We report an approach that extends the applicability of ultrasensitive force-gradient detection of magnetic resonance to samples with spin-lattice relaxation times (T 1 ) as short as a single cantilever period. To demonstrate the generality of the approach, which relies on detecting either cantilever frequency or phase, we used it to detect electron spin resonance from a T 1 = 1 ms nitroxide spin probe in a thin film at 4.2 K and 0.6 T. By using a custom-fabricated cantilever with a 4 μm-diameter nickel tip, we achieve a magnetic resonance sensitivity of 400 Bohr magnetons in a 1 Hz bandwidth. A theory is presented that quantitatively predicts both the lineshape and the magnitude of the observed cantilever frequency shift as a function of field and cantilever-sample separation. Good agreement was found between nitroxide T 1 's measured mechanically and inductively, indicating that the cantilever magnet is not an appreciable source of spin-lattice relaxation here. We suggest that the new approach has a number of advantages that make it well suited to push magnetic resonance detection and imaging of nitroxide spin labels in an individual macromolecule to single-spin sensitivity.MRFM | ESR | TEMPAMINE | mechanically detected magnetic resonance | molecular structure imaging A generally applicable approach for determining the tertiary structure of an individual macromolecule in vitro at angstrom or subangstrom resolution would create exciting opportunities for answering many longstanding questions in molecular biology. For macromolecules too large to characterize by NMR or X-ray diffraction, the tertiary structure of proteins (1-3), nucleic acids (4, 5), and biomolecular assemblies (6, 7) can be explored by using inductively-detected electron spin resonance (ESR) to measure distances between pairs of attached spin labels (2-5, 7, 8). These studies, however, require bulk quantities of sample (9) and demand multiple experiments with spin labels attached to different locations in the target macromolecule. Mechanical detection and imaging of single-electron spins has been demonstrated, in E centers in gamma-irradiated quartz (10), and it is natural to explore applying magnetic resonance force microscopy (MRFM) (11-15) to map the locations of individual spin labels attached to a single biomacromolecule.The ultimate limit of imaging resolution in MRFM is set by the intrinsic linewidth of the resonance and the applied magnetic field gradient. For a 0.1 mT homogeneous linewidth, typical of the organic radical studied here, a gradient of 4 × 10 6 T/m allows selective excitation of individual spin labels only 0.025 nm apart. A magnetic field gradient this large has recently been demonstrated in an MRFM experiment by using ferromagnetic pillars fabricated by electron-beam lithography (15). The force sensitivity required to detect single electrons in this gradient is 40 aN, above the minimum detectable force (in 1 Hz bandwidth) of 5 − 10 aN reported for a high-compliance cantilever operated with its metalized leading edge above ...

Effects of select electron mediators [9,10-anthraquinone-2,6-disulfonic acid disodium salt (AQDS), safranine O, resazurin, methylene blue, and humic acids] on metabolic end-products and current production from cellulose digestion by Clostridium cellulolyticum in microbial fuel cells (MFCs) were studied using capillary electrophoresis and traditional electrochemical techniques. Addition of the mediator resazurin greatly enhanced current production but did not appear to alter the examined fermentation end-products compared to MFCs with no mediator. Assays for lactate, acetate, and ethanol indicate that the presence of safranine O, methylene blue, and humic acids alters metabolite production in the MFC: safranine O decreased the examined metabolites, methylene blue increased lactate formation, and humic acids increased the examined metabolites. Mediator standard redox potentials (E (0)) reported in the literature do not coincide with redox potentials in MFCs due presumably to the electrolytic complexity of media that supports bacterial survival and growth. Current production in MFCs: (1) can be effected by the mediator redox potential while in the media, which may be significantly shifted from E (0), and (2) depended on the ability of the mediator to access the bacterial electron source, which may be cytoplasmic. In addition, some electron mediators had significant effects on metabolic end-products and therefore the metabolism of the organism itself.

We have batch-fabricated cantilevers with ~100 nm diameter nickel nanorod tips and force sensitivities of a few attonewtons at 4.2 kelvin. The magnetic nanorods were engineered to overhang the leading edge of the cantilever and, consequently, the cantilevers experience what we believe is the lowest surface noise ever achieved in a scanned probe experiment. Cantilever magnetometry indicated that the tips were well magnetized, with a ≤ 20 nm dead layer; the composition of the dead layer was studied by electron microscopy and electron energy loss spectroscopy. In what we believe is the first demonstration of scanned probe detection of electron-spin resonance from a batch fabricated tip, the cantilevers were used to observe electron-spin resonance from nitroxide spin labels in a film via force-gradient-induced shifts in cantilever resonance frequency. The magnetic field dependence of the magnetic resonance signal suggests a non-uniform tip magnetization at an applied field near 0.6 T.

