Non-Hermitian Bloch Oscillations

Abstract: 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.