  We show that a system of three trapped ultracold and strongly interacting
atoms in one-dimension can be emulated using an optical fiber with a
graded-index profile and thin metallic slabs. While the wave-nature of single
quantum particles leads to direct and well known analogies with classical
optics, for interacting many-particle systems with unrestricted statistics such
analoga are not straightforward. Here we study the symmetries present in the
fiber eigenstates by using discrete group theory and show that, by spatially
modulating the incident field, one can select the atomic statistics, i.e.,
emulate a system of three bosons, fermions or two bosons or fermions plus an
additional distinguishable particle. We also show that the optical system is
able to produce classical non-separability resembling that found in the
analogous atomic system.