Scanning probe microscopy is often extended beyond simple topographic imaging to study electrical forces and sample properties, with the most widely used experiment being frequency-modulated Kelvin probe force microscopy. The equations commonly used to interpret this frequency-modulated experiment, however, rely on two hidden assumptions. The first assumption is that the tip charge oscillates in phase with the cantilever motion to keep the tip voltage constant. The second assumption is that any changes in the tip-sample interaction happen slowly. Starting from an electro-mechanical model of the cantilever-sample interaction, we use Lagrangian mechanics to derive coupled equations of motion for the cantilever position and charge. We solve these equations analytically using perturbation theory, and, for verification, numerically. This general approach rigorously describes scanned probe experiments even in the case when the usual assumptions of fast tip charging and slowly changing samples properties are violated. We develop a Magnus-expansion approximation to illustrate how abrupt changes in the tip-sample interaction cause abrupt changes in the cantilever amplitude and phase. We show that feedback-free time-resolved electric force microscopy cannot uniquely determine sub-cycle photocapacitance dynamics. We then use first-order perturbation theory to relate cantilever frequency shift and dissipation to the sample impedance even when the tip charge oscillates out of phase with the cantilever motion. Analogous to the treatment of impedance spectroscopy in electrochemistry, we apply this approximation to determine the cantilever frequency shift and dissipation for an arbitrary sample impedance in both local dielectric spectroscopy and broadband local dielectric spectroscopy experiments. The general approaches we develop provide a path forward for rigorously modeling the coupled motion of the cantilever position and charge in the wide range of electrical scanned probe microscopy experiments where the hidden assumptions of the conventional equations are violated or inapplicable. arXiv:1807.01219v2 [cond-mat.mes-hall]

This article presents practical numerical recipes for simulating high-temperature and nonequilibrium quantum spin systems that are continuously measured and controlled. The notion of a "spin system" is broadly conceived, in order to encompass macroscopic test masses as the limiting case of large-j spins. The simulation technique has three stages: first the deliberate introduction of noise into the simulation, then the conversion of that noise into an informatically equivalent continuous measurement and control process, and finally, projection of the trajectory onto a Kählerian state-space manifold having reduced dimensionality and possessing a Kähler potential of multilinear (i.e., product-sum) functional form. These state-spaces can be regarded as ruled algebraic varieties upon which a projective quantum model order reduction (QMOR) is performed. The Riemannian sectional curvature of ruled Kählerian varieties is analyzed, and proved to be non-positive upon all sections that contain a rule. It is further shown that the class of ruled Kählerian state-spaces includes the Slater determinant wave-functions of quantum chemistry as a special case, and that these Slater determinant manifolds have a Fubini-Study metric that is Kähler-Einstein; hence they are solitons under Ricci flow. It is suggested that these negative sectional curvature properties geometrically account for the fidelity, efficiency, and robustness of projective trajectory simulation on ruled Kählerian state-spaces. Some implications of trajectory compression for geometric quantum mechanics are discussed. The resulting simulation formalism is used to construct a positive P -representation for the thermal density matrix and to derive a quantum limit for force noise and measurement noise in monitoring both macroscopic and microscopic test-masses; this quantum noise limit is shown to be consistent with wellestablished quantum noise limits for linear amplifiers and for monitoring linear dynamical systems. Single-spin detection by magnetic resonance force microscopy (MRFM) is then simulated, and the data statistics are shown to be those of a random telegraph signal with additive white noise, to all orders, in excellent agreement with experimental results. Then a larger-scale spin-dust model is simulated, having no spatial symmetry and no spatial ordering; the high-fidelity projection of numerically computed quantum trajectories onto low-dimensionality Kähler state-space manifolds is demonstrated. Finally, the high-fidelity reconstruction of quantum trajectories from sparse random projections is demonstrated, the onset of Donoho-Stodden breakdown at the Candès-Tao sparsity limit is observed, and methods for quantum state optimization by Dantzig selection are given.