Wave-packet revival in a Floquet engineering quadratic potential system

Abstract

We investigate the quantum dynamics of a one-dimensional tight-binding lattice driven by a spatially quadratic and time-periodic potential. Both Hermitian ($J_1=J_2$) and non-Hermitian ($J_1\ne J_2$) hopping regimes are analyzed. Within the framework of Floquet theory, the time-dependent Hamiltonian is mapped onto an effective static Floquet Hamiltonian, enabling a detailed study of the quasi-energy spectrum as function of the driving frequency $\ddot{I}‰$. By applying a gauge transformation, we find that critical frequencies $\ddot{I}{‰}_c$ emerge, at which nearly equidistant quasi-energy ladders appear, as revealed by a pronounced minimum in the normalized variance $\hat{I}”(\ddot{I}‰)$ of the level spacings. This spectral regularity leads to robust periodic revivals and Bloch-like oscillations in the time evolution. Numerical simulations confirm that such coherent oscillations persist even in the non-Hermitian regime, where the periodic driving stabilizes an almost real and uniformly spaced quasi-energy ladder.