Quantum computers, while anticipated to address complex problems, currently exhibit sensitivity to environmental disturbances and susceptibility to information loss. Fault-tolerant quantum computing is a goal, with non-Abelian anyons considered as potential building blocks. A study by Dr. Yuval Ronen's lab at the Weizmann Institute of Science, published in Nature, presents evidence for the existence of non-Abelian anyons within bilayer graphene.
Particle Classification
In quantum mechanics, particles are described by a wave function. Particles are classified based on how their wave function changes when two identical particles exchange places:
- Bosons: Wave function remains unchanged (e.g., photons).
- Fermions: Wave function becomes inverted (e.g., electrons).
- Anyons: A third type of particle, observed under specific conditions, where the wave function can rotate through any angle between 0 and 180 degrees upon exchange.
Anyons appear under conditions of near absolute zero temperatures, strong magnetic fields, strong inter-particle interactions, and in two-dimensional systems. Under these circumstances, electrons can exhibit fractional behavior, manifesting as anyons.
Abelian and Non-Abelian Anyons
Theoretically, anyons are categorized into two types:
- Abelian Anyons: Exchanging places primarily adds a phase to the wave function. Fractional electrons with odd denominators (e.g., one-third) are classified as Abelian.
- Non-Abelian Anyons: Exchanging places not only adds a phase but also alters the shape of the wave function. Fractional electrons with even denominators (e.g., one-quarter) are hypothesized to be non-Abelian.
Non-Abelian anyons are significant because the order of particle exchanges leaves a distinctive imprint on the wave function's shape. This property could enable information encoding and storage in a topological system, offering resilience against local environmental disturbances—a key requirement for reliable quantum computing. While Abelian anyons have been measured, direct observation of non-Abelian anyons had not been reported prior to this study.
Experimental Methodology
The research, led by Dr. Jehyun Kim and Himanshu Dev, utilized bilayer graphene, a material composed of two atom-thin carbon layers. This material provides stable conditions for hosting non-Abelian anyons and allows for precise control of their motion paths.
The experiment employed a quantum interference setup, conceptually similar to a 19th-century optical interferometer. Researchers tuned electrons in bilayer graphene to a state anticipated to host non-Abelian anyons. A looped path was created where an anyon's wave encircled an island containing other anyons and a magnetic field before rejoining its original wave.
Results and Observations
Initially, the experiment focused on the magnetic field's effect on the orbiting anyon's phase. The interaction produced an interference pattern of alternating high and low electrical resistance bands. Analysis of this pattern indicated that a wave corresponding to half of an electron was orbiting the island. This observation diverged from the prevailing assumption that non-Abelian anyons carry a quarter of an electron's charge. Researchers hypothesize this may be due to two non-Abelian anyons orbiting together.
A subsequent experiment characterized particles within the island by varying electron density and observing effects on the orbiting anyon's wave function and the interference pattern. Changes in the slope of the interference lines suggested that the internal particles carried a charge of one-quarter of an electron, which aligns with theoretical expectations for non-Abelian anyons and is consistent with previous tunneling experiments conducted at the Weizmann Institute.
Conclusion
The study concludes that bilayer graphene likely hosts non-Abelian anyons. This research contributes to the identification and measurement of non-Abelian anyons, which is considered a step towards the development of fault-tolerant quantum computers.