High-sensitivity spin-based electrometry with an ensemble of nitrogen-vacancy centers in diamond

We demonstrate a spin-based, all-dielectric electrometer based on an ensemble of nitrogen-vacancy (${\mathrm{NV}}^{-}$) defects in diamond. An applied electric field causes energy-level shifts symmetrically away from the ${\mathrm{NV}}^{-}$'s degenerate triplet states via the Stark effect; this symmetry provides immunity to temperature fluctuations allowing for shot-noise-limited detection. Using an ensemble of ${\mathrm{NV}}^{-}\mathrm{s}$, we demonstrate shot-noise-limited sensitivities approaching 1 (V/cm)/$\sqrt{\text{Hz}}$ under ambient conditions, at low frequencies ($<10$ Hz), and over a large dynamic range (20 dB). A theoretical model for the ensemble of ${\mathrm{NV}}^{-}\mathrm{s}$ fits well with measurements of the ground-state electric susceptibility parameter $\langle k_{\perp }\rangle$. Implications of spin-based, dielectric sensors for micron-scale electric-field sensing are discussed.

Figure 1

(a) Diamond electrometry setup. For applying electric fields across the ensemble of ${\mathrm{NV}}^{-}\mathrm{s}$, gold electrodes were evaporated on both faces of the diamond plate ($3\times 3\times 0.32 {\text{mm}}^3$). A collimated laser beam ($\sim 200 \mu \mathrm{m}$ diameter) was used to excite a single pass of ${\mathrm{NV}}^{-}\mathrm{s}$ input from the edge of the diamond plate, and microwave (MW) excitation was delivered to the ensemble of ${\mathrm{NV}}^{-}\mathrm{s}$ by a stripline in an $\mathrm{\Omega }$ shape patterned on a printed circuit board. Inset: A cross section of the experiment depicting four of the eight total ${\mathrm{NV}}^{-}\mathrm{orientations}$ within an ensemble of ${\mathrm{NV}}^{-}\mathrm{s}$ used for detecting electric fields. (b) Generalized diagram depicting how crystal field $D$, hyperfine field $A$, and strain and the magnitude of transverse electric fields (${\mathrm{\Pi }}_{\perp }=\sqrt{{{\mathrm{\Pi }}_x^2+{\mathrm{\Pi }}_y^2}^{\phantom{0}}}$) affect energy splitting in both the ground- and excited-state spin configurations of the ${\mathrm{NV}}^{-}$. The spin labels ($m_s$ and $m_I$) indicate the quantum numbers of the electronic and hyperfine states, and the two eigenstates that are sensitive to electric fields are given by ${|+\rangle }_s^{\left(1\right)}{|0\rangle }_I$ ($m_I=+0$) and ${|-\rangle }_s^{\left(1\right)}{|0\rangle }_I$ ($m_I=-0$). The inset on the right shows the ground-state ODMR spectra of an ensemble of ${\mathrm{NV}}^{-}\mathrm{s}$.

Figure 2

(a) ODMR spectrum with correspondingly colored labels to indicate the detuning of transitions with stepwise increasing applied voltages. (b) Experimentally measured ODMR (points) at six different MW driving amplitudes overlaid with their respective numerical fits (black) using a model that accounts for an isotropic distribution of strain fields within an ensemble of ${\mathrm{NV}}^{-}\mathrm{s}$. The two transitions correspond to the ${|-\rangle }_s^{\left(1\right)}{|0\rangle }_I$ (red, bottom) and ${|+\rangle }_s^{\left(1\right)}{|0\rangle }_I$ (blue, top) eigenstates of the ${\mathrm{NV}}^{-}$ triplet ground state. (c) Ground-state shifts due to incremental, stepwise electric fields applied to an ensemble of ${\mathrm{NV}}^{-}\mathrm{s}$ at zero magnetic field. By comparing the stepwise detuning shifts of the electric-field transitions with the applied voltages, it is possible to accurately deduce the ensemble average value of $\langle k_{\perp }\rangle =7.0\pm 1.1\text{Hz}/\left(\mathrm{V}/\mathrm{cm}\right)$ at a bias field of 225 V. (d) Data for the ${|+\rangle }_s^{\left(1\right)}{|0\rangle }_I$ transition (top blue circles) overlaid with numerical results (solid blue line). Data for the ${|-\rangle }_s^{\left(1\right)}{|0\rangle }_I$ transition (bottom red crosses) overlaid with numerical results (dashed red line). See Eq. (A2) for details about the numerical results.

Figure 3

Measurements taken at 1.8-W laser excitation with a high-stability bias voltage of 225 V. (a) Time trace of both lock-in-amplifier channels monitoring frequency detuning of ensemble states ${|+\rangle }_s^{\left(1\right)}{|0\rangle }_I$ (blue crosses) and ${|-\rangle }_s^{\left(1\right)}{|0\rangle }_I$ (red circles) in units of transition frequency noise per $\sqrt{\text{Hz}}$. (b) Noise spectral density (NSD) of both channels. The noise floor of the red (blue) channel is calculated to be equivalent to $12.6\pm 6.4$ ($13.4\pm 7.4$) (V/cm)/$\sqrt{\text{Hz}}$, assuming the noise is entirely attributed to electric-field fluctuations. The electric-field sensitivity estimated by the shot-noise limit is given by the black line $[1.2\pm 0.1$ (V/cm)/$\sqrt{\text{Hz}}$].

Figure 4

Experimental measurements identical to those in Fig. 3 except the analysis takes advantage of the experimental methodology for deconvolving fluctuations from temperature and electric fields. (a) Time trace of the difference (orange circles, electric field) and sum (green crosses, temperature) of the lock-in-amplifier channels from Fig. 3. (b) NSD on the time-trace difference (sum) of the two channels, which corresponds to a sensitivity of $1.6\pm 1.2$ (V/cm)/$\sqrt{\text{Hz}}$ ($2.4\pm 1.2\text{mK}/\sqrt{\text{Hz}}$) due the transverse electric-field (temperature) fluctuations. The sum of the two correlated channels yields a shot-noise sensitivity limit of $0.9\pm 0.1$ (V/cm)/$\sqrt{\text{Hz}}$ (black line), which is $\sqrt{2}$ times lower than that of the individual channels as seen in Fig. 3.

Figure 5

Applied electric field with respect to the eight orientations of NVs in the ensemble.

Figure 6

Excited-state ODMR spectra measured on an ${\mathrm{NV}}^{-}$ ensemble at zero magnetic field. Excited-state shifts due to pulsed electric fields applied to an ${\mathrm{NV}}^{-}$ ensemble at zero magnetic field. The sensitivity of this measurement approaches $300\frac{\mathrm{V}/\mathrm{cm}}{\sqrt{\text{Hz}}}$.