  Characteristic dips appear in the coherence traces of a probe qubit when
dynamical decoupling (DD) is applied in synchrony with the precession of target
nuclear spins, forming the basis for nanoscale nuclear magnetic resonance
(NMR). The frequency of the microwave control pulses is chosen to match the
qubit transition but this can be detuned from resonance by experimental errors,
hyperfine coupling intrinsic to the qubit, or inhomogeneous broadening. The
detuning acts as an additional static field which is generally assumed to be
completely removed in Hahn echo and DD experiments. Here we demonstrate that
this is not the case in the presence of finite pulse-durations, where a
detuning can drastically alter the coherence response of the probe qubit, with
important implications for sensing applications. Using the electronic spin
associated with a nitrogen-vacancy centre in diamond as a test qubit system, we
analytically and experimentally study the qubit coherence response under CPMG
and XY8 dynamical decoupling control schemes in the presence of finite
pulse-durations and static detunings. Most striking is the splitting of the NMR
resonance under CPMG, whereas under XY8 the amplitude of the NMR signal is
modulated. Our work shows that the detuning error must not be neglected when
extracting data from quantum sensor coherence traces.
