Fractional resonances and prethermal states in Floquet systems

TL;DR

This paper explores fractional and integer resonances in periodically-driven quantum many-body systems, revealing how fractional resonances lead to less entanglement and localization, with implications for quantum memory development.

Contribution

It demonstrates the emergence of fractional resonances in Floquet systems and analyzes their effects on many-body dynamics using the Magnus expansion and entropy measures.

Findings

Fractional resonances dominate second-order processes leading to localized states.

Integer resonances are dominated by first-order processes with higher entanglement.

Coexistence of Floquet prethermalization and localization observed in the system.

Abstract

In periodically-driven quantum systems, resonances can induce exotic nonequilibrium behavior and new phases of matter without static analog. We report on the emergence of fractional and integer resonances in a broad class of many-body Hamiltonians with a modulated hopping with a frequency that is either a fraction or an integer of the on-site interaction. We contend that there is a fundamental difference between these resonances when interactions bring the system to a Floquet prethermal state. Second-order processes dominate the dynamics in the fractional resonance case, leading to less entanglement and more localized quantum states than in the integer resonance case dominated by first-order processes. We demonstrate the dominating emergence of fractional resonances using the Magnus expansion of the effective Hamiltonian and quantify their effects on the many-body dynamics via quantum states' von Neumann entropy and Loschmidt echo. Our findings reveal novel features of the nonequilibrium quantum many-body system, such as the coexistence of Floquet prethermalization and localization, that may allow to development of quantum memories for quantum technologies and quantum information processing.