Exactly solvable model behind Bose-Hubbard dimers, Ince-Gauss beams, and aberrated optical cavities
arXiv:2106.02712 · doi:10.1103/PhysRevA.107.L031502
Abstract
By studying the effects of quadratic anisotropy and quartic perturbations on the two-dimensional harmonic oscillator, 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.
References in corpus (19)
- Nonlinear atom interferometer surpasses classical precision limit
- Matter-wave interferometry in a double well on an atom chip
- Squeezing and entanglement in a Bose-Einstein condensate
- Coherent Oscillations in an Exciton-Polariton Josephson Junction
- Dynamics of a tunable superfluid junction
- Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point
- Dynamic generation of spin-squeezed states in bosonic Josephson junctions
- Entangled Singularity patterns of Photons in Ince-Gauss modes
- Rows of optical vortices from elliptically perturbing a high-order beam
- Quantum orbital angular momentum of elliptically-symmetric light
- Swings and roundabouts: Optical Poincaré spheres for polarization and Gaussian beams
- Semiclassical quantization of an N-particle Bose-Hubbard model
- Semiclassical analysis of Bose-Hubbard dynamics
- From many-body oscillations to thermalization in an isolated spinor gas
- Higher-order Hermite-Gauss modes as a robust flat beam in interferometric gravitational wave detectors
- Caustics in quantum many-body dynamics
- Catastrophes in non-equilibrium many-particle wave functions: universality and critical scaling
- Aberrated optical cavities
- Polarization dynamics in twisted fiber amplifiers: a non-Hermitian nonlinear dimer model