Figure 1

Schematic of a scanning NV qubit magnetometer-decoherence probe for the detection of nanoscale field fluctuations. (a) NV center diamond lattice defect. (b) NV spin detection through optical excitation and emission cycle. (c) Microwave control of the NV spin state and 532 nm optical pulse for readout. (d) Simulated magnetic field signals at the NV probe corresponding to regions I–IV of an inhomogeneous test sample with different fluctuation amplitudes and frequency spectra. (e) The corresponding NV ground state populations show that the regions can be distinguished by the dephasing information. I: Strong, rapid fluctuations $\to$ fast exponential dephasing. II: Strong, slow fluctuations $\to$ fast Gaussian dephasing. III: Weak, rapid fluctuations $\to$ slow exponential dephasing. IV: Weak, slow fluctuations $\to$ slow Gaussian dephasing.Reuse & Permissions

Figure 2

Simulated magnetic field traces, $B(t)/B^{\prime }$, for (a) a channel of dipoles in unidirectional motion and (b) a self-diffusing dipole bath. (c) Temporal correlation function $⟨B(t)B(t^{\prime })⟩/⟨B^2⟩$. Time axes are rescaled by ${\tau }_e$.Reuse & Permissions

Figure 3

(a) Plot of simulated dephasing envelopes for $N_s={10}^4$ runs, showing agreement with Eqs. (1, 2). Time is in units of $({\gamma }_p{B}^{\prime }{)}^{-1}$. (inset) Zoomed plot showing that fast fluctuating environments still exhibit nonexponential dephasing for short time scales $\tau$: ${\omega }^{\prime }\tau <\sqrt{2}/\Theta$. (b) dc [solid (blue) line] and ac [dashed (red) line] magnetic field sensitivities as a function of $f_e$ for different contours of $B^{\prime }$. The largest effect on ${\eta }_{\mathrm{ac}}$ comes from FC regimes in which $\Theta \sim 1$, away from which ${\eta }_{\mathrm{ac}}\to \frac{\pi \exp (\tau /T_2{)}^3}{2{\gamma }_{p}C\sqrt{\tau }}=3\mathrm{nT}{\mathrm{Hz}}^{-1/2}$. Assumed parameter values are $T_2^{*}=1\mu \mathrm{s}$, $T_2=300\mu \mathrm{s}$, and $C=0.3$.Reuse & Permissions

Figure 4

(a) Minimum resolvable FC field strength, $B_{\min }$, versus environmental fluctuation rate, $f_e$, for $T=1\mathrm{s}$ averaging time. In contrast to the ac case, a FC detection requires no prior knowledge of fluctuation time scales. (b) Minimum resolvable ac field amplitude, $B_{\min }^{\mathrm{ac}}$, versus field oscillation frequency, ${\nu }_e$, for $T=1\mathrm{s}$ averaging time in the absence of environmental noise ($B^{\prime }=0$). Here we have assumed that the ac field is initialized in phase with the probe qubit and that the $\pi$ pulse of a spin-echo sequence coincides with the first zero crossing of the field.Reuse & Permissions