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Achieving atomic resolution is the ultimate limit of magnetic resonance imaging (MRI), and attaining this capability offers enormous technological and scientific opportunities, from drug development to understanding the dynamics in interacting quantum systems. In this work, we present a new approach to nanoMRI utilizing nuclear magnetic resonance diffraction (NMRd) -- a method that extends NMR imaging to probe the structure of periodic spin systems. The realization of NMRd on the atomic scale would create a powerful new methodology for materials characterization utilizing the spectroscopic capabilities of NMR. We describe two experiments that realize NMRd measurement of $^{31}$P spins in an indium-phosphide (InP) nanowire with sub-\r{A}ngstrom precision. In the first experiment, we encode a nanometer-scale spatial modulation of the $z$-axis magnetization by periodically inverting the $^{31}$P spins, and detect the period and position of the modulation with a precision of $<0.8$ \r{A}. In the second experiment, we demonstrate an interferometric technique, utilizing NMRd, for detecting an \r{A}ngstrom-scale displacement of the InP sample with a precision of 0.07 \r{A}. The diffraction-based techniques developed in this work represent new measurement modalities in NMR for probing the structure and dynamics of spins on sub-\r{A}ngstrom length scales, and demonstrate the feasibility of crystallographic MRI measurements., Comment: Main text: 11 pages, 8 figures; supplemental material: 20 pages, 15 figures

Adiabatic operations are powerful tools for robust quantum control in numerous fields of physics, chemistry and quantum information science. The inherent robustness due to adiabaticity can, however, be impaired in applications requiring short evolution times. We present a single versatile gradient-based optimization protocol that combines adiabatic control with effective Hamiltonian engineering in order to design adiabatic operations tailored to the specific imperfections and resources of an experimental setup. The practicality of the protocol is demonstrated by engineering a fast, 2.3 Rabi cycle-long adiabatic inversion pulse for magnetic resonance with built-in robustness to Rabi field inhomogeneities and resonance offsets. The performance and robustness of the pulse is validated in a nanoscale force-detected magnetic resonance experiment on a solid-state sample, indicating an ensemble-averaged inversion accuracy of $\sim 99.997\%$. We further showcase the utility of our protocol by providing examples of adiabatic pulses robust to spin-spin interactions, parameter-selective operations and operations connecting arbitrary states, each motivated by experiments., Comment: Main text: 14 pages, 6 figures; supplemental material: 6 pages, 2 figures

In recent years, self-assembled semiconductor nanowires have been successfully used as ultra-sensitive cantilevers in a number of unique scanning probe microscopy (SPM) settings. We describe the fabrication of ultra-low dissipation patterned silicon nanowire (SiNW) arrays optimized for scanning probe applications. Our fabrication process produces, with high yield, ultra-high aspect ratio vertical SiNWs that exhibit exceptional force sensitivity. The highest sensitivity SiNWs have thermomechanical-noise limited force sensitivity of $9.7\pm0.4~\text{aN}/\sqrt{\text{Hz}}$ at room temperature and $500\pm20~\text{zN}/\sqrt{\text{Hz}}$ at 4 K. To facilitate their use in SPM, the SiNWs are patterned within $7~\mu\text{m}$ from the edge of the substrate, allowing convenient optical access for displacement detection., Comment: Main text: 16 pages, 3 figures and 2 tables. Supplements: 11 pages, 7 figures and 1 table

We present a new method for high-resolution nanoscale magnetic resonance imaging (nano-MRI) that combines the high spin sensitivity of nanowire-based magnetic resonance detection with high spectral resolution nuclear magnetic resonance (NMR) spectroscopy. By applying NMR pulses designed using optimal control theory, we demonstrate a factor of $500$ reduction of the proton spin resonance linewidth in a $(50\text{-nm})^{\text{3}}$ volume of polystyrene and image proton spins in one dimension with a spatial resolution below $2~\text{nm}$., Comment: Main text: 8 pages, 6 figures; supplementary information: 10 pages, 10 figures