Nanoscale electric field imaging with an ambient scanning quantum sensor microscope

Nitrogen-vacancy (NV) center in diamond is a promising quantum sensor with remarkably versatile sensing capabilities. While scanning NV magnetometry is well-established, NV electrometry has been so far limited to bulk diamonds. Here we demonstrate imaging external alternating (AC) and direct (DC) electric fields with a single NV at the apex of a diamond scanning tip under ambient conditions. A strong electric field screening effect is observed at low frequencies. We quantitatively measure its frequency dependence and overcome this screening by mechanically oscillating the tip for imaging DC fields. Our scanning NV electrometry achieved an AC E-field sensitivity of 26 mV μm−1 Hz−1/2, a DC E-field gradient sensitivity of 2 V μm−2 Hz−1/2, and sub-100 nm resolution limited by the NV-sample distance. Our work represents an important step toward building a scanning-probe-based multimodal quantum sensing platform.


INTRODUCTION
The recent decade has witnessed exciting developments in quantum science and technology, where controlled quantum systems are employed to carry out tasks that are challenging for existing classical techniques. Quantum sensing is a rapidlygrowing branch 1 , which exploits the fragility of quantum states to detect small external signals with high sensitivity. It has many potential applications in the real world, such as geophysical navigation 2,3 , disease diagnostics 4,5 , and discovery of new materials [6][7][8] . The nitrogen-vacancy (NV) center in diamonds is one of the most promising quantum sensors 9 . Its electron spin has a long coherence time even under ambient conditions. It is sensitive to a variety of signals, such as magnetic fields [10][11][12][13] , electric fields 14-20 , temperature [21][22][23][24] , and pressure [25][26][27] . Integrating this atomic-sized versatile quantum sensor into a scanning-probe microscope further allows mapping external signals with nanoscale resolution [28][29][30] . This holds great potential for probing condensed matter physics. More specifically, NV acts as either a magnetometer or electrometer, depending on the direction of the biased magnetic field. The ability of imaging both magnetic and electric fields can provide a unique insight into strongly correlated matter 31 and multiferroic materials 32 . It also has interdisciplinary applications, such as imaging charge and spin phenomena in chemistry and biology 9,[33][34][35][36] .
Scanning NV magnetometry, as a well-established technique 28 , has been utilized to image magnetic materials 6,37-39 , hydrodynamic current flows 7,8 , skyrmion structures 40 , and vortices in superconductors 41 . Recently, scanning NV electrometry has also been achieved, where fixed NVs in bulk diamonds are used to image electric fields from a conductive scanning tip 19,20 . However, NV electrometry has not yet been demonstrated in a diamond scanning tip, which is desired for imaging an arbitrary sample. Major challenges arise from the qubit's weak coupling strength to electric fields, a relatively short coherence time in nanostructures compared to bulk diamonds, and electric field screening by charge noise on the diamond surface and in the bulk [42][43][44] . In this work, we demonstrate utilizing a shallow NV at the apex of a diamond nanopillar to image external AC and DC electric fields under ambient conditions. Dynamical-decoupling sequences are used to extend the NV coherence times 45 . We achieve an AC electric field sensitivity of 26 mV μm −1 Hz −1/2 and sub-100 nm spatial resolution limited by the NV-sample distance. This AC sensitivity presents an improvement by two orders of magnitude as compared to the prior work by Barson et al. 19 , who demonstrated an AC voltage sensitivity of 310 mV Hz −1/2 over a distance of 50 nm. A strong electric field screening effect is observed at low frequencies, likely caused by mobile charges on the surface under ambient conditions 42 and in the bulk diamond 46 . We quantitatively characterize its frequency dependence, which reveals a resistivecapacitive (RC) time constant of our diamond tip surface~30 μs. To overcome this screening effect for imaging DC electric fields, we oscillate the diamond probe at a frequency of~190 kHz, and synchronize the quantum sensing pulse sequences with the mechanical motion. Hence, a local spatial gradient is upconverted to an AC signal, allowing for T 2 -limited DC sense. This motionenabled imaging technique has been explored in various scanning measurements [47][48][49][50][51][52] , and here we apply it to scanning NV electrometry. We achieve a DC electric field gradient sensitivity of 2 V μm −2 Hz −1/2 . This is two orders of magnitude better than the previous result by Bian et al. 20 who demonstrated a T Ã 2 -limited DC field sensitivity of 35.2 kV cm −1 Hz −1/2 using a 10 nm-in-diameter conductive tip scanning over a diamond. Our results pave the way for building a scanning-probe-based multimodal quantum sensing platform. and the sample can be independently scanned by piezoelectric nanopositioners. The probe is attached to a quartz crystal tuning fork, allowing for frequency modulation AFM (FM-AFM). The probe oscillates in a motion parallel to the sample surface, so the AFM operates in shear force mode. To improve the scanning robustness, we make multiple nanopillars on a single diamond probe and use different pillars for AFM contact and quantum sensing separately. The NV, at the apex of the sensing pillar, is kept at a fixed distance from the sample. The distance is controlled by the tilting angle of the probe. More details on AFM scanning control can be found in Supplementary Note 2F. To test the electrometry capabilities of our system, we fabricate a U-shaped gold structure on a quartz substrate and use the NV to map out its electric field distribution. An on-chip microwave (MW) stripline delivers MW fields to manipulate the NV spin states. A permanent magnet from beneath exerts a bias magnetic field at the NV.
