Sub-nanometer resolution of the nitrogen-vacancy center by Fourier magnetic imaging

Abstract

Solid-state spins in diamond are promising building blocks for quantum computing and quantum sensing, both of which require precise nanoscale addressing of individual spins. To explore the resolution limit of this approach, we demonstrate Fourier magnetic imaging of nitrogen-vacancy centers in diamond under state-of-the-art conditions. We constructed a highly compact experimental platform featuring thermal drift compensation under ambient conditions and generated a pulsed magnetic field gradient of up to 13.5 G/$μ$m. By implementing the Fourier magnetic imaging protocol, we achieved localization of a single nitrogen-vacancy center with a spatial resolution of 0.28 $\pm$ 0.10 nm and a magnetic field measurement deviation of 9 nT. This technique holds potential for applications such as localizing spins within proteins and cells.

Figures (4)

• Figure 1: The experimental setup. (a) The confocal microscope part of optically detected magnetic resonance (ODMR) platform. The overall outer dimension is 0.5(L) × 0.4(W) × 0.2 (H) $\mathrm{m}^{3}$. Inset: the microscopy photograph of the microwave (MW) stripe and gradient microwire fabricated on the diamond surface. The scale bar is 20 $\mu$m. Abbreviations: Obj: objective lens; XYZ Pos.: $xyz$ positioner; PS: $xyz$ piezo scanner; DM: dichroic mirror; LP: 650 nm long pass filter; AL: achromatic lens; SMF: single-mode fiber; HWP: half wave plate; Co: fiber collimator; MMF: multi-mode fiber with 50 $\mu$m core diameter. The SMF is connected to the laser pulse module and MMF is connected to APD. (b) The fluorescence tracking of a single NV center in 40 hours. The long time fluctuation is about ±10%. The fast noise is due to the short sampling time of about 10 ms at each data point. (c) Electric circuits for the generation of magnetic field gradient (MFG) pulse and the synchronization between MW and MFG.
• Figure 2: Characterization of the MFG. (a) the NV fluorescence map near the gradient microwire. On the top, the red stripe is the gradient microwire. (b) $m_{S}=0$ to $m_{S}=+1$ transition frequency shift $\Delta f$ of several NV centers vs. Positions (red dot) under a direct current $I$ = 1 mA. The red and blue curves show the fitting to the frequency and the calculation of the MFG projected on the NV-[111] axis, respectively. The red arrows in both (a) and (b) indicate the NV center for demonstration of Fourier magnetic imaging.
• Figure 3: Architecture for nanoscale MFG technique. (a) The pulse sequence consisting of spin echo pulses and synchronized MFG pulses for Fourier magnetic imaging. (b) The waveform for generating the MFG. It is not a continuous sine curve, where the gap between two period is used for laser initialization and readout of NV center. (c) The raw echo signal vs. current amplitude, with 2$\tau$=21 $\mu$s. The data is fitted by a cosine function.
• Figure 4: Demonstration of nanoscale localization of a single NV center by using the robust experimental apparatus. (a) The K-space signal with $2\tau\ =\ 80\ \mu s$, from which the single frequency oscillation can be clearly seen. (b) The detected signal in K-space, where the signal is obtained through undersampling as it consists of thousands of oscillations in total. Here the maximum current sent through the microwire is $I_{MAX}=10\ \mathrm{mA}$ and the total evolution time is $2\tau\ =\ 500\ \mu s$. (c) The real space localization of the single NV center after Fourier transformation of K-space signal. The red solid curve is Lorentz fit and the corresponding full width at half maximum (FWHM) is 0.28 ± 0.10 nm