(a) Fluorescence image of the diamond and a representation of the thin wire (80 μm diameter), which is used to produce small oscillating magnetic fields. A similar wire was used to produce the microwave field. A three-axis set of Helmholtz coils was used to produce B 0, while B MW was generated using a high frequency microwave source. The oscillating field B AC from the 80 -μm OD wire was produced using a function generator. (b) Schematic of modulated fluorescence detection technique, where frequency-modulated MW is applied. (c) Schematic of experimental setup. MO refers to the 20X microscope objective with NA of 0.4, and LF and DM are a long-pass filter (cut-off at 650 nm) and a dichroic mirror, respectively, and APD stands for avalanche photodetector. The two excitation spots (shown in the inset) were separated by ∼300 μm. The green refers to the 532 nm excitation, red to the fluorescence signal.
(a) Derivative spectra at optical excitation intensity of 2.3 MW/cm2 with various Rabi frequencies (), indicated in MHz in the figure. Center frequency shift due to heating effects was compensated for in the plot. All derivative spectra were measured with a microwave modulation amplitude of 250 kHz at a microwave modulation rate of 25 kHz. (b) A closeup of the curve for Rabi frequency of 0.06 MHz with an additional fit. Black circles indicate the experimental data, and the solid line shows a fit to the derivative of three summed Lorentzian line shape functions. Estimated from the ODMR spectrum was 130 ± 5 ns.
Comparison of simulation and experiment for a bandwidth measurement at laser intensity of 1.95 MW/cm2 and microwave field strengths, corresponding to MHz and 4.10 MHz, respectively. For MHz, the central microwave frequency was set to a resolved hyperfine peak at the edge of the derivative spectrum, which offset the microwave frequency by 0.6 MHz from the the nearest resonance of the ODMR spectrum. The magnetometer response at a given rate was characterized using frequency modulation of the microwave field with amplitude 1.0 MHz and modulation rate . The experimentally measured time constants usedforthe two NV-center ensemble simulation, described in Sec. III, were and (obtained from a biexponential fit to a repolarization curve), and . For MHz, the hyperfine splittings were not resolved, and the offset from resonance was 3.0 MHz. The modulation amplitude used for the measurement, as well as the time constants , used for the simulation, were the same as for MHz case. (Numbers in the figure correspond to the Rabi frequencies, and Exp and Sim refer to the experimental data and simulation data, respectively.)
Representative experimental data together with simulation data at an optical excitation intensity of 1.95 MW/cm2. Unlike Fig. 3, this simulation with 2 NV-center ensemble, use two sets of T 1 and T 2, i.e., , and , , which are NOT based on the measured values but adjusted to fit the data. (Numbers in the figure correspond to the Rabi frequencies, and Exp and Sim refer to the experimental data and simulation data, respectively.)
Experimentally estimated bandwidth in MHz is plotted as a function of the optical excitation intensity and the microwave Rabi frequency. The system shows saturation behavior at ∼0.6 MW/cm2 of optical excitation intensity, for 2.0 MHz.
Magnetic field sensitivity measurements in single modulation mode, using single fluorescence channels, labeled as APD1 and APD2 and a gradiometer with optical excitation intensity of 2.02 MW/cm2 and microwave Rabi frequency of 1.6 MHz, with one-second signal integration time. The inset shows the sensitivity as a function of optical excitation intensity using a single channel. Circles indicate measured data, and the solid line is a fit to Eq. (12).
Magnetic field sensitivity (nT/√Hz) of double modulation technique as a function of low modulation frequency (Hz) at various carrier frequencies (kHz). The optical excitation intensity was 2.3 MW/cm2, and the microwave-excitation strength corresponded to ω1/2π = 1.56 MHz.
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