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.

Automated summary

This study investigates the emergence of resonances in periodically driven quantum systems. The authors find that fractional and integer resonances appear when the hopping frequency changes periodically as a fraction or an integer of the on-site interaction. It is shown that there is a fundamental difference between these resonances when the system reaches a Floquet prethermal state, with second-order processes dominating in the case of fractional resonances and first-order processes dominating in the case of integer resonances. The study provides insights into the nonequilibrium quantum many-body system, and highlights the coexistence of Floquet prethermalization and localization, which have potential applications in quantum technologies and quantum information processing.