Figure 1

Measurement scheme: (a)–(b) Precision spectroscopy of a two-level system (level spacing ${\omega }_0$). Conventional Rabi spectroscopy realizes a highly frequency-selective excitation by a weak, rectangular excitation pulse (a) Optimal control pulses [(b), top half] can be tailored to generate multiple such resonance dips (lower half), thereby increasing bandwidth while retaining sensitivity. (c) Measurement geometry: a magnetic specimen is scanned by an AFM over an NV center in bulk diamond, inducing a spatially varying Zeeman splitting (right half). A wire allows for microwave (MW)-spectroscopy of the NV-center, whose spin state can be read out optically from below. (d) and (e) Expected fluorescence images for excitation with pulses (a) and (b), respectively. Every resonance dip translates into a dark resonance ring in the fluorescence image, corresponding to a contour line of the specimen’s magnetic field.Reuse & Permissions

Figure 2

Pulse optimization: (a) Target magnetization for the optimization algorithm. (b),(c) Optimized pulse as it was calculated by the GRAPE algorithm. (b) waveform of the pulse, (c) quadrature envelopes $x$ (blue) and $y$ (green) and detuning $z$ (red) of the same pulse. (d) Experimental verification: spectroscopy of a single NV center using pulse (b),(c). The grating pattern is clearly visible.Reuse & Permissions

Figure 3

Resonance fringe (contour line) images and reconstructions of the magnetic field of the MFM tip. (a) Resonance fringes taken in contact mode using excitation pulse Figs. 2b, 2c. (b) Reconstruction of the underlying magnetic field distribution (projection $B_z$ along the $z$ axis of the NV center) from (a). (c) Resonance fringes when the tip is lifted by 600 nm. (d) Corresponding reconstruction image of (c). For both reconstructions a bias field of 7.8 mT was subtracted from the field values.Reuse & Permissions

Figure 4

(a),(b): Verification of quantum-limited sensitivity. (a) Spectroscopy of an NV center for different spacings $\Delta$ of the employed excitation grating. For decreasing spacing, contrast decays due to the center’s intrinsic linewidth $\Gamma =(1/T_2^{*})$ (b) Free-induction-decay measurement (blue line) and image contrast (red dots) from (a), as a function of an “effective pulse duration” $t_{\mathrm{eff}}=1/\Delta$. Green line: estimate of the photon-shot-noise-limited sensitivity as a function of $t_{\mathrm{eff}}$, mind the inverted right-hand side y axis. The optimal sensitivity of ${\eta }_{\min }=4.50\mu \mathrm{T}/\sqrt{\mathrm{Hz}}$ is marked by the dashed line. (c) Analysis of the magnetic field maps. The magnetic field of the MFM tip distinctly differs from a magnetic monopole (lower half) but is well described by a recently introduced pseudopole model ([25] upper half).Reuse & Permissions