Slow quasiparticle dynamics and anyonic statistics in a fractional quantum Hall Fabry-P\'erot interferometer

Anyons are particles with fractional exchange statistics that emerge as elementary excitations of fractional quantum Hall phases. Experimentally, their exchange statistics can be measured in the edge-state Fabry-P\'erot interferometer. In these devices, the presence of $N_{qp}$ localized anyons in the bulk contributes a phase $N_{qp}\theta_a$ to the interference signal. Here we report the observation of large, hysteretic phase jumps in a monolayer graphene Fabry-P\'erot interferometer at $\nu=1/3$. When the filling factor is increased from $\nu<1/3$ towards the center of the plateau, we observe phase slips with magnitude $\Delta \theta \approx 2\pi/3$, consistent with the addition of individual quasiparticles to the interferometer bulk. In contrast to prior work, however, the phase slips occur as instantaneous jumps in the interference signal, indicative of quasiparticle equilibration times exceeding 20 minutes. We use this long timescale to investigate the effect of changes in interferometer area $A_I$ and $N_{QP}$ independently at fixed magnetic field, revealing a striking memory effect in the phase slip magnitude. In particular, as the $\nu=1/3$ plateau is approached from higher filling, we observed phase slips with $\Delta \theta$ significantly larger than $2\pi/3$ over the same range of gate voltage where quantized jumps are seen for increasing $\nu$. We discuss this asymmetry in terms of bulk-edge coupling of quasiparticles localized near the edge or in the bulk, and argue that this effect can be qualitatively reconciled with theoretical expectations for strongly interacting quasiparticles in the presence of weak disorder and strongly nonequilibrium charge dynamics. Our results highlight the key role played by charge dynamics on signatures of the anyon phase, and demonstrate that fractional quasiparticles can be indefinitely localized in nonequilibrium configurations.