  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.
