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

M.A. Garcia-March1,2, N.L. Harshman3, H. da Silva4, T. Fogarty5, Th. Busch5, M. Lewenstein1,6, and A. Ferrando7

1ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
2Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, E-46022 València, Spain
3Department of Physics, American University, 4000 Massachusetts Avenue NW, Washington, DC 20016, USA
4Universidade Federal de Itajubá, Av. BPS 1303, Itajubá, Minas Gerais 37500-903, Brazil
5Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, 1919-1 Tancha, Onna, Okinawa 904-0495, Japan
6ICREA, Pg. Lluis Companys 23, 08010 Barcelona, Spain
7Department d'Optica. Universitat de València, Dr. Moliner, 50, E-46100 Burjassot (València), Spain

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Abstract

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.

Two properties often considered essentially quantum are entanglement and indistinguishability. Understanding their interplay is necessary for fundamental descriptions of the nature of matter and for applications to quantum technologies. Delicate and precise experiments with ultracold atoms in optical traps probe how these seemingly quantum properties interplay in interacting few-body systems. However, we show that both entanglement and indistinguishability in an interacting three-particle system can be simulated by classical light propagating down a structured optical fiber.
The structured optical fiber we propose has a graded-index of refraction with a parabolic profile and is sectioned longitudinally by three thin metallic foils. Optical modes in the fiber obey dynamics in exact analogy to the Schrödinger equation for the relative motion of three particles with short-range interactions in a one-dimensional harmonic trap. We find expressions for the optical modes of this fiber, and equivalently the energy eigenstates for the three-particle system, and classify these solutions by symmetry. By controlling the orbital angular momentum of the input beam, modes with different symmetries can be excited, and these symmetries correspond to different types of indistinguishable or partially indistinguishable particles.
Optical fibers have been previously proposed as simulators for quantum systems and have been used to identify a classical analog to entanglement called classical non-separability. However, the structured optical fiber we propose can simulate entanglement among a broader range of degrees of freedom, and the analogy to the three-particle interacting system allows us to probe interaction, entanglement and indistinguishability in a quantum system with classical optics.

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Cited by

[1] Tomasz Sowiński and Miguel Ángel García-March, "One-dimensional mixtures of several ultracold atoms: a review", Reports on Progress in Physics 82 10, 104401 (2019).

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