Scanning probe microscopy is one of the most versatile windows into the nanoworld, providing imaging access to a variety of sample properties, depending on the probe employed.Tunneling probes map electronic properties of samples 1 , magnetic and photonic probes image their magnetic and dielectric structure 2,3 while sharp tips probe mechanical properties like surface topography, friction or stiffness 4 . Most of these observables, however, are accessible only under limited circumstances. For instance, electronic properties are measurable only on conducting samples while atomic-resolution force microscopy requires careful preparation of samples in ultrahigh vacuum 5,6 or liquid environments 7 .Here we demonstrate a scanning probe imaging method that extends the range of accessible quantities to label-free imaging of chemical species operating on arbitrary samples -including insulating materials -under ambient conditions. Moreover, it provides three-dimensional depth information, thus revealing subsurface features. We achieve these results by recording nuclear magnetic resonance signals from a sample surface with a recently introduced scanning probe, a single nitrogen-vacancy center in diamond. We demonstrate NMR imaging with 10 nm resolution and achieve chemically specific contrast by separating fluorine from hydrogen rich regions.Our result opens the door to scanning probe imaging of the chemical composition and atomic structure of arbitrary samples. A method with these abilities will find widespread application in material science even on biological specimens down to the level of single macromolecules.The development of a scanning probe sensor able to image nuclear spins has been a long and outstanding goal of nanoscience, proposed shortly after the invention of scanning probe microscopy itself 8 . To date, this goal is most closely met by magnetic resonance force microscopy (MRFM), an extension of atomic-force-microscopy with sensitivity to spins, which has successfully imaged nanoscale distributions of nuclear spins in three dimensions 9 .However, its operation is experimentally challenging, requiring low (sub-Kelvin) temperature and long (weeks/image) acquisition times, which has so far precluded its adoption as a routine technique. To surmount these problems, single electron spins with optical readout capability have been proposed as an alternative local probe for spin distributions 10 . This complementary approach has become a realistic prospect since recent research has established the nitrogenvacancy center, a color defect in diamond 11 , as a candidate system for this scheme 12,13 . This center serves as an atomic-sized magnetic field sensor, which has proven sufficiently sensitive to detect the field of single nuclear spins in its diamond lattice environment [14][15][16] as well as ensembles of 10-10 4 spins in a nanometer-sized sample volume on the diamond surface [17][18][19] .Here we employ a single NV center as a scanning probe to image distributions of nuclear spins in an external sample. All our ...
We present a novel spectroscopy protocol based on optimal control of a single quantum system. It enables measurements with quantum-limited sensitivity ( √ denoting the system's coherence time) but has an orders of magnitude larger dynamic range than pulsed spectroscopy methods previously employed for this task. We employ this protocol to image nanoscale magnetic fields with a single scanning NV center in diamond. Here, our scheme enables quantitative imaging of a strongly inhomogeneous field in a single scan without closed-loop control, which has previously been necessary to achieve this goal.Optimal control of quantum systems is an experimental technique that has evolved over the two past decades [1-3] as a generalization of related techniques like composite pulses [4] or adiabatic control [5]. It implements unitary operations ("quantum gates") of very high fidelity by irradiating a quantum system with numerically optimized excitation pulses. Amplitude and phase of this pulse are an arbitrary function of time, which is tailored such as to result in a specific unitary operation.Numerical optimization can generate pulses that achieve near-perfect operation (i.e. high fidelity) over a wide range of experimental parameters, such as excitation power or detuning, rather than a single specific set. This is in contrast to simple (e.g. rectangular) pulses and arises from the fact that optimization has access to the much larger space of arbitrary amplitude and phase profiles. Thanks to these additional degrees of freedom, the resulting pulse can satisfy a larger number of constraints. In practice, this has been used to generate "robust" pulses which are immune against fluctuations of the excitation power, or pulses that implement a specific operation within a large bandwidth of different system frequencies [3], as they may arise e.g. by inhomogeneous broadening.Here we show that optimal control can be used to achieve an opposite goal, a pulse that is maximally sensitive to fluctuations of one experimental parameter (in our case the static magnetic field) while it preserves robustness against fluctuations of all other parameters and, in particular, a large operating bandwidth. With these properties, such a pulse enables sensitive spectroscopy of a system even in the presence of large unknown frequency offsets. The concept is illustrated in more detail in Fig. 1(a-b). Sensitive spectroscopy classically relies on sharp selective excitation ( Fig. 1(a)), realized for instance by a long low-power excitation pulse (Rabi spectroscopy) or a suitable pulse sequence (Ramsey spectroscopy). We extend these schemes by designing an optimal control pulse which generates a grating of equally sharp excitation lines, evenly spaced over a large bandwidth (Fig. 1(b)). With this protocol, small changes of the system's resonance frequency can be tracked without tuning the excitation pulse to the system's frequency.
Supporting Information. Detailed description of the experimental setup and the data acquisition. Overview on sample and T2 dephasing fitting function. Dependence of the transfer function on the NV axis orientation. SQUID susceptometry measurements. Study of the fit parameters. Measurements of the collapses and revivals of the 13 C nuclei at different fields.Significance of simultaneous acquisition of T1 and T2 for the fit.
We introduce a simple and effective model of a commercial magnetic thin-film sensor for magnetic force microscopy (MFM), and we test the model employing buried magnetic dipoles. The model can be solved analytically in the half-space in front of the sensor tip, leading to a simple 1/R dependence of the magnetic stray field projected to the symmetry axis. The model resolves the earlier issue as to why the magnetic sensors cannot be described reasonably by a restricted multipole expansion as in the point pole approximation: the point pole model must be extended to incorporate a 'lower-order' pole, which we term 'pseudo-pole'. The near-field dependence (∝ R −1 ) turns into the well-known and frequently used dipole behavior (∝ R −3 ) if the separation, R, exceeds the height of the sensor. Using magnetic nanoparticles (average diameter 18 nm) embedded in a SiO cover as dipolar point probes, we show that the force gradient-distance curves and magnetic images fit almost perfectly to the proposed model. The easy axis of magnetization of single nanoparticles is successfully deduced from these magnetic images. Our model paves the way for quantitative MFM, at least if the sensor and the sample are independent.
We use non-close packed colloidal lithography to prepare hexagonal magnetic antidot arrays with varying diameters at a period of 205 nm. Smaller antidots are attractive for applications as spin waveguides in magnonics. Larger antidots form a magnetically frustrated system, i.e. Kagome spin-ice, as we prove by magnetic force microscopy. The simple but effective approach successfully extends the limits of top-down lithography previously used to study spin-ice configurations and emergent magnetic monopoles towards smaller structures.
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