An optical fiber simulator of three interacting atoms in one dimensional parabolic trap*

We introduce an optical fiber that simulates a system of three trapped ultracold and strongly interacting atoms in one-dimension. To simulate the contact interactions among the atoms, we consider a sharp and narrow jump in the refractive index. To this end, we consider here three thin metallic slabs. To simulate the parabolic trap we assume that the fiber has a graded refractive index profile. While the wave-nature of single quantum particles leads well-known analogies with classical optics, for interacting many-particle systems such analogs are not straightforward. We discuss: i) how 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 a distinguishable particle; ii) how this system can produce classical non-separability resembling that found in the analogous atomic system.

[1] M.A. Garcia-March et al. Arxiv: 1902.01748.