Physicists have traditionally divided all elementary particles in our three-dimensional universe into two categories: boparticles and fermions. Bosons primarily include force-carrying particles such as photons, while fermions make up ordinary matter such as electrons, protons, and neutrons.
This simple partition begins to break down in low-dimensional systems. Since the 1970s, scientists have predicted the existence of a third type of particle known as anion, which lies between bosons and fermions. In 2020, researchers experimentally observed these unusual particles at the interface of a supercooled, highly magnetized, one-atom-thick (and therefore two-dimensional) semiconductor.
Now, scientists at Okinawa Institute of Science and Technology (OIST) and the University of Oklahoma have taken this idea further. In two papers published in Physical review Athe team identified a one-dimensional system that can support anyons and investigated the theoretical behavior of the particles.
Recent advances in the control of individual particles in ultracold atomic systems may also make it possible to test these ideas in real laboratory experiments.
“All the particles in our universe seem to fit strictly into two categories: bosons or fermions. Why aren’t there others?” asks Professor Thomas Busch of OIST’s Quantum Systems Unit. “With these studies, we have opened the door to improving our understanding of the fundamental properties of the quantum world, so it’s very exciting to see where theoretical and experimental physics can take us from here.”
Why are quantum particles classified into two groups?
The distinction between boons and fermions depends on what happens when two identical particles exchange positions. In three dimensions, the experiment shows only two results. Either the system remains unchanged (this is the behavior of bosons), or it flips sign (this is what happens with fermions). No other possibilities seem to exist.
This behavior is related to one of the most important principles of quantum physics: indistinguishability. Even in everyday life, we can distinguish between two identical objects. For example, if two marbles are painted different colors, you can track which one goes where. Quantum particles don’t work that way.
Two identical particles, such as electrons, cannot be labeled individually if all their quantum properties match. Replacing them produces a state that is physically indistinguishable from the original state. This means that no measurable properties of the system are changed.
Raúl Hidalgo Sacoto, a PhD student in the OIST unit, says, “Since this exchange is the same as doing nothing, the mathematical statistics governing this phenomenon, known as the exchange coefficient, must follow a simple rule: the exchange coefficient. The square of must be equal to 1. The only two numbers that satisfy this rule are +1 and -1. Therefore, every particle must be a boson if the coefficient is 1, or a fermion if the coefficient is 1. -1. ”
These two particle families behave quite differently. Bosons naturally gather and act collectively. Lasers are one example, where photons of the same wavelength (color) move synchronously. Bose-Einstein condensates are different, in which extremely cold atoms occupy the same quantum state.
Fermions behave in the opposite way. Electrons, protons, and neutrons resist sharing the same state. This property is one of the reasons why the periodic table contains so many different elements.
How lower dimensions change quantum rules
If nature allows only two types of particles in three dimensions, why can lower dimensions produce different ones?
The answer lies in how the particles move around each other. In a low-dimensional system, there are fewer possible paths available to particles. As they exchange places, their trajectories are woven across time and space. Unlike in 3D, these paths cannot be easily solved later. As a result, the exchanged state is no longer equivalent to the original state.
Hidalgo-Sacoto continues. “In low dimensions, this exchange is no longer topologically equivalent to doing nothing. Satisfying the law of indiscernibility requires an exchange coefficient over a continuous range that accounts for the exchange, depending on the exact twists and turns of the path.”
This makes particles whose exchange coefficients can take values greater than +1 or -1 available to everyone. In other words, they are neither pure bosons nor pure fermions.
Anyons adjustable in one dimension
In a newly published study, researchers have demonstrated that the boson-fermion split remains broken even in one-dimensional systems. They also found something particularly interesting. This means that the exchange coefficient of a 1D system can be adjusted directly.
In one dimension, particles cannot move and exchange positions with each other. Instead, they must pass directly through each other. According to the researchers, this fundamentally changes exchange behavior compared to higher dimensions.
Studies have shown that the exchange factor in these systems is related to the strength of the short-range interactions of the particles. This means that scientists may be able to experimentally fine-tune exchange statistics and create opportunities to explore a wide range of new quantum phenomena.
“We have not only identified the possible existence of one-dimensional anyons, but also shown how their exchange statistics can be mapped and, interestingly, how their properties can be observed through their momentum distribution,” summarizes Professor Busch. “The experimental equipment needed to make these observations already exists, and we look forward to seeing what future discoveries will be made in this field and what they will tell us about the fundamental physics of our universe.”
