Floquet analysis of coherence in periodically driven diamond nitrogen-vacancy ensemble systems

Abstract 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, but a longer fitted lifetime does not necessarily imply improved magnetic-field sensitivity. Here, we experimentally demonstrate this disconnect experimentally. WAHUHA increases the fitted stroboscopic decay time from $T_{2}^{*}$ T 2 ∗ of 0.9 μs to $T_{2,\\mathit{eff}}^{*}$ T 2 , eff ∗ of 31 μs, 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 quasienergy branch folding of the one-cycle unitary. These effects reshape the stroboscopic spectrum, and the experimentally relevant folded branches exhibit a reduced local detuning-to-phase transduction slope, $d\\Phi /d\\Delta $ d Φ / d Δ , 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.