Boson-Anyon-Fermion Mapping and Anyon Construction in One Dimension

TL;DR

This paper presents an exact mapping between particles with different exchange statistics in one dimension, enabling the construction of anyons from bosons and fermions, and explores their potential realization in ultracold atomic systems.

Contribution

It introduces a general boson-anyon-fermion mapping in 1D and demonstrates how to engineer anyonic superfluidity using ultracold atoms with spin-dependent interactions.

Findings

Established an exact exchange statistics mapping in 1D

Demonstrated creation of anyons from superpositions of symmetric and anti-symmetric states

Proposed detection of anyonic states via asymmetric momentum distributions

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.