Three-period evolution in a photonic Floquet extended Su-Schrieffer-Heeger waveguide array

TL;DR

This paper presents a photonic waveguide array model exhibiting three-period evolution due to Floquet engineering, revealing anomalous edge states with potential applications in quantum computation.

Contribution

It introduces a Floquet extended SSH model with long-range couplings, demonstrating three-period dynamics and anomalous edge states through numerical simulation and optical parameter tuning.

Findings

Identification of anomalous edge states with quasienergies ±π/3T and ±2π/3T

Successful mapping of the model onto a photonic waveguide array

Observation of unique three-period evolution behavior

Abstract

Periodic driving can induce the emergence of topological pi modes, and their superposition with zero modes leads to two-period dynamics. Introducing long-range couplings enables the realization of larger topological winding numbers, which correspond to multiple pairs of degenerate edge states under open boundary conditions. In this work, we construct a Floquet extended Su-Schrieffer-Heeger (SSH) model by introducing a two-step periodic driving and next-nearest-neighbor coupling into the static SSH chain simultaneously. Remarkably, we identify anomalous edge states with quasienergies -+pi/3T and -+2pi/3T. In order to reveal the dynamical features of these anomalous edge states, we elaborately adjust the optical parameters and ultimately achieve a successful mapping of the model onto a photonic waveguide array. Subsequently, through numerical simulation of the wave equation, we observe the unique behavior of three-period evolution. Our work may serve as a reference for realizing period-multiplied dynamics, and the anomalous edge states discussed here might also find applications in quantum computation.