Non-Linear Interference Challenging Topological Protection of Chiral Edge States

Abstract: We report on a non-linear scattering effect that challenges the notion of topological protection for wave packets propagating in chiral edge modes. Specifically, in a Floquet topological system close to resonant driving and with a non-linear potential, we demonstrate how a wave packet propagating in a chiral edge mode may be irreversibly deflected by scattering off a localized wave-packet, or pass the collision region virtually unaffected in an approximately linear fashion. An experimentally accessible knob to tune between those two scenarios is provided by the relative phase between the involved wave-packets. This genuinely non-linear interference phenomenon is in stark contrast to linear scattering off a static impurity, which cannot destroy a topological edge state. Besides corroborating our findings with numerically exact simulations, we propose two physical platforms where our predictions may be verified with state of the art experimental techniques: First, a coupled waveguide setting where non-linearity has been engineered via an intensity-dependent optical index. Second, a Bose-Einstein condensate of cold atoms in an optical Honeycomb lattice governed by a non-linear Gross-Pitaevskii equation that effectively accounts for many-body interactions.