Paper
Bloch oscillation in a Floquet engineering quadratic potential system
Authors
J. Cao, H. Shen, R. Wang, X. Z. Zhang
Abstract
We investigate the quantum dynamics of a one-dimensional tight-binding lattice driven by a spatially quadratic and time-periodic potential. Both Hermitian () and non-Hermitian () 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 . We identify critical frequencies 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.