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 1 , generated by nuclei precessing around an applied magnetic field. While conventional NMR requires signals from 10 12 or more nuclei, recent advances in sensitive magnetometry 2,3 have dramatically lowered this number to a level where few or even individual nuclear spins can be detected [4][5][6][7][8] . 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 9-12 . Our experimental system consists of 13 C 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: measurementinduced decoherence 13 and frequency synchronization with the sampling clock 14,15 . 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 16-18 at atomic resolution.Measurement back-action, an important feature of quantum measurements 19,20 , can usually be neglected in NMR because the spin-detector coupling is extremely weak. One prominent exception is radiation damping 21 , where the collective coupling of the nuclear ensemble gives rise to a damping of the magnetic resonance by the electric detection circuit. As nuclear ensembles become smaller, eventually consisting of only few or even a single nuclear spin, the close coupling to the detector is expected to modify 22,23 or inhibit 24 the free evolution of the spin. Recent work on ensembles of cold atoms 25 and trapped ions 13 reported simultaneous tracking of spin angle and amplitude through the use of weak, quantumnon-demolition measurements, indicating an avenue for mitigating back-action. Here, we show that it is possible to track the precession of a single nuclear spin and to extract the two central pieces of information in NMR: the free precession frequency and the dephasing time.To probe the coherent precession of a single nuclear spin we implemented the measurement system depicted in Fig. 1a. Our system consists of a 13 C nucleus (spin I = 1/2) isolated in the nearly spin-free lattice of a diamond crystal. The nuclear spin undergoes a free precession around the Z axis with an angular velocity given by the Larmor frequency ω 0 = γ n B 0 , where B 0 is the local magnetic field and γ n the nuclear gyromagnetic ratio. To detect the nuclear precession, we periodically couple the nuclear spin to the electronic spin ...

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 θ between spins. In this Letter, we present a protocol to also retrieve the azimuth angle φ. 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 13 C 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.

Quantum sensing with shallow nitrogen-vacancy (NV) centers in diamond offer promise for chemical analysis. Preserving favorable NV spin and charge properties while enabling molecular surface functionalization remains a critical challenge.

Breast-conserving surgery (BCS) is a commonly utilized treatment for early stage breast cancers but has relatively high reexcision rates due to post-surgical identification of positive margins. A fast, specific, sensitive, easy-to-use tool for assessing margins intraoperatively could reduce the need for additional surgeries, and while many techniques have been explored, the clinical need is still unmet. We assess the potential of Magnetic Particle Imaging (MPI) for intraoperative margin assessment in BCS, using a passively or actively tumor-targeted iron oxide agent and two hardware devices: a hand-held Magnetic Particle detector for identifying residual tumor in the breast, and a small-bore MPI scanner for quickly imaging the tumor distribution in the excised specimen. Here, we present both hardware systems and demonstrate proof-of-concept detection and imaging of clinically relevant phantoms.