Our electrometry measurements were performed under a magnetic field oriented perpendicular to the NV axis, denoted by B ⊥ . The coordinate system is depicted in Fig. 1b, whereẑ is along the NV axis and the projection of one carbon atom in the perpendicular plane defines thex axis. Under B ⊥ , the NV electron spin eigenstates are 0 53 , where ϕ B is the angle between B ⊥ and thex axis (see Fig. 1c). Electric fields induce Stark shifts of the ± j i energy levels. The splitting between the ± j i states is approximately Δ % where ϕ B and ϕ E are the angles of magnetic and electric fields in the transverse plane as shown in Fig. 1c, D gs ≈ 2.87 GHz is the zero-field splitting (ZFS), γ B = 2.8 MHz G −1 is the electron spin gyromagnetic ratio and d ⊥ = (0.17 ± 0.03) MHz μm V −1 is the transverse electric field coupling strength 54 . We ignore the coupling to E z since the longitudinal coupling strength d ∥ = (3.5 ± 0.2) × 10 −3 MHz μm V −1 54 is much smaller. Strain is measured to be negligible in our diamond probe for the scope of this work.
We choose to work with 15 NV under B ⊥ > 70 G 53 . The splitting between the ± j i states is therefore much larger than the hyperfine coupling ≈ 3 MHz 55 , and both nuclear spin sublevels (m I = ± 1/2) are sensitive to electric fields. Consequently, the full NV optical contrast contributes to the signal without the need of resolving hyperfine states. We use NVs with moderate T Ã 2 dephasing times (T Ã 2 $ 1:5 μs, see Supplementary Note 2A) and apply relatively strong MW power to drive transitions between spin states (π pulse duration~100 ns). These are in contrast to NV electrometry performed under a weak magnetic field where typically B ⊥ < 20 G 14,15 . A detailed comparison between 15 NV and 14 NV electrometry under different magnetic field regimes can be found in Supplementary Note 1B. Figure 1 d shows a pulsed optically detected magnetic resonance (ODMR) spectrum under B ⊥ ≈ 73 G. The transition efficiencies between 0 j i and ± j i depend on the linear polarization of the MW fields (see Supplementary Note 1B). We use the 0 j i-toþ j i transition throughout this work for electric field sensing.
