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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi>ω</mml:mi> </mml:mrow> </mml:mrow> </mml:math> . 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. Analytical 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , respectively.