Realization of Discrete Quantum Billiard in 2D Optical Lattices

Abstract

We propose the method for optical visualization of Bose-Hubbard model with two interacting bosons in the form of two-dimensional (2D) optical lattices consisting of optical waveguides, where the waveguides at the diagonal are characterized by different refractive index than others elsewhere, modeling the boson-boson interaction. We study the light intensity distribution function averaged over direction of propagation for both ordered and disordered cases, exploring sensitivity of the averaged picture with respect to the beam injection position. For our finite systems the resulting patterns reminiscent the ones set in billiards and therefore we introduce a definition of discrete quantum billiard discussing the possible relevance to its well established continuous counterpart.

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• Observation of pair tunneling and coherent destruction of tunneling in arrays of optical waveguides
• Topological bound states in interacting Su-Schrieffer-Heeger rings
• Correlated metallic two particle bound states in quasiperiodic chains
• Probing the effects of interaction in Anderson localization using linear photonic lattices
• An introduction to arrays of coupled waveguides
• Arbitrary synthetic dimensions via multi-boson dynamics on a one-dimensional lattice
• Simulation of two-boson bound states using arrays of driven-dissipative coupled linear optical resonators
• Photonic lattice simulation of dissipation-induced correlations in bosonic systems
• Spectral analysis of two-dimensional Bose-Hubbard models
• Lattice scars: Surviving in an open discrete billiard
• Interaction-induced connectivity of disordered two-particle states
• Coherent population oscillations and an effective spin-exchange interaction in a $\mathcal{P}\mathcal{T}$ symmetric polariton mixture
• Effects of Peierls phases in open linear chains
• Anti-Newtonian dynamics and self-induced Bloch oscillations of correlated particles
• Random dimer model in pseudo two-dimensional lattices
• Non-Rayleigh signal of interacting quantum particles
• Localized-Interaction-Induced Quantum Reflection and Filtering of Bosonic Matter in a One-Dimensional Lattice Guide