Detection of electron paramagnetic resonance of two electron spins using a single NV center in diamond

A nitrogen-vacancy (NV) center is a fluorescent impurity center existing in the diamond lattice.¹ The unique electronic structure of the NV center allows the polarization and readout of the spin state through optical excitation and the optically detected magnetic resonance (ODMR) technique.^2–4 The NV center also has a long spin coherence time at room temperature.^5–7 It has been shown to be a promising quantum sensor, enabling measurement of an extremely small magnetic field,^8–11 magnetic resonance spectroscopy with single spin sensitivity,^12–19 and quantum simulations.^20–22 

A system with interacting spins is a great platform for fundamental physics and applications in quantum information science. For example, an interacting NV spin system is a great candidate for building a quantum sensing network for quantum entanglement sensing that provides enhanced sensitivity.²³ Interacting spin systems also exhibit novel phases and dynamics, such as spin liquids, time crystals, and non-equilibrium dynamics.^24–27 NV-detected electron paramagnetic resonance (NV-EPR) spectroscopy with a single NV center is a powerful method to study nanoscale environments of interacting electron spins. NV-EPR can determine the number of the detected spins and identify the type of the detected spins. It can also determine the coupling strengths between the NV and each surrounding spin.^14,18 NV-EPR has been demonstrated to detect P1 centers, N2 centers, and other unidentified spins.^18,28–32 Moreover, electron spins on diamond surfaces have been detected.³³ A characterizable and controllable network of spins can be used for entanglement-enhanced surface quantum sensing. However, only a few demonstrations have been performed to determine the number of interacting electron spins and individual coupling strengths to the NV center.^13,33 Identifying and modeling such configuration remains a challenge for single NV-EPR detection.

In this work, we discuss the demonstration of NV-EPR spectroscopy of a few electron spins. We employ a single shallow NV center in diamond as a sensor and utilize a double electron–electron resonance (DEER) technique to show the detection of EPR signals of surrounding spins. The observation of the NV-EPR signal confirms the detection of spins. The type of the detected spin is analyzed from their g-values and hyperfine splitting. Moreover, we present a simple model to determine the number of the detected spins and the strengths of their magnetic dipole interactions. We find a single NV center coupled to two electron spins with dipolar couplings of 1.12 ± 0.13 and 2.24 ± 0.17 MHz from the analysis of the NV-EPR signal. The presented spin system will be useful for the investigation of quantum effects that require a low number of spins³⁴ or open quantum dynamics.³⁵ The experimental methods can be used to realize entangled quantum reporters for quantum sensing.

In this study, we employ single NV centers in a diamond crystal sample purchased from Qnami.³⁶ The sample is a (111)-cut, specially designed diamond. Shallow NVs (∼10 nm depth) were created with nitrogen ion implantation with an energy of 6 keV and a subsequent annealing process. The sample has a unique nano-pillar structure that allows easy isolation and identification of single NV centers. We have studied four single NV centers in this sample. In the present paper, our investigation focuses on one of the single NV centers with a unique NV-EPR signal (denoted as NV1). The experimental results on the others (NV2-4) are also presented in the supplementary material. The setup of the experiment is illustrated in Fig. 1. The diamond sample is mounted on an XYZ piezo stage. A permanent disk magnet is placed under the stage to provide a static magnetic field (B₀) along the [111] direction of the diamond lattice. For ODMR spectroscopy of the NV center, two channels of microwave (MW1 and MW2) excitation are applied using sources (Stanford SG386) and an amplifier (Mini-Circuits ZHL-15W-422-S+). Both MW1 and MW2 excitations are applied with a 20 μm diameter gold wire attached close to the top of the sample. A diode-pumped solid-state laser (CrystaLaser, 100 mW) and a microscope dry objective (ZEISS, 100×, NA = 0.8) are employed for the laser excitation. Photoluminescence (PL) from the NV center is collected by the same objective and redirected by a dichroic mirror toward an avalanche photon detector (Excelitas, SPCM-AQRH-13-FC). A central computer is used to control the microwave and laser pulses and analyze the photon count signal.

Next, we characterize the spin decoherence time (T₂) using a Carr–Purcell–Meiboom–Gill (CPMG) sequence. The particular sequence used here consists of eight π pulses, which is referred to later as a CPMG-8 sequence [see Fig. 3(a)]. In the CPMG-8 experiment, after the preparation of the superposition state $12(|+1〉+|0〉)$ by the (π/2)_Y pulse, a chain of (π)_X pulses is applied at every 2τ to keep the coherence state for an extended period. The resultant coherent state is mapped into the |m_s = 0⟩ state with the application of the second (π/2)_Y pulse (SIG1). In addition, in a different signal channel, we use a (3π/2)_Y pulse instead of the (π/2)_Y pulse to map the state into the |m_s = 1⟩ state (SIG2). Two signal channels are used to improve the signal-to-noise ratio (SNR) by removing systematic noise and doubling signal contrast. PL intensity is normalized using the same method used in the Rabi oscillation experiment. As shown in Fig. 3(b), an oscillating and decaying difference in the normalized PL is observed. These features in the echo signal are attributed to the electron spin echo envelope modulation (ESEEM) effect due to hyperfine interaction with nearby nuclear spins.⁴ As shown in Fig. 3(c), we found that the simulation of the ESEEM signal can explain the observed signal taken with the CPMG sequence. In the simulation, we consider bath ¹³C nuclear spins and a ¹³C individual spin with the hyperfine couplings of A = 0.314 MHz and B = 2.827 MHz. We also obtained the spin decoherence time (T₂) to be 38 ± 3 μs. This detection of the individual ¹³C nuclear spin was observed only with NV1, not with other NVs studied in this work. The details of the simulation are included in the supplementary material.

