Realization of Discrete Quantum Billiard in 2D Optical Lattices

TL;DR

This paper presents a method to visualize the Bose-Hubbard model with two interacting bosons in 2D optical lattices, revealing patterns akin to quantum billiards and exploring effects of disorder and beam injection.

Contribution

It introduces a novel optical visualization technique for the Bose-Hubbard model in 2D lattices, modeling interactions via waveguide refractive index variations and defining discrete quantum billiards.

Findings

Patterns resemble quantum billiards in finite systems

Sensitivity of intensity distribution to beam injection position

Disorder effects on the observed patterns

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.