Quantum sensing with arbitrary frequency resolution

Quantum sensing takes advantage of well controlled quantum systems for performing measurements with high sensitivity and precision. We have implemented a concept for quantum sensing with arbitrary frequency resolution, independent of the qubit probe and limited only by the stability of an external synchronization clock. Our concept makes use of quantum lock-in detection to continuously probe a signal of interest. Using the electronic spin of a single nitrogen vacancy center in diamond, we demonstrate detection of oscillating magnetic fields with a frequency resolution of 70 uHz over a MHz bandwidth. The continuous sampling further guarantees an excellent sensitivity, reaching a signal-to-noise ratio in excess of 10,000:1 for a 170 nT test signal measured during a one-hour interval. Our technique has applications in magnetic resonance spectroscopy, quantum simulation, and sensitive signal detection.Comment: Manuscript resubmitted to Science. Includes Supplementary Material

Three-dimensional nuclear spin positioning using coherent radio-frequency control

Distance measurements via the dipolar interaction are fundamental to the application of nuclear magnetic resonance (NMR) to molecular structure determination, but they only provide information on the absolute distance $r$ and polar angle $\theta$ between spins. In this Letter, we present a protocol to also retrieve the azimuth angle $\phi$. Our method relies on measuring the nuclear precession phase after application of a control pulse with a calibrated external radio-frequency coil. We experimentally demonstrate three-dimensional positioning of individual carbon-13 nuclear spins in a diamond host crystal relative to the central electronic spin of a single nitrogen-vacancy center. The ability to pinpoint three-dimensional nuclear locations is central for realizing a nanoscale NMR technique that can image the structure of single molecules with atomic resolution.Comment: 5 pages, 4 figure

High-bandwidth microcoil for fast nuclear spin control

The active manipulation of nuclear spins with radio-frequency (RF) coils is at the heart of nuclear magnetic resonance (NMR) spectroscopy and spin-based quantum devices. Here, we present a microcoil transmitter system designed to generate strong RF pulses over a broad bandwidth, allowing for fast spin rotations on arbitrary nuclear species. Our design incorporates: (i) a planar multilayer geometry that generates a large field of 4.35 mT per unit current, (ii) a 50 Ohm transmission circuit with a broad excitation bandwidth of approximately 20 MHz, and (iii) an optimized thermal management for removal of Joule heating. Using individual 13C nuclear spins in the vicinity of a diamond nitrogen-vacancy (NV) center as a test system, we demonstrate Rabi frequencies exceeding 70 kHz and nuclear pi/2 rotations within 3.4 us. The extrapolated values for 1H spins are about 240 kHz and 1 us, respectively. Beyond enabling fast nuclear spin manipulations, our microcoil system is ideally suited for the incorporation of advanced pulse sequences into micro- and nanoscale NMR detectors operating at low (<1 T) magnetic field.Comment: 8 pages, 5 figures. Submitted to Rev. Sci. Inst

Elastometry of deflated capsules elastic moduli from shape and wrinkle analysis

Elastic capsules, prepared from droplets or bubbles attached to a capillary (as in a pendant drop tensiometer), can be deflated by suction through the capillary. We study this deflation and show that a combined analysis of the shape and wrinkling characteristics enables us to determine the elastic properties in situ. Shape contours are analyzed and fitted using shape equations derived from nonlinear membrane-shell theory to give the elastic modulus, Poisson ratio and stress distribution of the membrane. We include wrinkles, which generically form upon deflation, within the shape analysis. Measuring the wavelength of wrinkles and using the calculated stress distribution gives the bending stiffness of the membrane. We illustrate this method on two very different capsule materials: polymerized octadecyltrichlorosilane (OTS) capsules and hydrophobin (HFBII) coated bubbles. Our results are in agreement with the available rheological data. For hydrophobin coated bubbles the method reveals an interesting nonlinear behavior consistent with the hydrophobin molecules having\ud a rigid core surrounded by a softer shell

Evolutionary implications of a high selfing rate in the freshwater snail Lymnaea truncatula.

Self-compatible hermaphroditic organisms that mix self-fertilization and outcrossing are of great interest for investigating the evolution of mating systems. We investigate the evolution of selfing in Lymnaea truncatula, a self-compatible hermaphroditic freshwater snail. We first analyze the consequences of selfing in terms of genetic variability within and among populations and then investigate how these consequences along with the species ecology (harshness of the habitat and parasitism) might govern the evolution of selfing. Snails from 13 localities (classified as temporary or permanent depending on their water availability) were sampled in western Switzerland and genotyped for seven microsatellite loci. F(IS) (estimated on adults) and progeny array analyses (on hatchlings) provided similar selfing rate estimates of 80%. Populations presented a low polymorphism and were highly differentiated (F(ST) = 0.58). Although the reproductive assurance hypothesis would predict higher selfing rate in temporary populations, no difference in selfing level was observed between temporary and permanent populations. However, allelic richness and gene diversity declined in temporary habitats, presumably reflecting drift. Infection levels varied but were not simply related to either estimated population selfing rate or to differences in heterozygosity. These findings and the similar selfing rates estimated for hatchlings and adults suggest that within-population inbreeding depression is low in L. truncatula