Next, we introduce another NV-EPR experiment to determine the number of spins and strength of interactions detected in the NV-EPR signal. The sequence is shown in Fig. 5(a). This sequence is modified from the CPMG-DEER sequence to measure the Rabi oscillations of the NV-EPR signal, so we call it a DEER-Rabi sequence. In the DEER-Rabi sequence, the MW2 frequency is fixed at the EPR signal, and the pulse length (T_MW2) is varied while keeping the total echo evolution time fixed. Both SIG1 and SIG2 channels are used as well for better SNR. Data are shown in Fig. 5(b). The normalized DEER-Rabi signal (SIG2-SIG1) shows a strong oscillation in the population recovery [shown in Fig. 5(c)]. The observed oscillations are due to the change in dipole field from spins felt by the NV coherence state. The MW2 pulses rotate the spins according to the pulse length, changing the strength of the field along the NV axis. The accumulated phase shifts, therefore, undergo oscillations. To analyze the signal [shown in Fig. 5(c)] with Eq. (5), we consider three situations where the number of target spins ranges from 1 to 3. In the fit, the dipole interaction strength and decay constant are treated as fitting parameters. We set the range for interaction strength to be 2–312.5 MHz. The lower bound is taken to have one full oscillation in the total recorded pulse length, and the higher bound is taken to have one full oscillation for every four data points. This follows from the frequency resolution being 1/(measurement time) and maximum frequency being (sample rate)/2 for a discrete Fourier transform analysis. The fitted lines are plotted as dotted lines in Fig. 5(c). The adjusted R-square value $(1−(1−∑(yi−ŷi)2∑(yi−ȳ)2n−1n−k−1))$ is used, where k = 3. In general, the value is between 0 and 1, and the closer case to 1 means better agreement. The two electron spin model has the best fit with the adjusted R-square value of 0.314, while the one spin model gives 0.269 and the three spin model gives 0.233. From the fitting result, two interaction strengths are ω₁ = 2π × (1.12 ± 0.13) MHz and ω₂ = 2π × (2.24 ± 0.17) MHz. The time constant T₀ is fit to be 0.34 ± 0.06 μs. The inset of Fig. 5(c) summarizes the detected two electron spins and one nuclear spin from the present study with NV1.

Finally, we discuss the origin of the NV-EPR signal observed in the present investigation [see Figs. 4(c) and 4(d)]. The signal is a single peak of coherence population difference centered at 914.7 ± 0.9 MHz with a width of 9 ± 2 MHz. No signature of the hyperfine splitting is observed. We attribute this signal to an electron spin with S = 1/2 and g = 2.009 ± 0.003. Since there are no signatures of hyperfine peaks, the signal is not from P1 centers, which are commonly observed in diamonds with a high nitrogen concentration. The identification of the detected spins remains unclear, but based on the S and g-value and lack of hyperfine splitting, possible candidates of the observed spins are the tri-Nitrogen W21 center^38,39 and surface spins.^32,40,41

In summary, we demonstrated the detection of EPR from two electron spins using a single NV center in diamond. CPMG-DEER and DEER-Rabi sequences are used to study the spin interactions. The observed NV-EPR signal is in the absence of strong hyperfine peaks, and further measurement of Rabi oscillations of the signal suggests the interaction is of a single NV center with two electron spins. The physical system and method presented in this paper allow easy identification of a single defect center coupled to a small number of spins and characterization of the interaction strength. The analysis of the NV-EPR signal presented can be a method to distinguish the number of interacting spins up to five, which is limited by the detection time window of the oscillations.

The non-equal but measurable interaction strength is favorable in studying non-equilibrium quantum dynamics. Investigation of quantum phase dynamics, such as spin liquids or discrete time crystalline (DTC), requires interacting spin systems with disordered structures.^24,27 A kagome lattice formed by Cu²⁺ ions⁴² and a honeycomb lattice formed by Ru³⁺ ions⁴³ have been actively researched materials for the realization of spin liquid. This multi electron spin system could be a material to look for these emergent quantum effects with the similarity of being a spin 1/2 magnetic disordered type of material. A chain of nine ¹³C nuclear spins in diamond has been shown to be a programmable spin-based DTC.⁴⁴ The characterizable electron spin system in this study is potentially a smaller-sized system to realize DTC. Good knowledge of the interaction strengths in a spin system will also be significant in better characterization of non-classical correlations, namely, quantum entanglement, which can be key in modeling open quantum dynamics and developing entangled quantum sensing. Quantum-enhanced NMR with a 9.4-fold sensitivity increase has been demonstrated by entangling nine proton spins with a ³¹P spin.⁴⁵ The electron spins detected in this study can also be simultaneously controlled and potentially achieve entanglement enhancement beyond the standard quantum limit. In addition, further study can be done to reveal more information about the nature of the spin species and improve the understanding of the decoherence of shallow NV centers, paving the pathway to higher standard engineering for quantum sensing applications.

The supplementary material includes a discussion and simulation of the ESEEM effect observed in the experiment and additional measurement results on the other NV centers.

This work was supported by the National Science Foundation (Grant Nos. ECCS-2204667, CHE-2404463, and CHE-2004252 with partial co-funding from the Quantum Information Science program in the Division of Physics), the USC Dornsife, the USC Anton B. Burg Foundation, and the Searle Scholars Program (ST).

The authors have no conflicts to disclose.

Yuhang Ren: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (equal); Methodology (equal); Project administration (supporting); Resources (supporting); Software (supporting); Supervision (supporting); Validation (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Susumu Takahashi: Conceptualization (equal); Data curation (supporting); Formal analysis (equal); Funding acquisition (lead); Investigation (equal); Methodology (equal); Project administration (lead); Resources (lead); Software (lead); Supervision (lead); Validation (equal); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.