We study the quantum dynamics of two interacting anyons in the Anyon-Hubbard model on a four-site plaquette, a system that is exactly mappable to a Bose-Hubbard model. We reveal that static Aharonov-Bohm (AB) caging, induced by only specific statistical phases, emerges in the strongly interacting limit but breaks down under weak interparticle interactions. To address this, we demonstrate that statistical-factor-induced AB caging can be dynamically restored via Floquet engineering. This dynamical mechanism, governed by the synthetic Floquet flux and the anyonic statistical phase, extends the caging effect into the weakly interacting regime across the full spectrum of statistical phases. Furthermore, we show that the external drive enables the selective caging of anyons, providing an efficient approach for manipulating anyons and identifying statistical phases.
We show that a non-interacting gas of charge-
e/3 anyons with exchange statistics
θ=−π/3 can superconduct through a hidden weak-pairing mechanism. Such an anyon gas arises naturally in doped fractional Chern insulators at filling
1/3 or
2/3, where projective lattice translations enforce three degenerate anyon pockets. Exploiting this three-pocket structure, we develop a flux-attachment construction in which the average statistical flux vanishes, thereby mapping the problem to three species of composite fermions (CFs) in zero effective magnetic field. We show that the anyon statistics itself, encoded in statistical gauge field fluctuations, supplies the pairing glue and drives the CFs into a
p−ip paired state, which corresponds to a
f−if physical superconductor. The CF strong-pairing phase is adiabatically connected to Laughlin's picture of anyon superconductivity, where charge-
e/3 anyons bind into charge-
2e/3 molecules, which then lead to superconductivity. By contrast, the more natural weak-pairing phase of CFs realizes a distinct superconducting phase - its edge is characterized by a chiral central charge
c−=−1/2, in contrast to the prediction of integer
c− for the anyon superconductor based on Laughlin's picture, thereby resolving the discrepancy between previous theories and recent numerical results. Our theory provides a natural framework for understanding superconductivity near fractional Chern insulators, as observed in recent experiments. Finally, we discuss extensions of our theory that predict new chiral superconductors adjacent to FCIs at other fillings.