Brief Reviews on Atomic-scale Imaging of a 27-nuclear-spin Cluster Using a Quantum Sensor

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A noteworthy breakthrough has emerged in the arena of atomic-resolution 3D imaging of extensive nuclear-spin structures. This pioneering technique relies on superior spectral resolution for discerning minute couplings among individual nuclear spins. The process eliminates these couplings from intricate spectra, subsequently translating the revealed connectivity into a three-dimensional spatial structure with unmatched sub-ångström precision.

Crucial to these groundbreaking experiments is a cluster of $^{13}C$ nuclear spins situated near a solitary NV center in diamond at 4K. This configuration makes the magnetic imaging of single molecules and spin structures viable. An NV electron spin takes on the role of a sensor, responsible for gauging nuclear-nuclear interactions via spin-echo double-resonance methods.

Implementing quantum sensing sequences to polarize and detect spins in any direction from the NV enables the collection of data from a multitude of spins. When a Ramsey-type measurement is executed without echo pulses, the resulting complex spectra indicate the presence of several spins and nuclear-nuclear spin interactions.

While the one-dimensional measurement sheds light on the presence of multiple spins, it falls short in providing direct information on spin connectivity or the underlying structure of individual spins and their couplings. However, the use of a double-resonance sequence can isolate and measure specific spin couplings with high resolution. Furthermore, the spectral resolution can be enhanced by applying additional echo pulses, making it possible to detect sub-hertz interactions.

The application of 3D spectroscopy allows for the comprehensive characterization of a spin cluster’s composition and connectivity by modifying probe and target frequencies along with evolution time. This approach allows the simultaneous probing of multiple spins with similar frequencies and the retrieval of nuclear-nuclear couplings, even when spins overlap spectrally.

Potential ambiguities caused by overlapping spins can be resolved by extracting an over-determined dataset with numerous couplings. This process facilitates the unique identification of individual spins based on their connections within the cluster. In the experimental setting, the NV electron spin doubles as a quantum sensor to measure nuclear-nuclear spin couplings in a cluster of 13C nuclear spins near a single NV center in diamond.

By implementing a double-resonance sequence of N echo pulses, it’s possible to selectively detect the coupling between the probe and target spins. Sweeping the target frequency reveals all spins coupled to the probe spins, and sweeping the evolution time exposes the strength of couplings between spins. Although the presence of electronic spins can alter nuclear couplings, averaging the measured couplings for different electron spin states mitigates the deviations.

The structure of the spin cluster is determined sequentially by adding spins and matching the measured couplings within a certain tolerance. Two distinct methodologies are employed to impose spin coordinate constraints: one based on the diamond lattice and the other on a general cubic lattice. While the latter method is computationally intensive, it is universally applicable across any spin system.

The precision in characterizing the NV environment at a microscopic level offers exciting possibilities for enhanced control of quantum bits and investigating many-body physics in coupled spin systems. The method employs the NV sensor spin for creating polarization and detection, offering high-contrast readout and negligible electron relaxation at 4K.

Reference

1. Abobeih, M. H. et al. Atomic-scale imaging of a 27-nuclear-spin cluster using a quantum sensor. Nature 576, 411–415 (2019).