Dynamics of non-Hermitian Floquet Wannier-Stark system

Abstract

We study the dynamics of the non-Hermitian Floquet Wannier-Stark system in the framework of the tight-binding approximation, where the hopping strength is a periodic function of time with Floquet frequency \(\omega \). It is shown that the energy level of the instantaneous Hamiltonian is still equally spaced and independent of time \(t\) and the Hermiticity of the hopping term. In the case of off resonance, the dynamics are still periodic, while the occupied energy levels spread out at the resonance, exhibiting \(t^z\) behavior. Analytic analysis and numerical simulation show that the level-spreading dynamics for real and complex hopping strengths exhibit distinct behaviors and are well described by the dynamical exponents \(z=1\) and \(z=1/2\), respectively.