Fractional resonances and prethermal states in Floquet systems

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.