Abstract
The quantum Hall (QH) effect represents a unique playground where quantum coherence of electrons can be exploited for various applications, from metrology to quantum computation. In the fractional regime, it also hosts anyons, emergent quasiparticles that are neither bosons nor fermions and possess fractional statistics. Their detection and manipulation represent key milestones in view of topologically protected quantum computation schemes. Exploiting the high degree of phase coherence, edge states in the QH regime have been investigated by designing and constructing electronic interferometers, able to reveal the coherence and statistical properties of the interfering constituents. Here, we review the two main geometries developed in the QH regime, the Mach–Zehnder and the Fabry–Pérot interferometers. We present their basic working principles, fabrication methods and the main results obtained in both the integer and the fractional QH regimes. We will also show how recent technological advances led to the direct experimental demonstration of fractional statistics for Laughlin quasiparticles in a Fabry–Pérot interferometric setup.
Key points
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The quantum Hall effect represents the first known example of topological quantum matter, whose intrinsic robustness is pivotal for many applications, from metrological standard to quantum information purposes.
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Transport is mediated by charge carriers moving along the edge of the system with a high degree of phase coherence, which has been exploited to build electronic analogues of quantum optic experiments.
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Electronic interferometry in the integer and the fractional quantum Hall regimes has emerged as a unique playground to study and exploit the coherence and correlations of propagating quasiparticles. Two main geometries have been studied and realized, Mach–Zehnder and Fabry–Pérot interferometers.
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Excitations in the fractional quantum Hall regime are predicted to be anyons, quasiparticles with fractional charges and fractional statistics. The fractional statistics, in particular, has attracted a lot of interest in view of potential applications in topological quantum computation.
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Recent experimental advances in quantum Hall interferometry have led to the first direct observation of fractional statistics in a Fabry–Pérot setup.
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Acknowledgements
This activity was partially supported by the SuperTOP project, QuantERA ERA-NET Cofund in Quantum Technologies and by the FET-Open project AndQC. L.C. acknowledges funding by the EU Marie Curie Global Fellowship TOPOCIRCUS 841894 - Simulations of Topological Phases in Superconducting Circuits.
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Carrega, M., Chirolli, L., Heun, S. et al. Anyons in quantum Hall interferometry. Nat Rev Phys 3, 698–711 (2021). https://doi.org/10.1038/s42254-021-00351-0
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DOI: https://doi.org/10.1038/s42254-021-00351-0
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