Demonstration of NV-detected ESR spectroscopy at 115 GHz and 4.2 T

The nitrogen-vacancy (NV) center has unique properties that make it an excellent candidate for high sensitivity magnetic sensing.^1–3 The NV center is a two-atom defect in the diamond lattice, with the capacity for optical spin-state initialization and readout, long coherence times, and high sensitivity to external magnetic fields.^4–6 NV-detected electron spin resonance (ESR) offers the capability to detect a single or a small number of electron spins^7–12 and to investigate biological molecules at the single molecule level.^13,14 Such an ESR technique with single spin sensitivity potentially eliminates ensemble averaging in heterogeneous and complex systems and has great promise to directly probe fundamental interactions and biochemical functions. In ESR, the measurement of the g-factor is extremely useful for the identification of spin species. However, a featureless “g = 2” signal is often observed, causing the spectral overlap with target ESR signals, which may prevent spin identification.^14–17 

Similar to nuclear magnetic resonance (NMR) spectroscopy, pulsed ESR spectroscopy at higher frequencies (HFs) and magnetic fields becomes more powerful for finer spectral resolution, enabling clear spectral separation of systems with similar g values.^18,19 This is advantageous in the investigation of complex and heterogeneous spin systems.^20,21 A high frequency of Larmor precession is also less sensitive to motional narrowing, enabling the ESR investigation of structures for molecules in motion.^22,23 In addition, a high Larmor frequency provides greater spin polarization: improving sensitivity^18,19 and providing control of spin dynamics.^24,25 On the other hand, pulsed HF ESR often has the disadvantage of long pulse times due to low HF microwave power. The low microwave power limits the excitation bandwidth and, consequently, the sensitivity of pulsed ESR measurements. NV-detected ESR (indicated as NV-ESR) will overcome this limitation and improve the sensitivity of HF ESR drastically. However, only a few investigations of NV centers have been performed at high magnetic fields,^26–28 and NV-ESR has not been demonstrated at a high magnetic field.

In this work, we demonstrate NV-ESR at a Larmor frequency of 115 GHz, corresponding to a magnetic field of ∼4.2 T. The HF NV-ESR experiment is performed with both an ensemble and a single NV system. Within the ensemble experiment, we start the characterization of NV centers using optically detected magnetic resonance (ODMR), a measurement of Rabi oscillations, and a spin echo measurement to determine the spin decoherence time (T₂). Then, we utilize a double electron-electron resonance (DEER) sequence to perform NV-ESR spectroscopy of single-substitutional nitrogen (P1) centers in diamond. We find that the observed NV-ESR spectrum is in excellent agreement with the spectrum of P1 centers. In the single NV-ESR experiment, we start the identification and the characterization of a single NV center. For high fidelity coherent control, we apply chirp pulses that improve population inversion and optical contrast. We then implement a DEER sequence with chirp pulses. The observed NV-ESR signal is in agreement with P1 centers. This work provides a clear demonstration of HF NV-ESR and provides a foundation for the study of external spins with high spectral resolution NV-ESR. Furthermore, the presented experimental strategies are applicable to NV-ESR at higher magnetic fields.

