Nonsmooth Bloch Oscillations in Non-Hermitian Systems

Abstract

Bloch oscillations (BOs) represent a paradigmatic manifestation of force-driven band dynamics in lattices, conventionally characterized by continuous quasimomentum evolution and smooth periodic trajectories. Here we show that non-Hermiticity qualitatively changes this paradigm, introducing nonsmooth BOs characterized by cusp-like real-space trajectories and abrupt momentum jumps. Reversing the force switches the dynamics between smooth and nonsmooth BOs, enabling strongly nonreciprocal dynamics. We derive a universal relation for the critical force that governs the nonsmooth-to-smooth dynamical transition in general one-dimensional lattices, which is induced by a pitchfork bifurcation in momentum space. Our work establishes a unified framework for non-Hermitian BOs and uncovers a fundamental bifurcation mechanism that can generate nonsmooth wave transport in entirely linear systems.