Measuring reliable electron spin coherence times with dynamical decoupling sequences that use selective mw pulses

Dynamical decoupling methods like the Carr-Purcell-Meiboom-Gill (CPMG) or XY4- and XY8-based sequences play a key role in the measurement of reliable electron spin coherence times as they help to disentangle different sources of decoherence. Although these methods are mainly evaluated for their robustness and ability to mitigate pulse imperfections, to date little attention has been paid to the selectivity of the microwave pulses (mw), which is a factor that affects the determination of T₂ in two ways: first, unwanted stimulated echoes, which decay with T₁, overlap with desired refocused echoes, resulting in overestimated values of T₂. Second, under selective mw excitation, the amplitude of the different refocused echoes shows an additional time decay even in the absence of relaxation processes. Here, we investigate the characteristics of CPMG, XY4 and XY8-based sequences by performing numerical simulations for a two-level spin system. Using the Liouville space representation of the spin state, we introduce relaxation effects in the simulations. We show that our numerical calculations reproduce well all the features of the experimental echoes and allow for the accurate determination of T₂ times without the need to perform tedious phase-cycle protocols to eliminate unwanted signals.