Nuclear quadrupole resonance spectroscopy with a femtotesla diamond magnetometer

Abstract

Radio frequency (RF) magnetometers based on nitrogen vacancy centers in diamond are predicted to offer femtotesla sensitivity, but previous experiments were limited to the picotesla level. We demonstrate a femtotesla RF magnetometer using a diamond membrane inserted between ferrite flux concentrators. The device provides ~300-fold amplitude enhancement for RF magnetic fields from 70 kHz to 3.6 MHz, and the sensitivity reaches ~70 fT√s at 0.35 MHz. The sensor detected the 3.6-MHz nuclear quadrupole resonance (NQR) of room-temperature sodium nitrite powder. The sensor's recovery time after an RF pulse is ~35 μs, limited by the excitation coil's ring-down time. The sodium-nitrite NQR frequency shifts with temperature as -1.00±0.02 kHz/K, the magnetization dephasing time is T₂*=887±51 μs, and multipulse sequences extend the signal lifetime to 332±23 ms, all consistent with coil-based studies. Our results expand the sensitivity frontier of diamond magnetometers to the femtotesla range, with potential applications in security, medical imaging, and materials science.

Fig. 1.. Experimental setup and RF detection scheme.

(A) Schematic of the experimental setup for detecting RF test fields. A permanent magnet (not shown) outside the Al shield was used to apply weak bias magnetic fields along the z axis, B₀ = 2 μT to 15 μT. Additional details of the setup can be found in Materials and Methods, section S1, and (3). (B) Diamond RF magnetometry is performed with a continuous series of repeated XY8-N pulse sequences on the NV electron spins (8). Each XY8-N sequence begins and ends with a resonant MW π/2 pulse. Between the π/2 pulses, 8N resonant π-pulses, spaced by 2τ = 1/(2f_test), are applied with alternating phase. Following each XY8-N sequence, a 12-μs laser pulse (0.2 W and 532 nm) is applied for optical readout and repolarization of the NV centers. The resulting time trace of NV fluorescence readouts is proportional to an aliased version of the RF test field.

Fig. 2.. Femtotesla diamond RF magnetometry.

(A) Real-time NV fluorescence signal with (blue) and without (red) ferrite cones in the magnetometer assembly. In each case, an XY8-4 synchronized readout sequence was used, and a 0.35-MHz test field with 100 pT_rms amplitude was applied. The NV fluorescence photodetector voltage is converted to magnetic field units using the procedure described in section S3a. For the same applied field amplitude, the photodetector voltage signal with cones is ∼220 times larger than that without cones, primarily because of the flux concentrator enhancement (and, to a lesser extent, differences in the photon collection efficiency). A digital 4.5-kHz low-pass filter was applied to the data without cones for better visualization. (B) Fourier transform spectra of the NV signals with and without the cones. No digital filtering was applied. The noise floor reaches ∼70 fT s^1/2 with the cones and ∼18 pT s^1/2 without them. A reference spectrum (green), obtained by detuning the MW frequency 200 MHz off the NV resonance, shows an effective noise floor of ∼60 fT s^1/2. Peaks due to the test field appear prominently, but there are several smaller peaks in the spectra. The features that are absent in the MW off resonance spectrum are likely from magnetic noise. The remaining features are of unknown origin (section S4). (C) Noise floor with the cones present as a function of acquisition time, t. (D) Ferrite cone enhancement factor versus the test field frequency (section S3b). (E) Diamond RF magnetometer sensitivity as a function of test field frequency with (blue circles) and without (red squares) the ferrite cones (section S4). For all data in this figure, except for the “MW off resonance” spectrum in (B), the MW frequency was tuned to one of the NV f_± resonances.

Fig. 3.. NQR setup.

