Floquet realization and signatures of one-dimensional anyons in an optical lattice

We propose a simple scheme for realizing the physics of 1D anyons with ultracold bosonic atoms in an optical lattice. It relies on lattice-shaking-induced resonant tunneling against potential off-sets created by a combination of a lattice tilt and strong on-site interactions. No lasers additional to those used for the creation of the optical lattice are required. We also discuss experimental signatures of the continuous interpolation between bosons and fermions when the statistical angle $\theta$ is varied from 0 to $\pi$. Since the anyonic momentum distribution is not measurable in the bosonic representation of the anyon model, we propose to use Friedel oscillations in small systems as an alternative probe.