Floquet solitons in square lattices: Existence, Stability and Dynamics

TL;DR

This paper studies topological 2D lattices with time-dependent interactions, identifying exact Floquet solitons, analyzing their stability, and exploring multi-soliton configurations, revealing conditions for stability and instability.

Contribution

It provides the first systematic analysis of exact Floquet solitons in topological lattices, including stability and multi-soliton dynamics, extending previous experimental and numerical observations.

Findings

Floquet solitons are exact, localized, periodic solutions in the lattice.

Solutions are generally stable, with instabilities linked to spectral band collisions.

Multi-soliton states exhibit stability or instability depending on phase configurations.

Abstract

In the present work, we revisit a recently proposed and experimentally realized topological 2D lattice with periodically time-dependent interactions. We identify the fundamental solitons, previously observed in experiments and direct numerical simulations, as exact, exponentially localized, periodic in time solutions. This is done for a variety of phase-shift angles of the central nodes upon a period oscillation of the coupling strength. Subsequently, we perform a systematic Floquet stability analysis of the relevant structures. We analyze both their point and their continuous spectrum and find that the solutions are generically stable, aside from the possible emergence of complex quartets due to the collision of bands of continuous spectrum. The relevant instabilities become weaker as the lattice size gets larger. Finally, we also consider multi-soliton analogues of these Floquet states, inspired by the corresponding discrete nonlinear Schr\"odinger (DNLS) lattice. When exciting initially multiple sites in phase, we find that the solutions reflect the instability of their DNLS multi-soliton counterparts, while for configurations with multiple excited sites in alternating phases, the Floquet states are spectrally stable, again in analogy to their DNLS counterparts.