Frequency dependence of the electric field screening A strong electric field screening effect is observed at DC and low frequencies (see Supplementary Fig. 10), likely caused by mobile charges on the diamond surface and in the bulk 42 . Possible sources include adsorbed water layer under ambient conditions, electronic trapping states due to near-surface band-bending 43,56 , and internal charge defects such as vacancy complexes and substitutional nitrogen generated during diamond growth or NV creation 46,57 . We characterize this screening effect by measuring its frequency dependence. NV is positioned within a metal gap. An AC reference voltage is applied across the gap, generating an electric field at the NV. Lock-in detection is employed in order to confocal objective lens, a diamond probe, a U-shaped gold structure and microwave stripline fabricated on a quartz substrate, and an external magnet. The NV center is located at the apex of the diamond tip at a depth of~40 nm. The tip has a diameter of 300 nm and hovers above the sample. The NV-sample distance is typically ≲100 nm. The gap between the two electrodes is 500 nm, and Au is (150 ± 5) nm thick. b NV center in the presence of a perpendicular magnetic field, denoted by B ⊥ in the XY plane in yellow. Thex direction is defined by the projection of one of the carbon atoms. E ⊥ is the electric field component in the XY plane, which causes Stark shifts of the NV spin states. ϕ B and ϕ E denote the azimuth angle of B ⊥ and E ⊥ relative to thex-axis. c Zoom-in of the XY plane. Gray lines represent the projections of carbon atoms. d NV electron spin energy level under At low frequencies, we use a Ramsey-based lock-in sequence, where a train of equally spaced Ramsey measurements is synchronized with the reference signal, as shown in Fig. 2a. In each Ramsey measurement, the NV spin is prepared in a superposition of 0 j i and þ j i, and then accumulates phase induced by the DC electric field within the free evolution time τ = 800 ns. The accumulated phase ϕ NV can be extracted from the NV fluorescence signal measured after the final π/2 pulse (see Supplementary Note 2D). This phase is proportional to the local electric field, hence each Ramey measurement samples the electric field strength at the corresponding time step. The first Ramsey starts at 4 μs after the reference trigger, and the spacing between neighboring Ramsey measurements is also 4 μs. To have a sufficient number of sampling points, we performed measurements at reference signal frequencies below 50 kHz. As shown in Fig. 2b, the NV Ramsey phase ϕ NV oscillates in time, with the amplitude increasing with the reference frequency. Sinusoidal curve fitting extracts the amplitude and phase relative to the reference, which is represented by blue dots in Fig. 2e.
At high frequencies, the lock-in detection is based on a dynamicaldecoupling pulse sequence 58 , such as XY-4 shown in Fig. 2c. The spacing between neighboring π pulses is set to be half of the period of the reference signal. More π pulses are inserted to match high frequencies. Due to the finite coherence time T 2 , these measurements were performed above 200 kHz (see Supplementary Note 2A for NV T 2 characterizations using various dynamical-decoupling sequences). The NV spin, prepared in a superposition of 0 j i and þ j i, accumulates a phase induced by the AC electric field within the evolution time τ. The coherent phase signal ϕ NV is maximized when the detected local field is 'in-phase' (φ = 0) with the XY-4 sequence and minimized when '90°out-of-phase' (φ = π/2). To measure the amplitude and phase of the detected signal relative to the reference, we vary the initial phase offset by sweeping the delay between the reference trigger and the first π/2 pulse. As shown in Fig. 2d, ϕ NV is maximized at zero initial phase offset, and minimized near π/2, which indicates very little relative phase between the detected and reference signal. In contrast to the low-frequency regime, here, the oscillation amplitude shows no obvious dependence on the frequency. The extracted amplitude and phase by sinusoidal curve fitting are represented by orange dots in Fig. 2e. Figure 2e summarizes the results in both low and highfrequency regimes. The trend resembles the frequency response of a high-pass filter. The red solid curves represent an ideal highpass filter with a cut-off frequency f c at 35.4 kHz, corresponding to an RC time constant~30 μs. A simplified circuit model in Fig. 2f illustrates a possible high-pass filter consisting of the resistive diamond surface and capacitance between the tip and electrodes. For a general sample, Fig. 2g shows the capacitive coupling between the diamond surface and the sample. Screening is significantly reduced at high frequencies due to the finite mobility of charge carriers. The specific frequency cut-off can vary between different probes since the NV location, the geometry of the tip surface, and diamond purity all affect the screening effect. We emphasize that this circuit model is only phenomenological. Figure 2e mainly allows us to identify the frequency at which the screening effect significantly diminishes, which is essential  information for implementing motion-enabled DC sensing, as will be discussed in the next section.

