Emulating a many-body topological transition with an aberrated optical cavity

The Ince-Gauss modes of a cavity with aberrated mirrors are shown to constitute a system that is mathematically analogous to the Bose-Hubbard dimer (Bosonic Josephson junction). The latter involves interacting quantum particles while the former involves purely linear optics. The roles of particle interactions and hopping are played by spherical aberration and astigmatism, respectively, and particle number difference corresponds to net optical orbital angular momentum. Both systems feature a topological transition which in the ray-optical/mean-field limit is represented by a Viviani curve on a generalized Poincare/Bloch sphere. The possibility of emulating the squeezing of a coherent state input is also demonstrated.