Non-Hermitian Bloch Oscillations

We establish a general framework for non-Hermitian Bloch oscillations by investigating the wave-packet dynamics in one-dimensional non-Hermitian lattices driven by a dc force. The equations of motion for the momentum, center of mass, and group velocity of a wave packet are derived, where an anomalous group velocity due to the non-Hermiticity is identified. We show that nonreciprocal non-smooth Bloch oscillations, characterized by periodic jumps in group velocity, can emerge, and we analyze the role of finite-size effects. In non-Hermitian lattices with unidirectional hopping under open boundary conditions, we further uncover the emergence of periodic temporal Goos–Hänchen shifts together with an anomalous wave propagation along the direction of vanishing hopping.