Bloch oscillation in a Floquet engineering quadratic potential system

TL;DR

This paper explores how periodic quadratic potentials induce Bloch oscillations in a driven one-dimensional lattice, revealing critical frequencies that produce stable, regular quasi-energy spectra and persistent coherent dynamics.

Contribution

It introduces a Floquet-based analysis of quadratic potential driving in both Hermitian and non-Hermitian lattices, identifying conditions for stable quasi-energy ladders and oscillations.

Findings

Critical frequencies induce equidistant quasi-energy ladders

Periodic revivals and Bloch oscillations are observed

Coherent oscillations persist in non-Hermitian regimes

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 $\omega$. We identify critical frequencies $\omega_c$ 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.