Fourier magnetic imaging with nanoscale resolution and compressed sensing speed-up using electronic spins in diamond

Abstract

Optically-detected magnetic resonance using Nitrogen Vacancy (NV) color centres in diamond is a leading modality for nanoscale magnetic field imaging, 1-3 as it provides single electron spin sensitivity, 4 three-dimensional resolution better than 1 nm, 5 and applicability to a wide range of physical 6-8 and biological 9 samples under ambient conditions. To date, however, NV-diamond magnetic imaging has been performed using "real space" techniques, which are either limited by optical diffraction to ≈250 nm resolution 10 or require slow, point-by-point scanning for nanoscale resolution, e.g., using an atomic force microscope, 11 magnetic tip, 5 or superresolution optical imaging. 12 Here we introduce an alternative technique of Fourier magnetic imaging using NV-diamond. In analogy with conventional magnetic resonance imaging (MRI), we employ pulsed magnetic field gradients to phase-encode spatial information on NV electronic spins in wavenumber or "k-space" 13 followed by a fast Fourier transform to yield real-space images with nanoscale resolution, wide field-of-view (FOV), and compressed sensing speed-up. 2Key advantages of NV-diamond Fourier magnetic imaging, relative to real-space imaging, are: (i) spatially multiplexed detection, 14 which enhances the signal-to-noise ratio (SNR) for typical NV centre densities; (ii) a high data acquisition rate that can be further boosted with compressed sensing; 15,16 and (iii) simultaneous acquisition of signal from all NV centres in the FOV, which allows probing of temporally correlated dynamics and provides isolation from system drift. As described below, we apply the Fourier technique using a relatively simple apparatus, and demonstrate one-dimensional imaging of individual NV centres with <5 nm resolution; two-dimensional imaging of multiple NV centres with ≈30 nm resolution; and two-dimensional imaging of nanoscale magnetic field patterns, with magnetic gradient sensitivity ~14 nT/nm/Hz 1/2 and spatial dynamic range (FOV/resolution) ~500. We also show that compressed sensing can accelerate the image acquisition time by an order-of-magnitude using sparse sampling followed by convex-optimization-based signal recovery. With further improvements, NV Fourier magnetic imaging may enable MRI with atom-scale resolution and centimeter FOV, with applications ranging from mapping the structure of individual biomolecules to functional MRI in living cells to studies of quantum phenomena in magnetic materials. Similar Fourier techniques could also be applied to NV-diamond imaging of nanoscale electric fields, temperature, and pressure, as well as to other optically-addressable solid-state spin systems.Schematic views of the Fourier magnetic microscope are shown in Figs. 1a and 1b.The diamond sample has a thin layer of NV centres at the surface created via ion implantation (see Methods). NV electronic spin states (Fig. 1c) are optically polarized with green illumination (λ=532 nm), coherently manipulated using resonant microwave fields applied by a microwave loop, and detected via sp...

Nanomechanical Sensing Using Spins in Diamond

“…The NV center has been used to locate single elementary charges, 7 to perform thermometry within living cells 8 and to realize nanoscale MRI in ambient conditions. [9][10][11] However, there is yet to be a nanosensing application of the NV center that exploits its susceptibility to local mechanical stress/ strain.…”

“…6 Unlike existing NEMS techniques, NSMS can also measure the mode coupling coefficients magnetic field gradients to NV centers has been demonstrated using microcoils. 11 The unique capability of NSMS to determine the mode frequency shifts as well as their coupling coefficients allows direct imaging of the adsorbate mass distribution (rather than evaluating its mass moments) via …”

Role of exchange interaction in nitrogen vacancy center based magnetometry

“…Recently, the nitrogen-vacancy centers (NVC's) in diamond have been employed as extremely sensitive vector magnetic field sensors operating at room temperature and capable of nanoscale spatial resolution [16][17][18][19][20][21][22][23][24][25]. NVC's are atomic-scale defects which are formed either naturally or by implantation, using high-energy nitrogen ion beam [26], annealing [27,28], and nitrogen doping [29].…”

Selective addressing of solid-state spins at the nanoscale via magnetic resonance frequency encoding

“…1). This gradient strength is several orders of magnitude larger than in conventional MRI; see our prior work 20 for comparison details. The microcoil field gradient is spatially uniform to 5%, can be modulated at~1 MHz, and its application requires no active cooling of the sample.…”

“…17 However, it remains a challenge to realize the intermediate regime of mesoscopic arrays of NV spins with selective nanoscale addressing and coherent control of NVs at each site in the array. Such a capability could be a platform technology for applications such as high-spatialdynamic-range magnetic imaging [18][19][20] and quantum-assisted sensing, [21][22][23] as well as scalable quantum information processing 24,25 and simulation. 26,27 In the present work, we experimentally demonstrate selective coherent manipulation of an array of four NV spin sites, equally spaced by~100 nm, using a frequency encoding technique inspired by magnetic resonance imaging (MRI).…”