Tracking the precession of single nuclear spins by weak measurements

Abstract

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 ...

Construction and operation of a tabletop system for nanoscale magnetometry with single nitrogen-vacancy centers in diamond

“…Second, in XY16-16, we observe that the spectral overlap between D and E causes the signals to become weaker, due to Eq. (25). The same mechanism is also responsible for feeble oscillations observed in Fig.…”

Atomic-scale imaging of a 27-nuclear-spin cluster using a quantum sensor

“…Our results demonstrate a key capability towards magnetic imaging of individual molecules and other complex spin systems [9][10][11][12][13].The nitrogen-vacancy (NV) centre in diamond has emerged as a powerful quantum sensor [2-13, 22, 23]. The NV electron spin provides long coherence times [5, 6,20] and high-contrast optical readout [5,24,25], enabling high sensitivity over a large range of temperatures [5, 6,20,25,26]. Pioneering experiments with near-surface NV centers have demonstrated spectroscopy of small ensembles of nuclear spins in nano-scale volumes [2, 3,[5][6][7][8], and electron-spin labelled proteins [4].…”

Structural Analysis of Nuclear Spin Clusters via 2D Nanoscale Nuclear Magnetic Resonance Spectroscopy

“…The 2D nanoscale NMR spectroscopy reported here, together with previous work on nanoscale NMR, can yield valuable structural information as opposed to bulk NMR, where the couplings typically hamper structure analysis. The spectral resolution can be improved by, for example, the Qdyne technique and weak measurement readout . The sensitivity can be improved by more efficient readout method and speed‐up algorithm .…”