Decoherence of NV Spin Ensembles in a Paramagnetic Defect Bath in Diamond

Nitrogen-vacancy (NV) centers in diamond have been developed into essential hardware units to develop a wide range of solid-state quantum technologies. For such applications, the long coherence time of NV centers is crucial. Numerous previous studies identified the main source of the NV’s decoherence being the magnetic noise produced by the ¹³C nuclear spin bath and electron spin baths due to paramagnetic defects in a diamond. While the ¹³C-induced decoherence has been well understood, the understanding of the electron-spin-driven decoherence is still incomplete. In this study, we aim at a systematic investigation on the decoherence of NV ensembles induced by paramagnetic defects by combining experiment and first-principles theory based on cluster correlation expansion theory (CCE) and density functional theory (DFT). For the paramangetic defects, we consider nitrogen (P1 centers), hydrogen, vacancies, and their complexes. For the P1 bath, we investigate the quantum nature of the bath imprinted on the NV decoherence under dynamical decoupling pulse sequences. We compute the coherence time (T₂) as a function of the number of CPMG pulses and we show that our quantum mechanical calculations yield the scaling exponent of the T₂ time to be in much better agreement with previous experimental results than the result predicted by a widely used semi-classical theory. We then explore the effect of paramagnetic defects that could co-exist in the P1 bath on the NV decoherence as a function of magnetic field and as a function of the P1 concentration. We categorize dominant paramagnetic defects in diamond into two different groups: nitrogen-related defects such as NV^-, NV⁰, NVH^-, and N²⁺, and vacancy/hydrogen-related defects such as VH⁰, VH^-, V⁰, V^-, and V⁺. For the nitrogen-related defects, we compute the NV coherence time by considering different proportion of the defects, while fixing the total amount of nitrogen in diamond. For vacancy/hydrogen defects, we investigate the change of T₂ induced by addition of the extra paramagnetic defects to the P1 bath of a given concentration. Our study provides an in-depth understanding of the effect of electronic spin defects having complex internal structures on the NV decoherence. This information would be essential for guiding experiments and optimizing the performance of diamond-based quantum sensing devices.