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

We show that optical fibers with a graded-index profile and thin metallic slabs can be used to emulate a system of three ultracold strongly interacting atoms. We study the symmetries present in the eigenstates by using discrete group theory, always comparing our results with those previously found from the atomic physics approach. The symmetry analysis allows us to prove 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 show that the optical system is able to produce classical non-separability resembling that found in the analogous atomic system.