Figure 1 shows an overview of a home-built HF ODMR system used in the experiment. The HF ODMR system consists of a HF microwave source (Virginia Diodes, Inc.), quasi-optics, a 12.1 T cryogenic-free superconducting magnet (Cryogenics), and a confocal microscope system for ODMR. The HF ODMR system is built upon the existing HF ESR spectrometer, which was described previously.^29,30 Therefore, the system enables in situ experiments of both ESR and ODMR. As seen in Fig. 1, the HF source contains two microwave synthesizers (MW1 and MW2), a power combiner, and a frequency multiplier chain. An IQ mixer (Miteq) controlled by an arbitrary wave generator (AWG; Keysight) has recently been implemented in MW1 for pulse shaping of high-frequency microwaves. Two synthesizers are employed for DEER experiments. The frequency range of the microwave source is 107–120 GHz and 215–240 GHz. In this experiment, we use a frequency range of 107–120 GHz where the output power of the HF microwave is 480 mW at 115 GHz. HF microwaves are propagated to a sample using a home-built quasi-optical bridge and a corrugated waveguide (Thomas-Keating). As demonstrated previously, quasi-optics are suitable for a high-frequency ESR spectrometer because of their capacity for low-loss and broadband propagation.^31,32 A sample is mounted at the end of the corrugated waveguide and positioned at the field center of a room temperature bore within a superconducting magnet system. No microwave resonator is employed for implementation of wide bandwidth DEER techniques. The magnetic field at the sample is adjustable between 0 and 12.1 T. For the single-NV HF ODMR experiment, we employ a conventional confocal microscope setup routinely used for NV ODMR experiments.^33,34 The details of the single-NV ODMR system have been described previously.²⁶ For the ensemble HF ODMR experiment, we direct the fluorescence (FL) to a photodiode (Thorlabs), implemented before the coupling stage to the single mode fiber. This is connected to a fast oscilloscope (Le Croy) for the measurement of the time-domain FL signal. The detection volume in the ensemble experiment is in the range of a few μm³. The results presented here have been obtained using two samples, both are 2.0 × 2.0 × 0.3 mm³ sized, (111)-cut high-pressure high-temperature type-Ib diamonds from Sumitomo Electric Industries. The crystal used for the single NV experiment had been previously shown to contain single NV centers with reasonably long spin-relaxation times and coupling to P1 centers.³⁴ The other crystal, used for the ensemble experiment, was subjected to successive irradiation using high energy (4 MeV) electron beam and annealing processes (at 1000 °C) in order to increase the NV center density. Exposure to a total fluence of $1.2×1018$ e⁻/cm² resulted in an NV/N ratio of approximately 8%, as determined from the X-band (∼9 GHz) ESR spectrum of the sample (see the supplementary material). Characterization using ensemble HF ESR measurements reveals strong ESR signals from both P1 and NV centers, indicating that both NV and P1 concentrations are more than 1 ppm.

We first perform ODMR of ensemble NV centers. This experiment was performed by monitoring the FL intensity, while the frequency of a 500 ns MW pulse was varied. As seen in Fig. 2(a), a reduction in FL was observed at 114.78 GHz and 120.51 GHz, which correspond to the lower (⁠$|ms=0⟩↔|ms=−1⟩$⁠) and upper (⁠$|ms=0⟩↔|ms=+1⟩$⁠) transitions of a [111] oriented NV with a polar angle of 1.8 degrees. By fixing the frequency at 114.78 GHz and varying the length of the pulse, Rabi oscillations were observed as seen in Fig. 2(b). From this measurement, $π/2$ and π pulse lengths of 212 and 402 ns were extracted, respectively. The extracted pulse times were used in a spin echo experiment. A spin echo relaxation time of 2.4 ± 0.3 μs was observed, as seen in Fig. 2(c). We next perform NV-ESR using the ensemble NV system with a DEER sequence. In the DEER sequence, a separate MW pulse (MW2) is applied during the spin echo sequence as shown in the inset of Fig. 3. When the frequency of the pulse matches the ESR frequency of target spins, the target spins flip, and then the dipolar field from the target spins experienced by the NV center changes. This change results in a reduction of the refocused echo intensity. In this manner, an ESR signal of weakly dipolar coupled spins located in the nanometer scale region surrounding the NV center can be detected.^8,9 As shown in Fig. 3, the application of this pulse sequence reveals five distinct reductions in FL intensity at 117.49, 117.52, 117.61, 117.69, and 117.72 GHz. These dips are in excellent agreement with the spectrum simulated from the P1 center's Hamiltonian (S = 1/2, I = 1, g = 2.0024, $A⊥=82$ MHz, and $A∥=114$ MHz).^35,36

Having resolved the spectrum of P1 centers from the ensemble system, we next discuss the demonstration of NV-ESR using a single NV center. For this, we begin by taking a FL image of the diamond, as is shown in Fig. 4(a). From the observed FL image, a well isolated FL spot is selected (denoted as NV1). An autocorrelation measurement performed on the FL spot, as shown in the upper inset of Fig. 4(a), confirms that the observed FL is from a single quantum emitter. As can be seen in the lower inset of Fig. 4(a), upon increasing the magnetic field, we observe the level anti-crossing of both the ground and excited states, thereby confirming the FL spot as a single NV center.^26,37 After the detection of a single NV center, the superconducting magnet was set in a persistent field mode at ∼4.2 T. The magnetic field strength was then measured via an in situ ESR measurement of P1 centers. Next, we perform pulsed ODMR on the NV center and resolve clear reductions in FL intensity at both 114.80 and 120.53 GHz, corresponding to the lower and upper transitions (data not shown). From these ODMR signals, we determined the NV center to be aligned in the magnetic field with a polar angle of 1.6° from the [111] axis. We next perform a measurement of the Rabi oscillations for NV1 at 114.80 GHz. The FL intensity against the pulse length is shown in Fig. 4(b), which shows clear Rabi oscillations. Analysis of the signal was then performed by simulating dynamics of a two-level system using the Liouville–von Neumann equation with a resonance-frequency distribution due to the hyperfine coupling of ¹⁴N (2.2 MHz). As shown in Fig. 2(b), the experiment and the simulation show excellent agreement. The analysis also reveals that the limited excitation bandwidth results in incomplete population inversion of the NV center spin state. The estimated population inversion is only ∼40%.