(A) Schematic of the setup used for NQR spectroscopy. A bias field B₀ ≈ 15 μT is applied along the z axis. A NaNO₂ sample is housed in a plastic cylinder container and placed d ≈ 4 mm above the ferrite-cone diamond RF magnetometer. A resonant RF coil is wrapped around the sample container. The 3.6-MHz NQR transition of ¹⁴N nuclei in NaNO₂ is excited by applying RF pulses along the z axis. The resulting oscillating nuclear magnetic field is also along the z axis and is simultaneously detected by the ferrite-cone diamond RF magnetometer and the resonant RF coil (see section S5c). (B) Energy levels and nuclear spin transitions of ¹⁴N in NaNO₂ at room temperature and low (≲1 mT) magnetic field. (C) Initial magnetic field amplitude within the diamond, B_gap,i (left axis), and equivalent magnetic field, B_equiv,i = B_gap,i/300 (right axis), as a function of sample volume. Expt., experiment. (D) Pulse sequence used for NV NQR detection (section S5a). After an RF excitation pulse, an XY8-20 synchronized readout pulse sequence is used to detect an aliased version of the nuclear AC magnetic field. The entire sequence is repeated every T_rep = 0.5 s.

Fig. 4.. NQR spectroscopy of ¹⁴N in NaNO₂.

(A) Room-temperature time-domain NQR signal of ¹⁴N in a 21-g NaNO₂ powder sample acquired by the resonant RF coil (top) and diamond RF magnetometer (bottom). A 50-μs RF pulse at 3605 kHz was used to excite the sample via the resonant RF coil with loaded quality factor Q ≈ 23 (see section S5c). The sequence was repeated every 500 ms, and the signal was averaged over 86,000 repetitions. A digital band-pass filter is applied for better visualization: 3.58 to 3.63 MHz for the coil signal and 4.6 to 11.7 kHz for the NV signal. (B) Imaginary part of the Fourier transform of the time-domain NQR signals shown in (A), along with Lorentzian fits. (C) NQR signal amplitude as a function of RF pulse amplitude, V_rf (measured in volts, before amplification), applied at 3607.5 kHz for 300 μs. For each RF pulse amplitude, the imaginary part of the Fourier transform of the first 810 μs of the signals is calculated such that the NQR resonance is contained in a single frequency point. The value of that point is taken as the NQR amplitude, and the error bars are the SD of points within a 5-kHz band near resonance. The dashed black line is a fit to a function $J_{3/2}(\mathrm{\alpha })/\sqrt{\mathrm{\alpha }}$ with the first peak occurring at the nutation angle α = 119° (49, 54). (D) NV NQR spectra (imaginary part of Fourier transform) obtained for three different ambient temperatures, along with Lorentzian fits. RF pulses were applied at 3605 kHz for 50 μs. (E) NQR resonance frequency as a function of ambient temperature, along with linear fit.

Fig. 5.. NV NQR recovery time.

(A) Time-domain NV NQR signal of 4 g of NaNO₂ powder enclosed in a Q ≈ 8 resonant RF coil. The RF pulse was applied at 3608 kHz for 200 μs. A digital band-pass filter (4.7 to 10.8 kHz) was applied for better visualization. (B) NV NQR spectrum (absolute value of Fourier transform) for three different deadtimes. T_dead is defined in Fig. 3D.

Fig. 6.. SLSE NV NQR signal.

(A) SLSE pulse sequence. Following an initial RF pulse, 100 echo pulses are applied every 2 ms. All RF pulses are applied at 3608 kHz for 50 μs (α ≈ 119°), and the initial pulse has a 90° phase shift with respect to all the echo pulses. Meanwhile, a synchronized XY8-20 MW pulse sequence is applied to the NV centers, with f_ref = 3600.07 kHz. The entire sequence is repeated every second. No additional phase cycling was used. (B) Time-domain NV SLSE signal (coherent average of the first 20 echos) from the 21-g sample. (C) SLSE NQR spectrum obtained from the absolute value of the Fourier transform of data in (B). (D) SLSE signal magnitude as a function of the time passed since the first RF pulse. The fitted exponential decay constant is $T_2^{\mathrm{SLSE}}=332\pm 23\mathrm{ms}$. (E) SNR of NV NQR signals as a function of total acquisition time, t, for both SLSE and single–RF pulse protocol. The dashed black lines are fits to a $\sqrt{t}$ dependence.