Avoiding power broadening in optically detected magnetic resonance of single NV defects for enhanced dc magnetic field sensitivity

We report a systematic study of the magnetic field sensitivity of a magnetic sensor consisting of a single nitrogen-vacancy (NV) defect in diamond, by using continuous optically detected electron spin resonance (ESR) spectroscopy. We first investigate the behavior of the ESR contrast and linewidth as a function of the microwave and optical pumping power. The experimental results are in good agreement with a simplified model of the NV defect spin dynamics, leading to an optimized sensitivity around $2\mu$T$/\sqrt{\mathrm{Hz}}$ for a single NV defect in a high-purity diamond crystal grown by chemical vapor deposition. We then demonstrate an enhancement of the magnetic sensitivity by one order of magnitude by using a simple pulsed-ESR scheme. This technique is based on repetitive excitation of the NV defect with a resonant microwave $\pi$ pulse followed by an optimized readout laser pulse, allowing to fully eliminate power broadening of the ESR linewidth. The achieved sensitivity is similar to that obtained by using Ramsey-type sequences, which is the optimal magnetic field sensitivity for the detection of a dc magnetic field.

Figure 1

(a) Energy-level diagram of the NV defect as a function of the amplitude of a static magnetic field $B$ applied along the NV-defect axis. The ground state ${}^3{A}_2$ and the excited state ${}^{3}E$ are electron spin triplets. Optical transitions ${}^3{A}_2\to {}^{3}E$ are spin-conserving, while nonradiative ISC to an intermediate singlet state ${}^1{A}_1$ is strongly spin dependent [rightmost (blue) arrows]. The shaded circle indicates the excited-state level anticrossing (LAC), achieved for a magnetic field amplitude $B\approx 510$ G applied along the NV axis. (b) Typical ESR spectrum of a single NV defect recorded with a static magnetic field $B\approx 20$ G applied along the NV axis. Solid line is data fit using Lorentzian functions. (c) The NV-defect spin dynamics is studied by considering a two-level system in interaction with a resonant microwave field. Notations are defined in the main text.

Figure 2

ESR spectra recorded for a magnetic field amplitude $B=20$ G (upper traces) and at the excited-state LAC for $B\approx 510$ G applied along the NV-defect axis (bottom traces). Since the ${}^{14}$N nuclear spin is fully polarized at the excited-state LAC, unambiguous measurements of the contrast and linewidth of the ESR can be obtained. Solid lines are data fits using Lorentzian functions. Data are recorded for (a) $s=0.08$ and ${\Omega }_R=2.5\times {10}^6$ rad.s${}^{-1}$ and (b) $s=0.3$ and ${\Omega }_R=3.6\times {10}^6$ rad.s${}^{-1}$.

Figure 3

(a–d) ESR contrast and linewidth as a function of the Rabi frequency ${\Omega }_R$ and the saturation parameter $s$ plotted in log scale. The solid lines are data fits using Eqs. (10) and (11) as discussed in the main text. (e, f) Corresponding magnetic field sensitivities plotted in log-log scale using Eq. (3). (g) Two-dimensional plot of the magnetic field sensitivity obtained by using Eqs. (3), (10), and (11) and the results of data fitting: ${\Gamma }_p^{\infty }=5\times {10}^6$ s${}^{-1}$, ${\Gamma }_c^{\infty }=8\times {10}^7$ s${}^{-1}$, $\Theta =0.2$, and ${\mathcal{R}}^{\infty }=250\times {10}^3$ counts.s${}^{-1}$. The solid lines correspond to isomagnetic field sensitivities.

Figure 4

(a) Time-resolved PL response of a single NV defect initially prepared either in the $\left|0\right.\rangle$ state (upper trace in red) or in the $\left|1\right.\rangle$ state (lower trace in blue). Preparation in $\left|0\right.\rangle$ is done by optical pumping with a 2-$\mu$s laser pulse. A subsequent resonant MW $\pi$ pulse (50 ns) is applied for initialization in the $\left|1\right.\rangle$ state. The time binning is 1 ns. (b) ESR contrast $\mathcal{C}\left(T\right)$ as a function of the integration time $T$.

Figure 5

(a) Pulse sequence used to eliminate power broadening effects. (b) Pulsed-ESR spectra recorded for different values of the $\pi$-pulse duration $T_{\pi }$. The three resonances correspond to the three hyperfine components associated with the ${}^{14}$N nuclear spin. The laser power corresponds to $s=1.2$. (c) ESR linewidth as a function of the $\pi$-pulse duration plotted in log scale. The solid line is the convolution between a sinc function of width ${\Gamma }_{\pi }\propto T_{\pi }^{-1}$ and a Gaussian function of width ${\Gamma }_2^{*}=2\times {10}^5$ s${}^{-1}$. The inset shows the evolution of the ESR contrast as a function of the $\pi$-pulse duration $T_{\pi }$. (d) Ramsey fringes recorded for the same NV defect with a microwave detuning of $0.7$ MHz from the central hyperfine line of the ESR spectrum. The (red) solid line denotes data fit with the function $\exp \left[{(\tau /T_2^{*})}^2\right]{\sum }_{i=1}^3\cos \left(2\pi f_i\tau \right)$, where $f_i$ values are the microwave detunings from each hyperfine component of the spectrum. A value $T_2^{*}=3.0\pm 0.2\mu$s is achieved. (e) Fourier-transform spectrum of Ramsey fringes. Solid lines are data fit with Gaussian functions, leading to ${\Gamma }_2^{*}=\left(2.08\pm 0.05\right)\times {10}^5$ s${}^{-1}$.

Figure 6

(a) Pulsed-ESR spectra recorded at the excited-state LAC for different values of the $\pi$-pulse duration $T_{\pi }$. (b) ESR contrast as a function of $T_{\pi }$. (c) Averaged rate of detected photons $\mathcal{R}$ measured while running the pulsed-ESR sequence as a function of $T_{\pi }$. The solid line denotes data fit with the function $\mathcal{R}={\mathcal{R}}_0\frac{T_L}{T_S}$, where ${\mathcal{R}}_0$ is the rate of detected photons for a continuous laser excitation and $T_S$ is the total duration of the pulse sequence, including initialization, $\pi$-pulse rotation, and spin-state readout. (d) Corresponding magnetic field sensitivity plotted in log-log scale using Eq. (3). An enhancement by roughly one order of magnitude is achieved compared to continuous (CW) ESR spectroscopy.