Nonlinear dynamics of Aharonov-Bohm cages

Marco Di Liberto, Sebabrata Mukherjee, Nathan Goldman

Research output: Contribution to journalArticlepeer-review

37 Citations (Scopus)
28 Downloads (Pure)


The interplay of π-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 single-particle level, this full-localization effect is attributed to the collapse of Bloch bands into a set of perfectly flat (dispersionless) bands. While interparticle interactions generally break the cages, not much is known regarding the fate of Aharonov-Bohm caging in the presence of classical nonlinearities, as captured by a discrete nonlinear Schrödinger equation. This scenario is relevant to recent experimental realizations of photonic Aharonov-Bohm cages, using classical light propagating in arrays of coupled waveguides. In this article, we demonstrate that caging always occurs in this nonlinear setting, as long as the nonlinearities remain local. As a central result, we identify special caged solutions that are accompanied by a breathing dynamics of the field intensity that we describe in terms of an effective two-mode model reminiscent of a bosonic Josephson junction. Also, motivated by a formal similarity with the Gross-Pitaevskii equation describing interacting bosons, we explore the quantum regime of Aharonov-Bohm caging using small ensembles of interacting particles, and reveal quasicaged collapse-revival dynamics. The results stemming from this work open an interesting route towards the characterization of nonlinear dynamics in interacting flat-band systems.

Original languageEnglish
Article number043829
JournalPhysical Review A
Issue number4
Publication statusPublished - 22 Oct 2019

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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