A new class of strange one-dimensional particles
For the first time, researchers describe the properties of one-dimensional anyons and provide the recipe for observing these particles with present-day setups.
Okinawa Institute of Science and Technology (OIST) Graduate University
image:
Graphic illustration of the papers’ findings. A knob labelled with α can be dialed between 0 and 1, showing how it affects the symmetry of two particles during an exchange operation, shown as two Ψs inside mathematical bra-ket notation.
view moreCredit: Jack Featherstone
Physicists have long categorized every elementary particle in our three-dimensional universe as being either a boson or a fermion—the former category mostly capturing force carriers like photons, the latter including the building blocks of everyday matter like electrons, protons, or neutrons.
But in lower dimensions of space, the neat categorization starts to break down. Since the ‘70s, a third class capturing anything in between a fermion and a boson, dubbed anyon, has been predicted to exist — and in 2020, these odd particles were observed experimentally at the interface of supercooled, strongly magnetized, one-atom thick (that is, two-dimensional) semiconductors. And now, in two joint papers published in Physical Review A, researchers from the Okinawa Institute of Science and Technology (OIST) and the University of Oklahoma have identified a one-dimensional system where such particles can exist and explored their theoretical properties.
Thanks to the recent developments in experimental control over single particles in ultracold atomic systems, these works also set the stage for investigating the fundamental physics of tunable anyons in realistic experimental settings. “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.”
Breaking the boson/fermion binary
The elementary categorization is based on how two identical particles behave when they swap places. Experimental observations suggest a strict binary in 3D: either the particles remain completely unchanged, as in the case of bosons, or the system inverts, as with fermions — no other options seem to exist.
This binary arises from the core principle of indistinguishability in quantum physics. In classical physics, if you’ve got two identical marbles and you paint one red and the other blue, you can tell them apart even if they swap places. But at the quantum level, two identical particles — say, electrons — cannot be painted red or blue. If their quantum properties are identical, they cannot be distinguished. As such, if they swap places, their new configuration is physically indistinguishable from the previous. And because the physical state must remain the same, the measurable properties of this two-particle system cannot change. Raúl Hidalgo-Sacoto, 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.”
This categorization has physical consequences. Bosons tend to act in uniformity: think of lasers, where photons of the same wavelength (color) move in harmony with each other, or Bose-Einstein Condensates, where ultracold atoms adopt the same state. Fermions, on the other hand, are antisocial: electrons, protons, and neutrons cannot inhabit the same state, which incidentally is why we have a periodic table of different elements.
If we only have two kinds of particles in three dimensions, why can more appear in lower dimensions? The reason is that here, the particles have fewer options for wiggling around one another, and when they cross paths — when they change places — the exchange becomes braided in space and time, meaning that the particles cannot be untangled, ergo the new state is no longer indistinguishable from the previous. 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.”
Thus, a new class of particles that captures particles with an exchange factor other than +1 or -1 can exist: anyons, any -ons that are neither boson nor fermion.
A recipe for adjustable anyons
In the works just published, Hidalgo-Sacoto and colleagues have shown that in 1D space, the binary stays broken with the interesting addition of a directly tunable exchange factor. In 1D, particles can no longer swap places by moving around each other but must instead pass through one another. As such, the exchange factor becomes fundamentally different to the one in higher dimensions — and in fact, the papers show that it is connected to the strength of the short-range interaction between the particles. Experimentally, this allows for fine-grained control over the resulting exchange statistics, suggesting a host of exciting experiments and questions to be both asked and answered. “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.”
In three dimensions (plus one time dimension), particles do not cross paths (or braid) when exchanging places, as their trajectories through time can easily be unwound – this is topologically equivalent to doing nothing. As such, the exchange operator, denoted here as P̂, is either plus or minus the original state (or wavefunction, ψ); a boson or a fermion respectively. In 1D, there is no room for the trajectories to wiggle around one another through time — they must cross, and as such the exchange operator depends on the twists and turns of the path, here operationalized as α. Excitingly, the researchers have found the experimental recipe for directly influencing α, allowing researchers control over how bosonic or fermionic the 1D particle is.
Credit
Jack Featherstone
Journal
Physical Review A
Method of Research
Data/statistical analysis
Subject of Research
Not applicable
Article Title
Universal momentum tail of identical one-dimensional anyons with two-body interactions
