Bloch oscillation in a Floquet engineering quadratic potential system

We investigate the quantum dynamics of a one-dimensional tight-binding lattice driven by a spatially quadratic and time-periodic potential. Both Hermitian $J₁ = J₂$ and non-Hermitian $J₁ neq J₂$ 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 and eigenstate localization as function of the driving frequency ω. We identify critical frequencies ω_c at which nearly equidistant quasi-energy ladders emerge, characterized by a pronounced minimum in the normalized variance of level spacings. This spectral regularity, which coincides with a peak in the mean inverse participation ratio textrm{MIPR}, 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.