Enhanced spectral resolution by finite duration pulses using Floquet analysis

Nanoscale nuclear magnetic resonance (NMR) can be achieved with paramagnetic defects such as nitrogen vacancy (NV) centres under the control of periodic dynamical decoupling (DD) pulse sequences. While the application of DD can significantly extend the coherence time of the electron spin in the defect and amplify weak signals, spurious resonances occur due to the finite duration of DD pulses and lead to false identification of NMR signals. In this work we use Floquet theory to obtain an analytic expression for emph{all} experimental signals generated by periodic DD even at high duty cycles. Furthermore it is shown that, counterintuitively, spurious resonances can provide with improved spectral resolution.