Spatial mapping of AC and DC electric field distribution
We now demonstrate imaging of the AC electric field distribution. A single NV at the apex of a diamond nanopillar (300 nm in diameter) scans over a U-shaped gold structure (Fig. 3a). Our spatial resolution is limited by the NV-sample distance, which can be ≲100 nm. The diamond is attached to a piezoelectric tuning fork, which oscillates on resonance (~32 kHz) and provides frequency feedback to regulate the distance to the sample. In our AC electric field imaging, the oscillation amplitude is kept small (estimated to be <1 nm), and no reduction of the NV coherence time is observed. The probe motion is therefore represented by a flat line in Fig. 3a. An AC signal V pp = 0.96 V at 250 kHz is applied to the middle electrode and synchronized in-phase with the XY-4 pulse sequence with a free evolution time τ = 8 μs. The accumulated phase is whereζ denotes the maximum electric coupling direction, and E ζ is theζ component of E ⊥ . Figure 3b plots ϕ NV as a function of the AC input amplitude, measured by the NV at a fixed point within the gap. ϕ NV grows proportionally as expected. The cosine and sine values are measured by rotating the phase of the final π/2 pulse (see Supplementary Note 2D). Dashed traces in Fig. 3c show 1D line scans of ϕ NV and the corresponding e-field E ζ at different NV-sample distances (controlled by the probe tilting angle). They are in good agreement with the simulated E ζ distribution shown by the solid traces. The azimuth and zenith angles ofζ in the simulation are at ϕ = 20°and θ = 45°, respectively ( Supplementary Fig. 14a). Based on a NV fluorescence rate >100 kcps, an optical contrast >20%, and a phase accumulation time τ = 8 μs in our experiment, we have achieved an AC electric field sensitivity of 26 mV μm −1 Hz −1/2 under ambient conditions (see Supplementary Note 2E). A 2D map of the AC electric field is shown in Fig. 3d, and a simulated field distribution at a distance of d = 90 nm is shown in Fig. 3e. To map DC electric fields, we employ a motion-enabled imaging technique 12 that converts the DC signal to AC in order to overcome the screening effect. More concretely, the probe oscillates with a relatively large amplitude (>10 nm) such that the NV experiences an AC local field proportional to the local spatial gradient E 0 ζ ðxÞ (Fig. 4a). In addition, the bending of the tuning fork induces a rotational motion of the NV axis, giving rise to an AC modulation proportional to the local static field E ζ . This latter effect cannot be ignored as shown by the data below. The amplitude of the total motion-enabled AC signal has a form of E amp ¼ E 0 ζ ðxÞA þ βE ζ , where A is the probe oscillation amplitude, and β is an empirical constant capturing the NV axis rotation. To operate at a sufficiently high frequency at which the screening diminishes, we drive the clang mode of the tuning fork at 190 kHz 59 ( Supplementary Fig. 11). The sensing pulse sequence is synchronized with the mechanical motion, so the NV accumulates a coherent phase ϕ NV = d ⊥ E amp τ. Figure 4b shows the NV measurement at a fixed point within the gap, where ϕ NV is proportional to the applied DC voltage V dc . Based on our experimental parameters, we achieved a DC field gradient sensitivity of 2 V μm −2 Hz −1/2 (Supplementary Note 2E). Figure 4c compares a 1D line scan of ϕ NV along thex-axis at V dc = 16 V with the expected signal deduced from the measurements in Fig. 3c and simulated  considered. The sign of the discrepancy coincides with the sign of E ζ shown in Fig. 3c. Including the term βE ζ in E amp leads to an improved agreement between data and model (using A = 13 nm and β = −0.03 in the model), as shown in the middle panel. Since the probe oscillates at a large amplitude while performing contact-mode AFM scanning, the actual motion highly depends on the details of the probe-sample engagement. This is challenging to simulate accurately and could account for the remaining discrepancy. A 2D map of ϕ NV is shown in Fig. 4d, showing a reasonable agreement with the simulation result in Fig. 4e.

DISCUSSION
In conclusion, we demonstrated electric field imaging with a single NV at the apex of a diamond scanning tip under ambient conditions.
External electric fields are significantly screened at low frequencies.
