In a ground-breaking theoretical study, two physicists have identified a new class of quasiparticle called the paraparticle. Their calculations suggest that paraparticles exhibit quantum properties that are fundamentally different from those of familiar bosons and fermions, such as photons and electrons respectively.
Using advanced mathematical techniques, Kaden Hazzard at Rice University in the US and his former graduate student Zhiyuan Wang, now at the Max Planck Institute of Quantum Optics in Germany, have meticulously analysed the mathematical properties of paraparticles and proposed a real physical system that could exhibit paraparticle behaviour.
“Our main finding is that it is possible for particles to have exchange statistics different from those of fermions or bosons, while still satisfying the important physical principles of locality and causality,” Hazzard explains.
Particle exchange
In quantum mechanics, the behaviour of particles (and quasiparticles) is probabilistic in nature and is described by mathematical entities known as wavefunctions. These govern the likelihood of finding a particle in a particular state, as defined by properties like position, velocity, and spin. The exchange statistics of a specific type of particle dictates how its wavefunction behaves when two identical particles swap places.
For bosons such as photons, the wavefunction remains unchanged when particles are exchanged. This means that many bosons can occupy the same quantum state, enabling phenomena like lasers and superfluidity. In contrast, when fermions such as electrons are exchanged, the sign of the wavefunction flips from positive to negative or vice versa. This antisymmetric property prevents fermions from occupying the same quantum state. This underpins the Pauli exclusion principle and results in the electronic structure of atoms and the nature of the periodic table.
Until now, physicists believed that these two types of particle statistics – bosonic and fermionic – were the only possibilities in 3D space. This is the result of fundamental principles like locality, which states that events occurring at one point in space cannot instantaneously influence events at a distant location.
Breaking boundaries
Hazzard and Wang’s research overturns the notion that 3D systems are limited to bosons and fermions and shows that new types of particle statistics, called parastatistics, can exist without violating locality.
The key insight in their theory lies in the concept of hidden internal characteristics. Beyond the familiar properties like position and spin, paraparticles require additional internal parameters that enable more complex wavefunction behaviour. This hidden information allows paraparticles to exhibit exchange statistics that go beyond the binary distinction of bosons and fermions.
Paraparticles exhibit phenomena that resemble – but are distinct from – fermionic and bosonic behaviours. For example, while fermions cannot occupy the same quantum state, up to two paraparticles could be allowed to coexist in the same point in space. This behaviour strikes a balance between the exclusivity of fermions and the clustering tendency of bosons.
Bringing paraparticles to life
While no elementary particles are known to exhibit paraparticle behaviour, the researchers believe that paraparticles might manifest as quasiparticles in engineered quantum systems or certain materials. A quasiparticle is particle-like collective excitation of a system. A familiar example is the hole, which is created in a semiconductor when a valence-band electron is excited to the conduction band. The vacancy (or hole) left in the valence band behaves as a positively-charged particle that can travel through the semiconductor lattice.
Experimental systems of ultracold atoms created by collaborators of the duo could be one place to look for the exotic particles. “We are working with them to see if we can detect paraparticles there,” explains Wang.
In ultracold atom experiments, lasers and magnetic fields are used to trap and manipulate atoms at temperatures near absolute zero. Under these conditions, atoms can mimic the behaviour of more exotic particles. The team hopes that similar setups could be used to observe paraparticle-like behaviour in higher-dimensional systems, such as 3D space. However, further theoretical advances are needed before such experiments can be designed.
Far-reaching implications
The discovery of paraparticles could have far-reaching implications for physics and technology. Fermionic and bosonic statistics have already shaped our understanding of phenomena ranging from the stability of neutron stars to the behaviour of superconductors. Paraparticles could similarly unlock new insights into the quantum world.
“Fermionic statistics underlie why some systems are metals and others are insulators, as well as the structure of the periodic table,” Hazzard explains. “Bose-Einstein condensation [of bosons] is responsible for phenomena such as superfluidity. We can expect a similar variety of phenomena from paraparticles, and it will be exciting to see what these are.”
As research into paraparticles continues, it could open the door to new quantum technologies, novel materials, and deeper insights into the fundamental workings of the universe. This theoretical breakthrough marks a bold step forward, pushing the boundaries of what we thought possible in quantum mechanics.
The paraparticles are described in Nature.
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