The ability to perform three-dimensional imaging of nanoscale structures using magnetic resonance techniques holds significant potential for various applications, including studying spin-labeled proteins and label-free chemical contrast imaging within opaque samples. While single spin detection has been achieved using techniques like magnetic resonance force microscopy (MRFM) and NV centers, extending this to three-dimensional imaging at the nanoscale has been challenging. Existing methods, such as those using intrinsic field gradients from color centers, are limited in their imaging range. Previous work has demonstrated one- and two-dimensional imaging using various gradient sources, but three-dimensional Fourier-accelerated imaging with nanoscale resolution has remained elusive. This paper aims to address this gap by developing a novel method for three-dimensional Fourier-accelerated imaging with nanometer-scale resolution.

The paper reviews existing techniques for nanoscale magnetic resonance imaging, highlighting the limitations of current approaches in achieving three-dimensional imaging with high resolution. It discusses MRFM and NV centers as single spin detection methods and mentions previous attempts at multi-dimensional imaging using various gradient sources. The limitations of these approaches, such as scalability and the inability to switch gradients fast enough for Fourier acceleration at the nanoscale, are discussed. The review sets the stage for the introduction of the new method presented in the paper, which overcomes these limitations.

The core of the methodology is a device that generates three linearly independent magnetic field gradients using a two-dimensional layout of microfabricated wires arranged in a U-shape structure. These wires, fabricated on a diamond substrate containing densely doped NV centers, create gradient fields a few micrometers below the structure. One-dimensional MRT is initially demonstrated, where the oscillatory signals from NV centers are linearly superposed, and the various frequencies are recovered via inverse Fourier transform. The experimental setup addresses challenges such as creating sufficiently rectangular current pulses for accurate frequency measurement and maintaining stability to minimize signal blurring. This involves using a stable voltage source and fast switches, along with online post-processing correction for residual nonlinearities and fluctuations. The one-dimensional technique is then extended to three dimensions by applying pulses from the three wires consecutively during a Hahn Echo sequence. The resulting spin signal is analyzed using a 3D inverse Fourier transform to produce a three-dimensional image. A compressed sensing scheme is also implemented to reduce the number of data points required, leveraging the knowledge that the signal is restricted to a narrow region of interest. This scheme effectively achieves a 'zoom' into the region of interest by undersampling the signal, inducing aliasing in frequency space.

The key finding is the successful demonstration of Fourier-accelerated three-dimensional imaging of NV centers with sub-10 nm resolution. The researchers achieved a resolution down to 5.9 ± 0.1 nm. The three-dimensional images obtained reveal individual NV centers within the confocal volume of the microscope. The compressed sensing method significantly reduces the acquisition time, demonstrating a tenfold speed-up in acquiring two-dimensional images. Analysis of the spatial resolution shows that it is primarily limited by spatial drifts of the current in the wires rather than electrical fluctuations. The achieved resolution surpasses that of standard localization microscopy techniques (PALM, STORM), demonstrating the superior capabilities of the developed method.

The results demonstrate the feasibility of high-resolution three-dimensional magnetic resonance imaging at the nanoscale. The sub-10 nm resolution achieved significantly improves upon previous techniques, opening new possibilities for studying nanoscale structures. The compressed sensing approach further enhances the practicality and speed of the method, making it applicable to larger data sets. The study identifies spatial current drifts as the main limiting factor for resolution, suggesting avenues for future improvements by addressing this issue. The demonstrated technique has broad implications for various fields, including quantum information science, materials science, and biophysics.

This work presents a groundbreaking advance in nanoscale magnetic resonance imaging, demonstrating three-dimensional imaging with sub-10 nm resolution using Fourier-accelerated MRT and a novel compressed sensing approach. The achieved resolution outperforms existing super-resolution techniques and opens up exciting new possibilities in various scientific domains. Future research could focus on improving the stability of the current paths to further enhance resolution and explore the application of the technique to other spin systems and broader scientific problems.

The current resolution is primarily limited by spatial drifts of the current within the microfabricated wires. While the researchers implemented correction methods, further improvements could be achieved through refinements in device fabrication and current control. The technique is currently focused on NV centers in diamond; extending it to other spin systems would require further development and adaptation. The compressed sensing approach, while effective, relies on the assumption of a localized region of interest, limiting its applicability to situations where this assumption doesn't hold.