Quantitative study of the response of a single NV defect in diamond to magnetic noise

The nitrogen-vacancy (NV) defect in diamond is an efficient quantum sensor of randomly fluctuating signals via relaxometry measurements. In particular, the longitudinal spin relaxation of the NV defect accelerates in the presence of magnetic noise with a spectral component at its electron spin resonance frequency. We look into this effect quantitatively by applying a calibrated and tunable magnetic noise on a single NV defect. We show that an increase of the longitudinal spin relaxation rate translates into a reduction of the photoluminescence (PL) signal emitted under continuous optical illumination, which can be explained using a simplified three-level model of the NV defect. This PL quenching mechanism offers a simple, all-optical method to detect magnetic noise sources at the nanoscale.

Figure 1

(a) Principle of the experiment. A calibrated noise signal is sent through a copper microwire spanned on a bulk diamond sample. This noise signal produces a fluctuating Oersted field with a tunable spectral density at the electron spin resonance frequency $f_{\mathrm{NV}}$ of a single NV defect located at a distance $d$ from the microwire. The ground state spin sublevels of the NV defect, $m_s=0,\pm 1$, are shown on the right. The NV quantization axis forms an angle $\theta$ with the direction of the magnetic field noise. (b) Typical noise spectrum used in the experiments. (c) Optically detected electron spin resonance spectrum recorded for a single NV defect at zero external magnetic field.

Figure 2

(a) Experimental sequence used to measure the longitudinal spin relaxation time $T_1$. The duration of the laser pulses is 3 $\mu \mathrm{s}$. The spin-dependent PL signal is integrated in a detection window corresponding to the first 300 ns of the readout laser pulse and normalized with the value measured for $\tau \gg T_1$. (b) NV spin relaxation curves recorded in the absence (blue triangle) and presence (purple circles) of a magnetic noise with a frequency window $\mathrm{\Delta }f=50\mathrm{MHz}$, a center frequency $f_{\text{c}}=f_{\text{NV}}=2.87\mathrm{GHz}$, and a field spectral density at the NV center position around $3\mu {\mathrm{T}}^2{\mathrm{MHz}}^{-1}$. The data are fitted to a single exponential decay $e^{-\frac{\tau }{T_1}}$. The optical excitation power during the measurement is 1.4 mW, corresponding to a PL rate of 140 kcounts/s. The distance between the NV defect and the copper microwire is $d=28\pm 4\mu \mathrm{m}$. (c) Dependence of the spin relaxation rate with the field spectral density. The black dashed line is a linear fit with Eq. (2), leading to $\theta ={41}^{\circ }$.

Figure 3

(a) Sketch of the three-level model used to describe the NV defect. (b) Measurement procedure used to infer the ratio between the PL signals in the presence (${\mathcal{R}}_{\mathrm{cw}}$) and absence (${\mathcal{R}}_0$) of magnetic noise. The two laser pulses have a duration of 1 ms and are separated by $50\mu \mathrm{s}$. (c) Dependence of the ratio ${\mathcal{R}}_{\mathrm{cw}}/{\mathcal{R}}_0$ with the spin relaxation time $T_1$ for different optical excitation powers. $T_1$ is tuned by varying $S_{B_{\perp }}$ as in Fig. 2. The dashed lines show the predictions of the closed three-level model [Eq. (6)] using $\beta =0.68$. This value is compatible with the $\sim 30\%$ contrast observed in the optically detected electron spin resonance spectrum [see Fig. 1].