Figure 1

Illustration of rotating frame magnetometry using the Bloch sphere: (a) An electron spin is initialized into the $|0⟩$ state and transferred into the coherent superposition $|x+⟩=\frac{1}{\sqrt{2}}(|0⟩+e^{i{\omega }_{0}t}|1⟩)$. (b) A microwave field $B_1^{\mathrm{mw}}{e}^{i{\omega }_{0}t}$ is applied in-phase with the spin precessing around the $z$ axis. (c) During sensing period $\tau$, transitions are induced between $|x+⟩$ and $|x-⟩=\frac{1}{\sqrt{2}}(|0⟩-e^{i{\omega }_{0}t}|1⟩)$ states by weak radio-frequency fields $B^{\mathrm{rf}}{e}^{i\Omega t}$ if the rf frequency $\Omega$ matches the Rabi frequency ${\omega }_1=\gamma B_1^{\mathrm{mw}}$. (d) $|x+⟩$ ($|x-⟩$) states are transferred to detectable $|0⟩$ ($|1⟩$) polarization. The transition probability $|x+⟩\leftrightarrow |x-⟩$ is equal to the probability of measuring $|1⟩$.Reuse & Permissions

Figure 2

Coherent oscillation between $|x+⟩$ and $|x-⟩$ states induced by a rf probe field of $B_1^{\mathrm{rf}}=1.6\mu \mathrm{T}$. Solid line is a fit to a decaying sinusoid [18]. $\Omega$ and ${\omega }_1$ are both $2\pi \times 7.5\mathrm{MHz}$. Symbols are explained in Table .Reuse & Permissions

Figure 3

(a) Optically detected electron spin resonance (ESR) spectrum of one of the NV centers used for the experiments. Dots are data, solid lines are Gaussian fits. $m_I=\pm 1$, $m_I=0$ indicate hyperfine lines ($a=2.2\mathrm{MHz}$) associated with the ${}^{14}\mathrm{NV}$ nuclear spin ($I=1$). Microwave frequency used in spin-lock experiments was always centered on the $m_I=-1$ line, indicated by an arrow. The dc bias field was 17 mT. (b) Rotating-frame spectrum with 7.5 MHz probe field present (feature ★). Other features are explained with Fig. 4. Evolution time was $\tau =15\mu \mathrm{s}$. (c) High-resolution spectra of the main peak (★) for longer evolution times and weaker probe fields. Dots are data, solid lines are Gaussian fits. Linewidths are full width at half maximum. Numbers indicate $B_1^{\mathrm{rf}}$ and $\tau$. Baseline noise of the 41-nT spectrum corresponds to 8 nT (${\sigma }_p=0.020$), and an integration time of 840 s per point was used.Reuse & Permissions

Figure 4

(a) Rotating-frame spectrum showing the three peaks associated with $m_I=-1(\star )$, $m_I=0(•)$, and $m_I=1(▾)$. Solid line is a calculation based on Eq. (4) and the EPR spectrum shown in Fig. 3a. Parameters are identical to Fig. 3 except for $\Omega /2\pi =8\mathrm{MHz}$. (b) Spectra as recorded using spin state selection. (c) Linear recombination of pure-state spectra from data in (b). Solid line is the calculated response.Reuse & Permissions

Figure 5

Relaxation time measurements for bulk (black squares and blue circles) and shallow implanted (5 nm deep, red triangles) NV centers show approximately $T_1$-limited behavior.Reuse & Permissions