Landau-Zener-Stückelberg-Majorana (LZSM) transitions occur between quantum states when parameters in the system's Hamiltonian are varied continuously and rapidly. In magnetic resonance, losses in adiabatic rapid passage can be understood using the physics of LZSM transitions. Most treatments of LZSM transitions ignore the T2 dephasing of coherences, however. Motivated by ongoing work in magnetic resonance force microscopy, we employ the Bloch equations, coordinate transformation, and the Magnus expansion to derive expressions for the final magnetization following a rapid field sweep at fixed irradiation intensity that include T2 losses. Our derivation introduces an inversion-function, Fourier transform method for numerically evaluating highly oscillatory integrals. Expressions for the final magnetization are given for low and high irradiation intensity, valid in the T2≪T1 limit. Analytical results are compared to numerical simulations and nuclear magnetic resonance experiments. Our relatively straightforward calculation reproduces semiquantitatively the well known LZSM result in the T2→0 limit.

Bose-Einstein condensate (BEC)-based atom interferometry exploits low temperatures and long coherence lengths to facilitate high-precision measurements. Progress in atom interferometry promises improvements in navigational devices like gyroscopes and accelerometers, as well as applications in fundamental physics such as accurate determination of physical constants. Previous work demonstrates that beam splitters and mirrors for coherent manipulation of dilute BEC momentum in atom interferometers can be implemented with sequences of non-resonant standing-wave light pulses. While previous work focuses on the optimization of the optical pulses' amplitude and duration to produce high-order momentum states with high fidelity, we explore how varying the shape of the optical pulses affects optimal beam-splitter performance, as well as the effect of pulse shape on the sensitivity of optimized parameters in achieving high fidelity in high-momentum states. In simulations of two-pulse beam splitters utilizing optimized square, triangle, and sinc-squared pulse shapes applied to dilute BECs, we, in some cases, reduce parameter sensitivity by an order of magnitude while maintaining fidelity.

Scanning probe microscopy is often extended beyond 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 experiment, however, rely on two hidden assumptions: (1) the tip charge oscillates in phase with the cantilever motion to keep the tip voltage constant, and (2) 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. 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 (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.

Measurement-Device-Independent Quantum Key Distribution (MDI-QKD) is a two-photon protocol devised to eliminate eavesdropping attacks that interrogate or control the detector in realized quantum key distribution systems. In MDI-QKD, the measurements are carried out by an untrusted third party, and the measurement results are announced openly. Knowledge or control of the measurement results gives the third party no information about the secret key. Error-free implementation of the MDI-QKD protocol requires the crypto-communicating parties, Alice and Bob, to independently prepare and transmit single photons that are physically indistinguishable, with the possible exception of their polarization states. In this paper, we apply the formalism of quantum optics and Monte Carlo simulations to quantify the impact of small errors in wavelength, bandwidth, polarization and timing between Alice’s photons and Bob’s photons on the MDI-QKD quantum bit error rate (QBER). Using published single-photon source characteristics from two-photon interference experiments as a test case, our simulations predict that the finite tolerances of these sources contribute (4.04± 20/ √ Nsifted)% to the QBER in an MDI-QKD implementation generating an Nsifted-bit sifted key.

Measurement-Device-Independent Quantum Key Distribution (MDI-QKD) is a two-photon protocol devised to eliminate eavesdropping attacks that interrogate or control the detector in realized quantum key distribution systems. In MDI-QKD, the measurements are carried out by an untrusted third party, and the measurement results are announced openly. Knowledge or control of the measurement results gives the third party no information about the secret key. Error-free implementation of the MDI-QKD protocol requires the crypto-communicating parties, Alice and Bob, to independently prepare and transmit single photons that are physically indistinguishable, with the possible exception of their polarization states. In this paper, we apply the formalism of quantum optics and Monte Carlo simulations to quantify the impact of small errors in wavelength, bandwidth, polarization and timing between Alice’s photons and Bob’s photons on the MDI-QKD quantum bit error rate (QBER). Using published single-photon source characteristics from two-photon interference experiments as a test case, our simulations predict that the finite tolerances of these sources contribute ( 4.04 ± 20 / N sifted ) % to the QBER in an MDI-QKD implementation generating an N sifted -bit sifted key.

We apply the formalism of quantum measurement theory to the idealized measurement of the position of a particle with an optical interferometer, finding that the backaction of counting entangled photons systematically collapses the particle’s wavefunction toward a narrow Gaussian wavepacket at the location xest determined by the measurement without appeal to environmental decoherence or other spontaneous collapse mechanism. Further, the variance in the particle’s position, as calculated from the post-measurement wavefunction, agrees precisely with shot-noise limited uncertainty of the measured xest. Both the identification of the absolute square of the particle’s initial wavefunction as the probability density for xest and the de Broglie hypothesis emerge as consequences of interpreting the intensity of the optical field as proportional to the probability of detecting a photon. Linear momentum information that is encoded in the particle’s initial wavefunction survives the measurement, and the pre-measurement expectation values are preserved in the ensemble average.

We have batch-fabricated cantilevers with ∼100 nm diameter nickel nanorod tips and force sensitivities of a few attonewtons at 4.2 K. 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 nonuniform tip magnetization at an applied field near 0.6 T.

We introduce and demonstrate a method of measuring small force gradients acting on a harmonic oscillator in which the force-gradient signal of interest is used to parametrically up-convert a forced oscillation below resonance into an amplitude signal at the oscillator's resonance frequency. The approach, which we demonstrate in a mechanically detected electron spin resonance experiment, allows the force-gradient signal to evade detector frequency noise by converting a slowly modulated frequency signal into an amplitude signal.

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 μ m -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.

This article presents numerical recipes for simulating high-temperature and non-equilibrium 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 equivalent continuous measurement and control process, and finally, projection of the trajectory onto a state-space manifold having reduced dimensionality and possessing a Kahler potential of multi-linear form. The resulting simulation formalism is used to construct a positive P-representation for the thermal density matrix. Single-spin detection by magnetic resonance force microscopy (MRFM) is simulated, and the data statistics are shown to be those of a random telegraph signal with additive white noise. Larger-scale spin-dust models are simulated, having no spatial symmetry and no spatial ordering; the high-fidelity projection of numerically computed quantum trajectories onto low-dimensionality Kahler state-space manifolds is demonstrated. The reconstruction of quantum trajectories from sparse random projections is demonstrated, the onset of Donoho-Stodden breakdown at the Candes-Tao sparsity limit is observed, a deterministic construction for sampling matrices is given, and methods for quantum state optimization by Dantzig selection are given.

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 show that single alkanethiol-passivated gold nanocrystals can be identified by core size in scanning tunneling microscopy (STM) experiments, through a comparison of the measured STM heights with a direct determination of the gold core sizes by mass spectrometry. We take advantage of the discrete size distribution to correlate the peaks in a histogram of nanocrystal heights with the distinct abundance peaks in a mass spectrum. The correlation establishes a mapping from STM height to core mass or mean core diameter. This is vitally important for the interpretation of size-dependent "single-molecule" tunneling spectra from nanocrystal compounds.