Quantum signatures of mixed classical phase space in Floquet systems

Identifying quantum chaos in Floquet systems with mixed classical phase spaces requires robust experimentally accessible signatures. We investigate the time-averaged quantum Fisher information (QFI) and the fidelity out-of-time-ordered correlator (FOTOC) of continuous periodically driven systems. We uncover two distinct power-law scalings of the time-averaged QFI with respect to system size: the standard quantum limit and the Heisenberg limit. These scalings correspond to initial states localized in the regular and chaotic regions of the classical phase space, respectively. Remarkably, we show that the time-averaged FOTOC can accurately identify the transition from mixed phase space to fully chaotic sea (at a critical driving strength Bx≈5.3) as verified by the maximum Lyapunov exponent. The results suggest that both time-averaged QFI and FOTOC can be used as excellent quantum signatures for probing mixed phase-space structures and our adopted protocol for measuring the FOTOC eliminates the need for time-reversal operations. This work establishes a practical framework for investigating quantum chaos in Floquet systems, bridging theoretical insights with experimental applications.