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The Josephson frequency of fractionally charged anyons

M. Santin M. Kapfer P. Roulleau 1 I. Farrer 2 D. Ritchie D. Glattli 1
1 GNE - Groupe Nano-Electronique
SPEC - UMR3680 - Service de physique de l'état condensé, IRAMIS - Institut Rayonnement Matière de Saclay
Abstract : Anyons (intermediate between bosons and fermions) occur in two-dimensional electron systems in high magnetic field as fractional excitations with charge e*=e/q in the topological ordered states of the Fractional Quantum Hall Effect (FQHE). Owing to their importance for topological quantum phases and possible decoherence free quantum information approaches, understanding anyons is of utmost importance. However, experiments probing their dynamics are lacking. Here we report on a dynamical property of anyons: their long predicted Josephson frequency fJ=e*V/h for charge e*=e/3 and e/5. It manifests as marked signatures in the Photo Assisted Shot Noise (PASN) versus voltage V when irradiating contacts at microwaves frequency f=fJ. The validation of FQHE PASN models opens the way to realize on-demand anyon sources based on levitons to perform time-domain anyon braiding. The Quantum Hall Effect (QHE) occurs in two-dimensional electron systems (2DES) for strong magnetic fields quantizing the electron cyclotron energy into Landau levels. For integer Landau level filling factor =p, the Integer QHE (IQHE) shows a topologically protected quantized Hall conductance pe 2 /h with zero longitudinal conductance (1). For very low disorder samples, the Coulomb repulsion favors topologically ordered phases at rational =p/q showing a Fractional QHE (FQHE) with fractional Hall (2) and zero longitudinal conductance. For electrons filling the first Landau Level (<1), the states with =1/(2k+1) are well understood by Laughlin states (3). The elementary excitations, or quasiparticles, bear a fraction e*=e/(2k+1) of the elementary charge (3-6) and are believed to obey a fractional anyonic (7) statistics intermediate between bosons and fermions. For <1, the Jain states (8) with =p/(2kp+1), p and k integer, display e*=e/(2kp+1) fractionally charged excitations (9) which are composite fermions, i.e., electrons to which-2k flux quanta 0=h/e are attached. For higher Landau Level filling, even denominators FQHE states are found such as the 5/2 state showing Majorana excitations and e*=e/4 non-abelian anyonic quasiparticles (10,11) with possible application to topologically protected quantum computation. An important breakthrough would be the time domain manipulation of anyons allowing their
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M. Santin, M. Kapfer, P. Roulleau, I. Farrer, D. Ritchie, et al.. The Josephson frequency of fractionally charged anyons. Science, American Association for the Advancement of Science, 2019, 363 (6429), pp.846 - 849. ⟨10.1126/science.aau3539⟩. ⟨cea-02167003⟩

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