Anyon Statistics in Tiny Electronic Colliders

Project Information

ASTEC

Grant agreement ID: 101096610

DOI

10.3030/101096610

EC signature date 28 July 2023

Start date 1 November 2023

End date 31 October 2029

Funded under

• European Research Council (ERC)

Total cost

€ 2 499 941,25

EU contribution

€ 2 499 941,25

Coordinated by

SORBONNE UNIVERSITE
France

Periodic Reporting for period 1 - ASTEC (Anyon Statistics in Tiny Electronic Colliders)

Reporting period: 2023-11-01 to 2026-04-30

Summary of the context and overall objectives of the project

In three dimensional systems, elementary particles are divided exclusively between fermions (like electrons), which exclude each others, and bosons (like photons), which bunch together, according to the phase acquired by the wavefunction when two particles are exchanged. The situation is different in two-dimensional systems which can host new particles called anyons, for which the exchange phase can take any value, and which obey partial exclusion, between fermions and bosons. In the simplest case of abelian anyons, fractional statistics implies that moving one anyon around another (a braiding operation) results in the accumulation of a non-trivial phase factor. This robust
memory of braiding operations is at the heart of topological quantum computing, where unitary transformations are performed by braiding non-abelian anyons, for which also the order of exchanging the particles plays a role. As these operations would be protected from local fluctuations, the braiding of anyons could be used as the building blocks of quantum computing operations that would be protected from decoherence. The existence of these quasiparticles was predicted forty years ago in two-dimensional conductors in the fractional quantum Hall regime. However, despite intense experimental and theoretical efforts, direct signatures of their fractional statistics have only been observed recently, offering only now the possibility to characterize fractional statistics and to exploit it for new functionalities. The purpose of this project is to quantitatively investigate the statistics of anyons by probing their tendency to bunch together or exclude each others in a nanoscale collider. The different phases of the fractional quantum Hall effect offer a very vast and almost completely unexplored variety of anyons. Collider experiments rely on the emission of anyon excitations towards a beam-splitter implemented using metallic gates deposited on the top of the sample. Anyon braiding manifests as specific bunched tunneling events, where two anyon excitations are transferred together at the output of the splitter. This can be evidenced by measuring the cross-correlations of the current fluctuations at the splitter output that are strongly negative when these bunching events take place. The objective
of the project is to use this experimental technique to characterize the differences between different statistics, including the most interesting non-abelian case. The robustness of the signatures of fractional statistics and to which extent they can be considered as topologically protected will also be investigated. Finally, anyon statistics will be probed in the time-domain regime, where anyon emission is dynamically controlled, which is important step towards quantum information perspectives.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Two main experimental achievements have been realized thus far. The first, accomplished at the very beginning of the project, involved conducting anyon collider experiments using different types of anyon excitations, each corresponding to distinct ground states of the fractional quantum Hall effect. The first type consists of excitations from the ν=1/3 state, which exhibit both fractional charge and fractional statistics equal to one-third that of an electron. The second type involves excitations from the ν=2/5 fractional quantum Hall state, carrying a charge of e/5 but with statistics of 3π/5, which differs from their fractional charge. We observed that these different types of anyons, with their distinct statistics, produce different signatures in collider experiments. The current cross-correlations measured at ν=1/3 match expectations for statistics of π/3. However, the cross-correlations at ν=2/5 remain to be fully understood and suggest an effect of the finite width of the anyon pulses, which introduces a time-broadening of anyon braiding effects in collider experiments.
The second experimental achievement focused on investigating braiding effects in the time domain by generating anyon pulses directed toward the beam-splitter in triggered collider experiments. We observed that the emission of an anyon pulse could trigger tunneling events long after the incoming anyon pulse had exited the splitter. This phenomenon can be understood as a direct consequence of the long-time memory associated with anyon braiding effects. By contrast, when the incoming particle is an electron—with trivial braiding—tunneling occurs simultaneously as the electron pulse crosses the splitter. In this study, we employed a triggered source of anyon pulses (with a temporal width of a few tens of picoseconds) to probe the dynamics of anyon tunneling at a quantum point contact (QPC) in a fractional quantum Hall fluid at filling factor ν=1/3. The experiment utilized Hong-Ou-Mandel interferometry, where two mutually time-shifted anyon pulses were emitted toward the QPC. By measuring the correlations of electrical current fluctuations at the QPC output as a function of the time delay between pulses, we directly probed the characteristic anyon tunneling timescale. Our results demonstrate that anyon braiding increases this characteristic timescale, which is set by the temporal decay of the anyon correlation function and can be interpreted as the time at which the anyon memory is erased. This timescale increases as both the temperature and the scaling dimension δ (the parameter characterizing edge dynamics in a fractional quantum Hall fluid) decrease. Furthermore, by varying the number of anyons in the emitted pulses, we observed that braiding memory effects are suppressed for pulses containing three anyons, confirming the quantized braiding phase θ=2π/3 at filling factor 1/3.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The project’s objectives and potential impact are focused on fundamental science, specifically on understanding the basic properties of this new type of excitation found in two-dimensional strongly correlated systems. The defining characteristic of these exotic quasiparticles is their memory of braiding operations. The main objective of the project is twofold: to determine which experimental tools can be used to evidence and probe anyon braiding, and to explore the physical consequences of these braiding properties. Our recent time-domain anyon collision experiments demonstrate the crucial role of braiding in anyon dynamics, underscoring the distinctive properties of anyons compared to those of fermions or bosons.