Princeton University Team Studies Anyon Confinement for Topological Quantum Computation

A thorough investigation into the behaviour of anyons, quasiparticles possessing fractional charge confined within graphene, offers a key advancement towards topological quantum computation. Jeong Min Park and colleagues at Princeton University, in collaboration with University of Leeds, Washington University, National Institute for Materials Science; Namiki, University of Cambridge, and 3 other institutions, employed scanning tunneling microscopy/spectroscopy to examine the excitation spectrum of these anyons trapped near charged impurities in both integer and fractional quantum Hall states. Observations reveal a unique energy splitting in fractional states, specifically at filling factors of 1/3 and 2/5, attributable to multi-anyon configurations and dependent on the shape of the confining potential. Local tunneling spectroscopy is a direct method for probing anyon bound states, representing a sharp step in understanding and ultimately controlling these particles for potential quantum technologies.

Fractional quantum Hall states reveal multi-anyon interactions and anisotropic impurity potentials

A 2/5th electron charge energy splitting has been detected in fractional quantum Hall states, a phenomenon previously unobservable due to limitations in treating anyons as point-like objects. This splitting, observed at filling factors of 1/3 and 2/5, signifies a key threshold in understanding anyon behaviour, as prior methods lacked the sensitivity to resolve multi-anyon configurations trapped by impurities. The collaboration between Princeton University and the University of Leeds attributes this splitting to the complex interaction of multiple anyons confined within the electric potential of charged impurities. The fractional quantum Hall effect arises from the strong interaction between electrons in a two-dimensional electron gas subjected to a strong perpendicular magnetic field and low temperatures. This interaction leads to the formation of correlated many-body states with exotic properties, including the emergence of anyons. Unlike bosons or fermions, anyons exhibit fractional charge and obey exchange statistics differing from either of these conventional particle types; exchanging two identical anyons can alter the quantum state of the system.

Numerical calculations reveal the effect requires an anisotropic, rather than rotationally symmetric, confining potential. A rotationally symmetric trap would eliminate the observed splitting entirely. The modelling at Princeton University and the University of Leeds confirmed the anisotropy of the confining potential, demonstrating that the energy splitting vanished entirely when a rotationally symmetric trap was simulated. This anisotropy arises from the specific arrangement of the charged impurity and the surrounding graphene lattice. The precise shape of the potential well created by the impurity dictates how the anyons distribute themselves, influencing their energy levels. The simulations employed sophisticated computational techniques, including density functional theory and exact diagonalization, to accurately model the many-body interactions and the confining potential. Further calculations revealed the competing multi-anyon states possess nearly identical charge at the impurity’s core, but redistribute that charge differently at larger distances, directly influencing the observed spectral features. This redistribution is crucial, as it determines the overall energy landscape and the stability of the multi-anyon configurations.

The splitting at filling factors of 1/3 and 2/5 occurs exclusively within the fractional gaps, confirming its connection to many-body anyon configurations and distinguishing it from behaviour in integer or compressible regimes. This local tunneling spectroscopy technique successfully probes the internal structure of anyon bound states, offering a new method to study these quasiparticles. The fractional gaps represent the energy required to create excitations within the fractional quantum Hall state, and the observation of splitting within these gaps provides strong evidence for the involvement of anyons. Integer quantum Hall states, in contrast, exhibit gaps associated with the formation of Landau levels, and do not display the same behaviour. Achieving controlled braiding and fusion, however, remains a significant challenge beyond the scope of these initial spectroscopic observations. Braiding involves moving anyons around each other in a controlled manner, while fusion refers to combining two anyons into a single quasiparticle.

Identifying these multi-anyon configurations, even without immediate control, establishes an important foundation for future progress in topological quantum computation and understanding exotic matter. Teams at Princeton University and the University of California, Berkeley have directly observed multi-anyon configurations trapped by impurities in graphene. The significance of this observation lies in the potential for utilising anyons as qubits, the fundamental units of quantum information. Topological quantum computation leverages the inherent stability of anyons to protect quantum information from decoherence, a major obstacle in building practical quantum computers. Detailed mapping of anyon behaviour near impurities represents a key step towards realising topological quantum computation, a model promising inherently stable quantum bits. The stability arises from the fact that the quantum information is encoded in the topological properties of the anyon configurations, rather than in the state of individual particles.

Manipulating these configurations, however, remains a formidable challenge. Local tunneling spectroscopy reveals the internal structure of these bound states, while actively braiding or fusing anyons, essential operations for quantum algorithms, demands precise control over the confining potential. This control requires the development of novel techniques for manipulating the electric potential at the nanoscale, potentially using advanced gate electrodes or strain engineering. Scanning tunneling microscopy/spectroscopy now offers a means to directly probe these anyon bound states, providing a new pathway for investigating their internal structure and configurations. The technique involves scanning a sharp metallic tip across the surface of the graphene sample and measuring the tunneling current between the tip and the sample. Variations in the tunneling current reveal information about the local electronic structure, including the energy levels of the anyon bound states. This research moves beyond simply identifying the presence of multi-anyon arrangements, opening questions regarding the precise charge distribution within these configurations and its influence on spectral features. Understanding the charge distribution is crucial for optimising the interaction between anyons and external control mechanisms. Further research will likely focus on manipulating these confined anyons to explore their potential for topological quantum computation, potentially involving the application of external fields or the introduction of additional impurities to induce braiding or fusion events.

The research demonstrated an energy splitting of spectral features in fractional quantum Hall states of graphene, attributable to multiple anyons trapped by impurities. This is significant because it provides direct evidence of how these unusual quasiparticles behave when confined, a crucial step towards understanding and controlling them. Using scanning tunneling microscopy/spectroscopy, scientists observed this splitting only when the chemical potential was within a fractional gap, and calculations revealed it requires an uneven confining potential. The findings establish a method for locally probing anyon configurations and their internal structure, which is relevant to the development of stable quantum bits for potential quantum computation.