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arXiv · 2512.11675

Wave-packet revival in a Floquet engineering quadratic potential system

J. Cao·H. Shen·R. Wang·X. Z. Zhang
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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 ($J_1 \neq J_2$) 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 $\omega$. By applying a gauge transformation, we find that critical frequencies $\omega_c$ emerge, at which nearly equidistant quasi-energy ladders appear, as revealed by a pronounced minimum in the normalized variance $\Delta(\omega)$ 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.

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J. Cao, H. Shen, R. Wang, X. Z. Zhang. 2025-12-12. Wave-packet revival in a Floquet engineering quadratic potential system. https://arxiv.org/abs/2512.11675

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