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We show that a system of three trapped ultracold and strongly interactingatoms in one-dimension can be emulated using an optical fiber with agraded-index profile and thin metallic slabs. While the wave-nature of singlequantum particles leads to direct and well known analogies with classicaloptics, for interacting many-particle systems with unrestricted statistics suchanaloga are not straightforward. Here we study the symmetries present in thefiber eigenstates by using discrete group theory and show that, by spatiallymodulating the incident field, one can select the atomic statistics, i.e.,emulate a system of three bosons, fermions or two bosons or fermions plus anadditional distinguishable particle. We also show that the optical system isable to produce classical non-separability resembling that found in theanalogous atomic system.

Graded-index optical fiber emulator of an interacting three-atom system: illumination control of particle statistics and classical non-separability