Dimensions Unbound: The Enigmatic Existence of ‘Paraparticles’ Beyond Classification

Exotic ‘Paraparticles’ That Disobey Classification May Be Present in Multiple Dimensions

By Davide Castelvecchi & Nature magazine

Theoretical physicists have suggested the potential existence of a novel type of particle that doesn’t conform to the standard categories of fermions and bosons. Their proposed ‘paraparticle,’ outlined in Nature on January 8, is not the initial suggestion of its kind, but the intricate mathematical framework defining it could pave the way for experiments where it is generated using a quantum computer. The study also hints that yet-to-be-discovered elementary paraparticles may exist in nature.

In an unrelated study published late last year in Science, physicists successfully demonstrated another type of particle that is neither a boson nor a fermion — an ‘anyon’ — within a simulated one-dimensional universe for the first time. Anyons were previously generated exclusively in 2D environments.

Due to their exceptional characteristics, both paraparticles and anyons may eventually contribute to enhancing the reliability of quantum computers.

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Properties of Particles

Around the period when physicists began to decipher the atomic structure, a century ago, the Austrian-born theorist Wolfgang Pauli proposed that no two electrons could occupy the same state — and that if two electrons were forced close to being in the same state, a repulsive force emerged between them. This ‘Pauli exclusion principle’ is fundamental to the configuration of electrons orbiting an atomic nucleus in shells, as opposed to all collapsing into the lowest energy state.

Pauli and his contemporaries soon recognized that this empirical exclusion rule applied not just to electrons but to a wider category of particles, including protons and neutrons, which they collectively termed fermions. Alternatively, particles that prefer to share the same state — including the photons in a laser beam, for instance — were designated as bosons. (Pauli and his colleagues also understood the relation between being a fermion or a boson and a particle’s inherent angular momentum, or ‘spin’.)

Mathematically, the central characteristic of fermions is that when two of them exchange positions, the ‘wavefunction’ representing their combined quantum state alters sign, meaning it is multiplied by –1. In the case of bosons, the wavefunction remains unchanged. Early quantum theorists were aware that, theoretically, other types of particles could exist whose wavefunctions transformed in more complex manners during position exchanges. In the 1970s, researchers identified anyons, which can only manifest in universes with one or two dimensions.

Physicists Zhiyuan Wang, presently at the Max Planck Institute for Quantum Optics in Garching, Germany, along with Kaden Hazzard from Rice University in Houston, Texas, have developed a model for paraparticles that can exist across any number of dimensions — and possess distinct properties from those of fermions or bosons. Specifically, these paraparticles adhere to their own variation of the Pauli exclusion principle. “It’s not entirely surprising that it’s achievable,” remarks Kasia Rejzner, a mathematical physicist at the University of York, UK. “Yet, it remains fascinating.”

Wang recounts that he stumbled upon the unusual swapping rules accidentally in 2021, while pursuing his PhD. “It was the most exhilarating moment in my life,” he shares. Wang adds that realizing these paraparticle states on a quantum computer should be feasible — albeit challenging.

1D Anyons

Paraparticles possess a characteristic akin to fermions: swapping two particles and then reversing the swap returns them to their original state. Anyons, on the other hand, typically exhibit a different quantum state even after being returned to their prior positions, therefore they are not categorized as paraparticles.

In the Science investigation, physicists Joyce Kwan and Markus Greiner at Harvard University in Cambridge, Massachusetts, along with their team suspended atoms of the isotope rubidium-87 in a vacuum utilizing light waves. The atoms tended to remain at the troughs of the waves and only occasionally transitioned from one to another, less than one micrometer apart. Under these conditions, rubidium-87 atoms would normally act like bosons, leading to two of them sharing the same trough without issue. However, by periodically adjusting the light intensity, the researchers altered the behavior of the atoms, so that once two atoms swapped positions, their wavefunctions were twisted by a specific angle — a defining trait of anyons. Investigating the wavefunctions necessitated numerous repetitions of the experiment, enabling the atoms to roam before later freezing them and imaging the position of each atom, as Kwan explains.

“I am extremely thrilled that the Greiner group has successfully realized anyons in 1D,” states Martin Greiter, a theoretical physicist at Julius Maximilian University of Würzburg in Germany.

Given that anyons’ wavefunctions ‘remember’ how two have been exchanged, they could offer a sturdy method for encoding information. This memory property has already been harnessed in virtual 2D anyons developed by Google physicist and other research teams.

Paraparticles may not be as resilient as anyons, but they might also hold potential for quantum computation, Wang asserts. Interestingly, they can be present in 3D. Theoretically, some undiscovered elementary particles could indeed be paraparticles, he notes.

This article is reproduced with permission and was first published on January 8, 2025.