Engineering the Bogoliubov Modes through Geometry and Interaction: From Collective Edge Modes to Flat-band Excitations

TL;DR

This paper presents a method to engineer lattice models using Bose-Einstein condensates, enabling simulation of topological and flat-band excitations through tailored superlattices.

Contribution

It introduces a framework to map condensate excitations onto tight-binding models, allowing simulation of topological and flat-band phenomena in solid-state analogs.

Findings

Modeling of a 1D topological Su-Schrieffer-Heeger lattice

Simulation of 2D Lieb lattice with flat-band excitations

Demonstration of engineering condensate superlattices for desired modes

Abstract

We propose a procedure to engineer solid-state lattice models with superlattices of interaction-coupled Bose-Einstein condensates. We show that the dynamical equation for the excitations of Bose-Einstein condensates at zero temperature can be expressed in an eigenvalue form that resembles the time-independent Schr{\"o}dinger equation. The eigenvalues and eigenvectors of this equation correspond to the dispersions of the collective modes and the amplitudes of the density oscillations. This alikeness opens the way for the simulation of different tight-binding models with arrays of condensates. We demonstrate, in particular, how we can model a one-dimensional Su-Schrieffer-Heeger lattice supporting topological edge modes and a two-dimensional Lieb lattice with flat-band excitations with superlattices of Bose-Einstein condensates.