Bloch oscillation in a Floquet engineering quadratic potential system

• URL: http://arxiv.org/abs/2512.11675v1
• Date: Fri, 12 Dec 2025 15:54:01 GMT
• Title: Bloch oscillation in a Floquet engineering quadratic potential system
• Authors: J. Cao, H. Shen, R. Wang, X. Z. Zhang,
• Abstract summary: We investigate a one-dimensional tight-binding lattice driven by a spatially quadratic and time-periodic potential.<n>Time-dependent Hamiltonian is mapped onto an effective static Floquet Hamiltonian.<n> Numerical simulations confirm that coherent oscillations persist even in the non-Hermitian regime.
• Score: 0.22407858139580925
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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