Nonlinear dynamics of Aharonov-Bohm cages

TL;DR

This paper demonstrates that Aharonov-Bohm caging persists in nonlinear lattice systems, revealing stable caged solutions and collapse-revival dynamics, thus advancing understanding of nonlinear effects in flat band quantum systems.

Contribution

It shows that Aharonov-Bohm caging remains robust under local nonlinearities and introduces a two-mode model to describe caged solutions with breathing motion.

Findings

Caging occurs with local nonlinearities in lattice systems.

Existence of caged solutions with breathing motion.

Observation of collapse-revival dynamics in quantum regimes.

Abstract

The interplay of $\pi$-flux and lattice geometry can yield full localization of quantum dynamics in lattice systems, a striking interference phenomenon known as Aharonov-Bohm caging. At the level of the single-particle energy spectrum, this full-localization effect is attributed to the collapse of Bloch bands into a set of perfectly flat (dispersionless) bands. In such lattice models, the effects of inter-particle interactions generally lead to a breaking of the cages, and hence, to the spreading of the wavefunction over the lattice. Motivated by recent experimental realizations of analog Aharonov-Bohm cages for light, using coupled-waveguide arrays, we hereby demonstrate that caging always occurs in the presence of local nonlinearities. As a central result, we focus on special caged solutions, which are accompanied by a breathing motion of the field intensity, that we describe in terms of an effective two-mode model reminiscent of a bosonic Josephson junction. Moreover, we explore the quantum regime using small particle ensembles, and we observe quasi-caged collapse-revival dynamics with negligible leakage. The results stemming from this work open an interesting route towards the characterization of nonlinear dynamics in interacting flat band systems.