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 microhertz over a megahertz bandwidth. The continuous sampling further guarantees an enhanced sensitivity, reaching a signal-to-noise ratio in excess of 10 for a 170-nanotesla test signal measured during a 1-hour interval. Our technique has applications in magnetic resonance spectroscopy, quantum simulation, and sensitive signal detection.

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 ...

Detecting and controlling nuclear spin nano-ensembles is crucial for the further development of nuclear magnetic resonance (NMR) spectroscopy and for the emerging solid state quantum technology.Here we present the fabrication of a ≈ 1 nanometre thick diamond layer consisting of 13 C nuclear spins doped with Nitrogen-Vacancy centres (NV) embedded in a spin-free 12 C crystal matrix. A single NV in the vicinity of the layer is used for polarization of the 13 C spins and the readout of their magnetization. We demonstrate a method for coherent control of few tens of nuclear spins by using radio frequency pulses and show the basic coherent control experiments -Rabi oscillations, Ramsey spectroscopy and Hahn echo, though any NMR pulse sequence can be implemented. The results shown present a first steps towards the realization of a nuclear spin based quantum simulator. *

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 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.

We create low-entropy states of neutral atoms by utilizing a conceptually new optical-lattice technique that relies on a high-precision, high-bandwidth synthesis of light polarization. Polarization-synthesized optical lattices provide two fully controllable optical lattice potentials, each of them confining only atoms in either one of the two long-lived hyperfine states. By employing one lattice as the storage register and the other one as the shift register, we provide a proof of concept using four atoms that selected regions of the periodic potential can be filled with one particle per site. We expect that our results can be scaled up to thousands of atoms by employing an atom-sorting algorithm with logarithmic complexity, which is enabled by polarization-synthesized optical lattices. Vibrational entropy is subsequently removed by sideband cooling methods. Our results pave the way for a bottom-up approach to creating ultralow-entropy states of a many-body system.