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Nuclear magnetic resonance imaging (MRI) at the atomic scale offers exciting prospects for determining the structure and function of individual molecules and proteins. Quantum defects in diamond have recently emerged as a promising platform towards reaching this goal, and allowed for the detection and localization of single nuclear spins under ambient conditions. We present an efficient strategy for extending imaging to large nuclear spin clusters, fulfilling an important requirement towards a single-molecule MRI technique. Our method combines the concepts of weak quantum measurements, phase encoding and simulated annealing to detect three-dimensional positions from many nuclei in parallel. Detection is spatially selective, allowing us to probe nuclei at a chosen target radius while avoiding interference from strongly-coupled proximal nuclei. We demonstrate our strategy by imaging clusters containing more than 20 carbon-13 nuclear spins within a radius of 2.4 nm from single, near-surface nitrogen--vacancy centers at room temperature. The radius extrapolates to 7-8 nm for protons. Beside taking an important step in nanoscale MRI, our experiment also provides an efficient tool for the characterization of large nuclear spin registers in the context of quantum simulators and quantum network nodes., Comment: 10 pages, 5 figures. Includes Supplementary Material

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. Instr

We present a protocol for directly detecting time-dependent magnetic field waveforms with a quantum two-level system. Our method is based on a differential refocusing of segments of the waveform using spin echoes. The sequence can be repeated to increase the sensitivity to small signals. The frequency bandwidth is intrinsically limited by the duration of the refocusing pulses. We demonstrate detection of arbitrary waveforms with $\sim 20 {\rm ns}$ time resolution and $\sim 4\mu{\rm T}/\sqrt{\rm Hz}$ field sensitivity using the electronic spin of a single nitrogen-vacancy center in diamond., Comment: 5 pages, 4 figures

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 figures

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 submission

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.

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 Materials

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 material

We realize a two-qubit sensor designed for achieving high spectral resolution in quantum sensing experiments. Our sensor consists of an active "sensing qubit" and a long-lived "memory qubit", implemented by the electronic and the nitrogen-15 nuclear spins of a nitrogen-vacancy center in diamond, respectively. Using state storage times of up to 45 ms, we demonstrate spectroscopy of external ac signals with a line width of 19 Hz (~2.9 ppm) and of carbon-13 nuclear magnetic resonance (NMR) signals with a line width of 190 Hz (~ 74 ppm). This represents an up to 100-fold improvement in spectral resolution compared to measurements without nuclear memory., Comment: 4 pages with 5 figures. Supplemental material is included