Boson-anyon-fermion mapping and anyon construction in one dimension - Haitian Wang; Yu Chen; Xiaoling Cui (Physical Review Research)
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 antisymmetric 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 demonstrate the inadequacy of the contact interaction model for anyons in continuum and lattices, and have also suggested a convenient route for engineering fractional phases on the platform of ultracold atoms.