Nonlinear symmetry breaking of Aharonov-Bohm cages

TL;DR

This paper investigates how cubic nonlinearity affects Aharonov-Bohm caging in a diamond lattice, revealing a sharp transition from localized to spreading states due to symmetry breaking, observable in optical waveguides.

Contribution

It demonstrates a novel nonlinear symmetry breaking transition in Aharonov-Bohm cages, distinct from other flatband systems, with experimental relevance in photonic waveguides.

Findings

Persistence of caging at weak nonlinearity

Sharp transition to wavepacket spreading at critical nonlinearity

Experimental observability in femtosecond laser-written waveguides

Abstract

We study the influence of mean field cubic nonlinearity on Aharonov-Bohm caging in a diamond lattice with synthetic magnetic flux. For sufficiently weak nonlinearities the Aharonov-Bohm caging persists as periodic nonlinear breathing dynamics. Above a critical nonlinearity, symmetry breaking induces a sharp transition in the dynamics and enables stronger wavepacket spreading. This transition is distinct from other flatband networks, where continuous spreading is induced by effective nonlinear hopping or resonances with delocalized modes, and is in contrast to the quantum limit, where two-particle hopping enables arbitrarily large spreading. This nonlinear symmetry breaking transition is readily observable in femtosecond laser-written waveguide arrays.