Universal sign-control of coupling in tight-binding lattices

TL;DR

This paper introduces a universal method to invert the sign of coupling in tight-binding lattices using an ancillary site, enabling new topological and gauge-related studies in photonic systems.

Contribution

The authors develop a universal technique for sign control of coupling in tight-binding systems via eigenmode matching, verified experimentally in photonic lattices.

Findings

Successful experimental verification in laser-written photonic lattices

Ability to embed sign-flipped couplings into extended lattice structures

Potential to explore topological effects with engineered gauge transformations

Abstract

We present a method of locally inverting the sign of the coupling term in tight-binding systems, by means of inserting a judiciously designed ancillary site and eigenmode matching of the resulting vertex triplet. Our technique can be universally applied to all lattice configurations, as long as the individual sites can be detuned. We experimentally verify this method in laser-written photonic lattices and confirm both the magnitude and the sign of the coupling by interferometric measurements. Based on these findings, we demonstrate how such universal sign-flipped coupling links can be embedded into extended lattice structures to impose a $\mathbb{Z}_2$-gauge transformation. This opens a new avenue for investigations on topological effects arising from magnetic fields with aperiodic flux patterns or in disordered systems.