Two-site anyonic Josephson junction

Anyons are particles with intermediate quantum statistics whose wave function acquires a phase ei? by particle exchange. Inspired by proposals of simulating anyons using ultracold atoms trapped in optical lattices, we study a two-site anyonic Josephson junction, i.e., anyons confined in a one-dimensional double-well potential. We show, analytically and numerically, that many properties of anyonic Josephson junctions, such as Josephson frequency, imbalanced solutions, macroscopic quantum self-trapping, coherence visibility, and condensate fraction, crucially depend on the anyonic angle ?. Our theoretical predictions are a solid benchmark for near-future experimental quantum simulations of anyonic matter in double-well potentials.