Floquet analysis of coherence in periodically driven diamond NV ensemble systems

High-density nitrogen-vacancy (NV) ensembles are promising platforms for solid-state quantum sensing, but their performance is limited by dipolar interactions and inhomogeneous dephasing. Periodic decoupling sequences such as Waugh-Huber-Haeberlen (WAHUHA) can extend the observed stroboscopic decay time. However, it remains unclear that a longer effective dephasing time yield improved magnetic-field sensitivity. Here, we show that WAHUHA control increases the effective inhomogeneous dephasing time of a dense NV ensemble from $T_2^\ast$ of 0.9 ${\mu}$s to $T_{2,eff}^\ast$ of 31 ${\mu}$s, while producing little improvement in dc magnetic-field sensitivity. Using detuning-resolved stroboscopic spectroscopy and finite-pulse Floquet analysis, we show that the long-lived signal arises from phase wrapping and quasi-energy branch folding of the one-cycle unitary. These effects reshape the stroboscopic spectrum and suppress the detuning-to-phase transduction slope, $d\Phi/d\Delta$, which governs the dc magnetic-field response. Our results demonstrate that, under periodic driving, an extended effective dephasing time does not necessarily translate into enhanced dc sensitivity and establish finite-pulse Floquet analysis as a practical framework for evaluating coherence in spin ensembles.