Boson-Anyon-Fermion Mapping and Anyon Construction in One Dimension (2410.21632v3)

Abstract: We establish an exact mapping between identical particles in one dimension with arbitrary exchange statistics, including bosons, anyons and fermions, provided they share the same scattering length. This boson-anyon-fermion mapping facilitates the construction of anyons from a linear superposition of spatially symmetric and anti-symmetric states. This scheme is general and has been demonstrated in a spin-1/2 Fermi gas, where both s- and p-wave bound states can be supported by manipulating spin channels. With a suitable symmetry-breaking field, these bound states are hybridized to form a fractional-wave molecule. The condensation of these molecules in a many-body system leads to anyonic superfluidity, characterized by fractional statistics upon spin exchange within a Cooper pair. These anyonic states can be detected through asymmetric momentum distributions for each spin with a chiral $k^{-3}$ tail. Our results have demonstrated the inadequacy of contact interaction model for anyons in continuum and lattices, and meanwhile proposed a convenient route for engineering fractional phases in the platform of ultracold atoms.