Witnessing localization of a quantum state via quantum speed limits in a driven avoided-level crossing system

In this work, we investigate the witnessing of the localization of quantum states through quantum speed limits (QSLs) in a two-level driven avoided-level crossing system. As the characteristic natures of the localized quantum states, the QSL presents the periodic oscillations and coherence. The coherence partition of QSL is much bigger than the population partition of QSL. Our study gives us the possibilities to manipulate dynamics of quantum states locally by employing the coherent destruction of tunneling, which is significant in quantum information process. In addition, we analyze the effects of the rotating-wave approximation and the generalized Van Vleck approach on QSL and show that they wipe out the quantum coherence.