(a) Basic diamond-based magnetometry pulse sequence. (b) With the NV center at the reference frame origin, the grayscale indicates the relative contribution to field fluctuations from spins in a uniformly dense film. (c) In units of the relative radial coordinate , the upper set of curves shows a cross section of the graph in (b) (black curve) and the corresponding integral (white curve). The gray curve shows the effective spin noise “density” (see text). For comparison, the lower set shows the same curves but for the average field at the NV center. Note that the integral (dashed white curve) decays slowly to zero as a result of negative contributions from spins far from the center.
(Upper left insert) High-resolution SEM image of fixated E. Coli. Brighter (darker) regions correlate with high (low) spin density. (Main images) Simulated “raster scan” reconstructions of the corresponding two-dimensional (2D) spin lattice. The color code gauges the average NV center fluorescence as determined after observations during which the spin alignment changes randomly [see Eq. (10)]. The darker regions between and on the surface of the bacteria are artifacts resulting from artificial shadowing of the source SEM image. The tip-NV center distance and raster scan resolution is 30 nm (left) and 15 nm (right). The scale bar corresponds to 300 nm. Other parameters are as listed in the text.
(Insert) SEM image of the membrane of a red blood cell. Void spaces become apparent only after dehydration and fixation. (Main images) Simulated “raster scan” image. Unlike Fig. 2, the virtual 2D spin matrix is uniform (emulating the case of a “wet membrane”). This time the color scale of the source image was used to encode the local nuclear spin correlation time. In the example presented on the left, “mobile” regions (corresponding to dark regions in the source image) have a correlation time only 1.3 times shorter than the rest. The image on the right is based on identical conditions except that the correlation time difference was three times greater. The scale bar corresponds to 300 nm.
In this example the NV center repeatedly monitors a set of equivalent protons subject to a 6.5 Hz heteronuclear -coupling with a second (invisible) spin-1/2 species. Depending on the alignment of the latter, protons precess with one of two possible frequencies. (Top) Schematics of the pulse sequence; denotes the number of -pulses within the evolution interval . (Bottom) Reconstructed correlation (insert) and corresponding spectral density. Note the factor 2 in the observed splitting (13 Hz), a direct consequence of having assumed (quadratic response). In the simulation , , and . The nuclear correlation time is 100 ms and the number of single measurement pairs per point in the correlation curve is . The external magnetic field is 5 mT and pulses acting on nuclear spins are assumed to be broadband so as to invert proton spins as well as the -coupled species. Other conditions are as listed in the text.
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