, scientists have predicted the existence of a third type of particle known as an anyon, which falls somewhere between a boson and a fermion. In 2020, researchers experimentally observed these unusual particles at the boundary of supercooled, strongly magnetized, one-atom thick (that is, two-dimensional) semiconductors.
Now, scientists from the Okinawa Institute of Science and Technology (OIST) and the University of Oklahoma have pushed the idea further. In two papers published in Physical Review A, the team identified a one-dimensional system capable of supporting anyons and investigated the particles’ theoretical behavior.
Recent advances in controlling individual particles inside ultracold atomic systems could also make these ideas testable in real laboratory experiments.
“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.”
Why Quantum Particles Fall Into Two Groups
The distinction between bosons and fermions comes from what happens when two identical particles exchange places. In three dimensions, experiments show only two outcomes. Either the system remains unchanged, which is the behavior of bosons, or the system flips sign, which is what happens with fermions. No other possibilities appear to exist.
This behavior is tied to one of quantum physics’ most important principles: indistinguishability. In everyday life, two identical objects can still be told apart. If two marbles are painted different colors, for example, you can track which one moved where. Quantum particles do not work that way.
Two identical particles such as electrons cannot be individually labeled if all their quantum properties match. Swapping them produces a state that is physically indistinguishable from the original one, meaning the measurable properties of the system must remain unchanged.
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 particle families behave very differently. Bosons naturally group together and behave collectively. Lasers are one example, where photons of the same wavelength (color) move in sync. Bose-Einstein Condensates are another, with ultracold atoms occupying the same quantum state.
Fermions behave in the opposite way. Electrons, protons, and neutrons resist sharing the same state. This property is one reason the periodic table contains so many different elements.
How Lower Dimensions Change Quantum Rules
If nature only allows two types of particles in three dimensions, why can lower dimensions produce something different?
The answer lies in how particles move around one another. In lower dimensional systems, particles have fewer possible paths available. When they exchange places, their trajectories become braided together through space and time. 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, particles whose exchange factors can take values beyond just +1 or -1. In other words, they are neither purely bosons nor purely fermions.
Adjustable Anyons in One Dimension
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. Instead, they must pass directly through one another. According to the researchers, 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.”