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. 2019 May 6;9:6938. doi: 10.1038/s41598-019-43404-2

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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(a) Illustration of the Qdyne signal and the detected statistical magnetization by the NV center. The diffusion of nuclear spins in or out of the NV detection range leads to rapid fluctuations of the detected phase, introducing a short signal coherence time-scale, $τ_{D}$ , on the order of the interaction correlation time. (b) The adoption of M_z Qdyne enables the detection of the FID signal from the nuclear z magnetization (thermal or hyperpolarized), regardless of the molecular diffusion. (c) An atomistic simulation of the time-dependent magnetic field induced by the diffusing nuclear spins on a 6.2 nm deep NV, where the statistical polarization is still clearly stronger than the hyperpolarized $M_{z} = 0.1 %$ polarization. However, M_z Qdyne can be averaged over many runs N_m, significantly reducing the statistical polarization signal by 1/ $\sqrt{N_{m}}$ while the M_z signal remains unchanged (due to the same initial phase at every run). The bottom figure shows the averaged signal for nuclear $T_{2} = 5 m s$ with $N_{m} = 1500$ , where only the smaller M_z polarization (oscillates between ±0.05) remains visible.