We quantitatively measured its frequency dependence using lock-in detection sequences and therefore revealed the RC time constant of the tip surface (~30 μs). To overcome screening, we introduced a motion-enabled technique and demonstrated spatial mapping of the DC electric field gradients. Potential improvements to these demonstrations can be achieved as follows. First, AFM operating in tapping or noncontact mode would avoid direct contact between the probe and sample and allow the probe to oscillate with a larger amplitude more stably (see more in Supplementary Note 2G). This will give a higher field gradient sensitivity in motion-enabled imaging. Second, given an unknown sample, the DC field distribution along the maximum coupling axis ζ can be reconstructed by carefully pre-calibrating the probe oscillation direction and Eζ > 0 Eζ < 0 Eζ > 0 Eζ < 0 after correction for NV axis rotation before correction for NV axis rotation amplitude using a well-defined sample as described in this paper. Third, using multiple NVs of different orientations or multiple pillars with NVs of different orientations, one can extract both the magnitude and the direction of external electric fields, i.e. vector electrometry 16 . Finally, a higher spatial resolution is achievable by using even shallower NVs and motorized goniometers for better control of the probe tilting angle.
NV electrometry possesses a unique combination of properties as compared to other existing techniques. In this work, we achieved an AC electric field sensitivity of 26 mV μm −1 Hz −1/2 , DC electric field gradient sensitivity of 2 V μm −2 Hz −1/2 , and sub-100 nm spatial resolution limited by the NV-sample distance, all under ambient conditions. Most other electrometry techniques are based on measuring potentials, and many require cryogenic conditions. For example, scanning single-electron-transistor (SET) 60-63 is capable of measuring microvolt local potential; however, this remarkable sensitivity requires low-temperature operation and its spatial resolution is limited by the tip size (>100 nm). Kelvin probe force microscopy (KPFM) 64,65 and electrostatic force microscopy (EFM) 66 can achieve sub-10 nm spatial resolution and operate under ambient conditions; however, they are not optimal for quantitative electric field measurements. NV center is therefore a valuable addition as a unique electric field sensor with complementary advantages. We also highlight that NVs have unparalleled sensing versatility with a broad operating frequency range. Integrating electrometry and magnetometry into a single scanning probe will open up exciting opportunities in imaging nanoscale phenomena.

Diamond scanning probe and AFM control
The diamond probe was made from an electronic-grade CVD diamond purchased from Element Six, with a natural abundance (1.1%) of 13 C impurity spins. The probe is of~50 × 55 × 125 μm in dimension. Each probe has seven tips in a row with a spacing of 7 μm. Details of the multiple-pillar probe design and fabrication process are described in 8,67,68 .
The probe is attached to one prong of a quartz tuning fork using optical adhesive (Thorlabs NOA63). Two manual goniometers (Edmund) control its tilting angle and the NV-sample distance. The AFM contact between probe and sample is controlled by an attocube SPM controller (ASC500). Piezoelectric nanopositioners (attocube ANPxyz101 and ANPxyz100) were used for sample scanning. More details can be found in Supplementary Note 2F.
Optical setup NV experiments were performed on a home-built confocal laser scanning microscope. A 532 nm green laser (Cobolt Samba 100), focused by a ×100, NA = 0.7 objective (Mitutoyo M Plan NIR HR), was used to initialize the NV spin to the m S ¼ 0 j istate and generate spindependent photoluminescence for optical readout. An avalanche photodiode (APD, Excelitas Technologies Photon Counting Module SPCM-AQRH-13) was used to measure the NV fluorescence rate.

Quantum control setup
The microwaves were generated from a signal generator (Rohde & Schwarz SGS100A 6GHz SGMA RF Source) and amplified by a MW amplifier (Amplifier Research 30S1G6). All quantum measurements were performed on the Quantum Orchestration Platform (Quantum Machines). An Operator-X (OPX) generated control pulse sequences, output AC input voltages (V pp = 0.96 V), and measured the photon counts. DC input (V dc = 16 V) is provided by a voltage source (Yokogawa GS200).

Electrostatics simulation
The finite-element calculation package COMSOL performs the electrostatic simulations. To model the geometry, we use real device dimensions by importing the lithography design into the software. 2D simulation produces plots in Figs. 3c and 4c. 3D simulation produces the plots in Figs. 3e and 4e.

DATA AVAILABILITY
The data generated and analyzed during this study are available from the authors upon reasonable request.