Exactly solvable model behind Bose-Hubbard dimers, Ince-Gauss beams, and aberrated optical cavities

By studying the effects of quadratic anisotropy and quartic perturbations on two-dimensional harmonic oscillators, one arrives at a simple model, termed here the Ince oscillator, whose analytic solutions are given in terms of Ince polynomials. This one model unifies diverse physical systems, including aberrated optical cavities that are shown to support Ince-Gauss beams as their modes, and the two-mode Bose-Hubbard dimer describing two coupled superfluids. The Ince oscillator model describes a topological transition which can have very different origins: in the optical case, which is fundamentally linear, it is driven by the ratio of astigmatic to spherical mirror aberrations, whereas in the superfluid case it is driven by the ratio of particle tunneling to interparticle interactions and corresponds to macroscopic quantum self-trapping.

Automated summary

By studying the effects of quadratic anisotropy and quartic perturbations, a simple model called the Ince oscillator is proposed, which provides analytic solutions using Ince polynomials. This model unifies various physical systems, including aberrated optical cavities and two-mode Bose-Hubbard dimers, and explains topological transitions driven by different ratios in optical and superfluid cases.