The small population inversion of a rectangular pulse is a significant challenge for the NV-ESR experiment because of errors in the preparation and readout of the quantum coherent state used in the DEER sequence. The result can be poor signal-to-noise in the measurement. To overcome this, we employ a pulse shaping technique. The recent development of high temporal resolution (sub-ns) arbitrary waveform generators has triggered significant progress in various pulse shaping techniques for ESR. Here, we focus on chirp pulses, a class of pulses that have been used to demonstrate broadband control over wide frequency ranges. Chirp pulses are now routinely used in ESR spectroscopy at X- and Q- (34 GHz) bands.^38–40 In addition, it has recently been demonstrated at a frequency of 200 GHz.⁴¹ Chirp pulses offer wider spectral excitation, an ability to correct pulse imperfections, and generally higher fidelity than rectangular pulses.⁴² The effectiveness of chirp pulses is due to the principle of adiabatic passage, whereby population transfer is achieved by sweeping an applied electromagnetic field through resonance at a sufficiently slow rate.^43–45 

Here, we utilize a linear frequency-swept chirp pulse at 115 GHz. Figure 4(c) shows the efficiency of chirp pulses with two different frequency-swept rates, 10 MHz-swept at durations of 1 μs and 10 μs. A clear increase in contrast is observed via the application of chirp pulses, indicating an improvement in both the population transfer and the excitation bandwidth compared to the rectangular pulse. T₂ was also determined to be ∼20 μs from a spin echo measurement (see the supplementary material). Furthermore, we use the Liouville–von Neumann equation to calculate the observed behavior as a function of frequency based on the chosen pulse length and sweep width. As seen in Fig. 4(c), the observed result is in good agreement with the simulation, confirming that the usage of chirp pulses increases population transfer for the NV center to nearly 100%.

We next utilize chirp pulses to perform NV-ESR with the NV center by applying three pulses with a fixed delay between them. Similar to the previous work,³⁴ a long MW2 pulse (⁠$πMW2=1$ μs) was utilized for high spectral resolution NV-ESR. The result of this experiment is shown in Fig. 4(d). Clear reductions in intensity are observed compared to a sequence without the MW2 pulse. The obtained spectrum agrees very well with the three resolved peaks and the spectral splitting of the P1 center.^35,36 In addition, the ∼2 MHz linewidth of the observed peaks is of similar width to high resolution, inhomogeneously broadened NV-ESR signals resolved at low magnetic fields.³⁴ 

In summary, we have demonstrated NV-ESR of P1 centers at a Larmor frequency of 115 GHz and the corresponding magnetic field of 4.2 T. We have also shown that the application of chirp pulses improves the excitation bandwidth and population inversion of the NV center spin-state at high magnetic fields. The high magnetic field achieved in this measurement represents a step toward high-resolution NV-based spectroscopy. In the future, the presented HF ODMR system and technique can be further extended for the operation at a ESR Larmor frequency of 230 GHz (corresponding to 8.2 T) for higher spectral resolution. HF NV-ESR offers insight into complex radical spin systems, with high spectral resolution and the capability of the detection of nanoscale heterogeneity of external spins, spectral separation from unwanted ESR signals such as diamond surface spins, and applications for the study of spins within complex intracellular environments. Furthermore, the present demonstration sets the basis for HF NV-detected NMR spectroscopy, enabling high resolution NMR of a small number of molecules in spatially and temporally heterogeneous environments. HF NV-detected NMR spectroscopy will be useful for a variety of investigations, including structures and dynamics of biomacromolecules and chemical environments of solid-state surfaces and interfaces.

See the supplementary material for the X-band ESR characterization of the ensemble NV sample and the T₂ data of the single NV sample.

This work was supported by the National Science Foundation (Nos. DMR-1508661 and CHE-1611134), the USC Anton B. Burg Foundation, and the Searle Scholars Program (S.T.). K. H. acknowledges support from the Julien Schwinger Foundation. Steffen J. Glaser is acknowledged for helpful discussion regarding pulse shaping.