High resolution quantum sensing with shaped control pulses

We investigate the application of amplitude-shaped control pulses for enhancing the time and frequency resolution of multipulse quantum sensing sequences. Using the electronic spin of a single nitrogen vacancy center in diamond and up to 10,000 coherent microwave pulses with a cosine square envelope, we demonstrate 0.6 ps timing resolution for the interpulse delay. This represents a refinement by over 3 orders of magnitude compared to the 2 ns hardware sampling. We apply the method for the detection of external AC magnetic fields and nuclear magnetic resonance signals of carbon-13 spins with high spectral resolution. Our method is simple to implement and especially useful for quantum applications that require fast phase gates, many control pulses, and high fidelity.Comment: 5 pages, 4 figures, plus supplemental materia

Tracking the precession of single nuclear spins by weak measurements

Nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for analyzing the structure and function of molecules, and for performing three-dimensional imaging of the spin density. At the heart of NMR spectrometers is the detection of electromagnetic radiation, in the form of a free induction decay (FID) signal, generated by nuclei precessing around an applied magnetic field. While conventional NMR requires signals from 1e12 or more nuclei, recent advances in sensitive magnetometry have dramatically lowered this number to a level where few or even individual nuclear spins can be detected. It is natural to ask whether continuous FID detection can still be applied at the single spin level, or whether quantum back-action modifies or even suppresses the NMR response. Here we report on tracking of single nuclear spin precession using periodic weak measurements. Our experimental system consists of carbon-13 nuclear spins in diamond that are weakly interacting with the electronic spin of a nearby nitrogen-vacancy center, acting as an optically readable meter qubit. We observe and minimize two important effects of quantum back-action: measurement-induced decoherence and frequency synchronization with the sampling clock. We use periodic weak measurements to demonstrate sensitive, high-resolution NMR spectroscopy of multiple nuclear spins with a priori unknown frequencies. Our method may provide the optimum route for performing single-molecule NMR at atomic resolution.Comment: 29 pages including methods and extended data figures; for supplementary material, see v1 of this submissio

Climate change mitigation in aging societies: Motivational and cognitive aspects

The success of mitigating climate change depends on actions taken within the upcoming four decades. In Western societies, this timeframe coincides with a demographic shift increasing the age of the median voter and decision maker. The willingness to contribute to climate change mitigation may decrease with age since the benefi ts may lie beyond the life span whereas the costs are immediate. In several experimental studies, we investigate cognitive limitations and motivational factors in relation to climate change mitigation. In a fi rst set of studies subjects are given the chance to invest up to 10€ into the reduction of CO2 via the EU ETS. Contrary to theoretical considerations, we fi nd evidence for a strong and positive effect of age. Furthermore we show that social cues can be used to in uence contributions. Moreover we demonstrate that independent of age most subjects are able to understand complex stock flow problems if the mode of presentation is adequate. System thinking ability is not firmly linked with a motivation to contribute to climate change mitigation. In a training study we show however that an increase of information about climate change can lead to a reduction of contributions

A special irreducible matrix representation of the real Clifford algebra C(3,1)

4x4 Dirac (gamma) matrices (irreducible matrix representations of the Clifford algebras C(3,1), C(1,3), C(4,0)) are an essential part of many calculations in quantum physics. Although the final physical results do not depend on the applied representation of the Dirac matrices (e.g. due to the invariance of traces of products of Dirac matrices), the appropriate choice of the representation used may facilitate the analysis. The present paper introduces a particularly symmetric real representation of 4x4 Dirac matrices (Majorana representation) which may prove useful in the future. As a byproduct, a compact formula for (transformed) Pauli matrices is found. The consideration is based on the role played by isoclinic 2-planes in the geometry of the real Clifford algebra C(3,0) which provide an invariant geometric frame for it. It can be generalized to larger Clifford algebras.Comment: 23 pages LaTeX, to appear in the J. Math. Phys. (v2: appendix B on Pauli matrices and references are added, minor other changes

Three-dimensional localization spectroscopy of individual nuclear spins with sub-Angstrom resolution

We report on precise localization spectroscopy experiments of individual 13C nuclear spins near a central electronic sensor spin in a diamond chip. By detecting the nuclear free precession signals in rapidly switchable external magnetic fields, we retrieve the three-dimensional spatial coordinates of the nuclear spins with sub-Angstrom resolution and for distances beyond 10 Angstroms. We further show that the Fermi contact contribution can be constrained by measuring the nuclear g-factor enhancement. The presented method will be useful for mapping the atomic-scale structure of single molecules, an ambitious yet important goal of nanoscale nuclear magnetic resonance spectroscopy