Anyonic Molecules in Atomic Fractional Quantum Hall Liquids: A Quantitative Probe of Fractional Charge and Anyonic Statistics

Year: 2020

Authors: De Las Heras AM., Macaluso E., Carusotto I.

Autors Affiliation: Univ Trento, INO CNR BEC Ctr, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, I-38123 Trento, Italy.

Abstract: We study the quantum dynamics of massive impurities embedded in a strongly interacting, two-dimensional atomic gas driven into the fractional quantum Hall (FQH) regime under the effect of a synthetic magnetic field. For suitable values of the atom-impurity interaction strength, each impurity can capture one or more quasihole excitations of the FQH liquid, forming a bound molecular state with novel physical properties. An effective Hamiltonian for such anyonic molecules is derived within the Born-Oppenheimer approximation, which provides renomialized values for their effective mass, charge, and statistics by combining the finite mass of the impurity with the fractional charge and statistics of the quasiholes. The renormalized mass and charge of a single molecule can be extracted from the cyclotron orbit that it describes as a free particle in a magnetic field. The anyonic statistics introduces a statistical phase between the direct and exchange scattering channels of a pair of indistinguishable colliding molecules and can be measured from the angular position of the interference fringes in the differential scattering cross section. Implementations of such schemes beyond cold atomic gases are highlighted-in particular, in photonic systems.

Journal/Review: PHYSICAL REVIEW X

Volume: 10 (4)      Pages from: 41058-1  to: 41058-23

More Information: We acknowledge financial support from the European Union H2020-FETFLAG-2018-2020 project PhoQuS (No. 820392), from the Provincia Autonoma di Trento, from the Q@TN initiative, and from Google via the quantum NISQ award. Stimulating discussions with Atac Imamoglu, Gwendal Feve, and Giacomo Lamporesi are warmly acknowledged.
KeyWords: Scattering; Mechanics; Phase
DOI: 10.1103/PhysRevX.10.041058

Citations: 3
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