Zero-field identification and control of hydrogen-related electron-nuclear spin registers in diamond

TL;DR

The paper presents a zero-field DEER and NEETR framework to identify and control previously uncharacterized electron-nuclear defects in diamond at the single-spin level. By coupling ZF-DEER with NEETR, the authors extract principal hyperfine components and identify host nuclear spins for two defects, leading to the discovery of a novel hydrogen defect MIT1 and a nitrogen defect WAR9, with ab initio calculations guiding the structural assignments. Density functional theory provides self-consistent structural matches to the measured hyperfine tensors, while NEETR enables initialization, unitary control, and long-lived nuclear-spin coherence (T2 ≈ 1 ms) of the hydrogen defect, yielding a robust room-temperature quantum memory within hybrid electron-nuclear registers. Collectively, these results establish a concrete protocol for turning uncharacterized impurities into scalable quantum resources, expanding the defect landscape for quantum sensing and atomic-scale magnetic resonance imaging.

Abstract

Spin defects in diamond serve as powerful building blocks for quantum technologies, especially for applications in quantum sensing and quantum networks. Electron-nuclear defects formed in the environment of optically active spins, such as the nitrogen-vacancy (NV) center, can be harnessed as qubits to construct larger hybrid quantum registers. However, many of these defects have yet to be characterized, limiting their integration into scalable devices. Here, we introduce an approach to identify the hyperfine components and nuclear spin species of spin defects through measurements on a nearby NV center. This approach combines double electron-electron resonance performed at zero field (ZF-DEER) with nuclear-electron-electron triple resonance (NEETR), which we use to characterize two unknown defects at the single-spin level, yielding self-consistent results. These results provide a guide to resolving the defect structures using $\textit{ab initio}$ calculations, leading to the identification of a new hydrogen defect structure and an accurate match to a previously identified nitrogen defect. Building on the NEETR protocol, we then demonstrate initialization, unitary control, and long-lived coherence of the nuclear spin qubit of the hydrogen defect with $T_2 = 1.0(3)\,\mathrm{ms}$. Our characterization and control tools establish a framework to expand the accessible defect landscape for hybrid electron-nuclear registers and enable applications in quantum sensing, networks, and atomic-scale magnetic resonance imaging at room temperature.

Figures (11)

• Figure 1: Hyperfine component identification for X1 and X2 defects. (a) Double electron-electron resonance (DEER) performed under an external magnetic field ($B_0\approx365$ G) reveals the two electronic spin defects X1 and X2 coupled to the NV electronic spin. The two hyperfine transitions for each defect ($\omega_{e\pm}/2\pi$) are centered around $\gamma_eB_0 \approx 1020$ MHz, with hyperfine splittings $A_1 = 26.4(5)$ and $A_2 =8.6(4)\, \text{MHz}$, indicating both defects consist of an S = 1/2 electronic, I = 1/2 nuclear spin. Diagram above: the (larger) electronic spins of X1 and X2 are quantized along the external magnetic field direction parallel to the NV molecular axis, which is misaligned from each defect's principal hyperfine direction as indicated by the (smaller) nuclear spin direction. The hyperfine splittings as measured through the NV spin are determined by the principal components ($A_{\parallel}, A_{\perp}$) and this angular misalignment. Pulse sequence for DEER: a spin-echo is applied to the NV probe spin while sweeping the frequency of the target spin pulse, leading to phase accumulation of the NV spin when $\omega_e$ is on resonance and $\tau\sim1/(2d)$, where $d$ is the coupling strength frequency. (b) Principal hyperfine components for the defects are determined by repeating DEER at zero field (ZF-DEER) by probing the electron-nuclear transitions around their respective hyperfine splitting. Diagram above: at zero field the electronic spin is aligned along the principal hyperfine direction, leading to transition frequencies $\omega_{\mathrm{e},\pm}/2\pi = \left(A_{\parallel}\pm A_{\perp}\right)/2$ between Bell states. Two measurements were taken with different interaction times ($\tau = 8, 10 \, \mu\text{s}$) based on the different NV-X electron coupling strengths for X1 and X2. (c) With additional spins coupled to the NV (see Supplementary \ref{['sec:smMoredefects']}), we map out the spectrum for X1 and X2 transitions by measuring the coupling strength for each resonance dip. ZF-DEER with variable $\tau$ is performed with $\omega_e$ set to the frequencies corresponding to the colored dashed lines in (b), revealing two pairs of signals with matching coupling strength frequencies ($d_1,d_2 = 70, 47 \, \text{kHz}$), as confirmed by the overlapping Fast Fourier Transform (FFT) spectra on the right. We extract the hyperfine components for each defect using the frequencies from the Lorentzian fits in (b): $A_{\parallel,1} = 39(1)$ and $A_{\perp,1}=25(1)~\text{MHz}$ for X1, and $A_{\parallel,2} = 16(1)$ and $A_{\perp,2}=6(1)~\text{MHz}$ for X2. Details for NV data collection, error bars, and corresponding fits are included in Methods (\ref{['sec:methods']}C,D.)
• Figure 2: Nuclear spin identification for X1 and X2 defects. (a) Nuclear-electron-electron triple resonance (NEETR) pulse sequence and accompanying spin polarization diagram for the NV-X system (X, X-n represent the electronic and nuclear spins of the defect, respectively). Polarization is quantified by the difference in filled color between spin states (initially the NV is polarized in $\ket{0}$ while the X and X-n are mixed with each state 1/4 occupied). The NEETR sequence uses the NV as a probe to detect the defect's nuclear spin resonance through its electronic spin polarization. Hartmann-Hahn Cross Polarization (HHCP) is used to transfer polarization from the NV to X, conditioned on the nuclear spin state by driving a single hyperfine transition. By sweeping the frequency of the RF pulse applied to X-n, we can identify the two nuclear spin transitions when on resonance as the nuclear spin becomes partially polarized. This change in polarization is mapped to the electronic spin population and measured through the NV by repeating the conditional HHCP for readout. An additional $\pi$-pulse on the NV spin is applied every other sequence after initialization to reset the X nuclear spin polarization. (b,c) We perform the NEETR experiment on both X1 and X2 defects using the initial magnetic field conditions from DEER (\ref{['fig:DEER']}a) by sweeping the RF frequency around $A/2$. (b) The NEETR signal for X1 reveals the defect's nuclear spin resonance frequencies $\omega_{n\pm}$, with splitting $\Delta \omega_{n}$ consistent with the hydrogen gyromagnetic ratio, supporting the assignment of X1 as hydrogen-related. (c) The NEETR signal for X2 features nuclear spin resonances with splitting consistent with the $^{15}\mathrm{N}$ gyromagnetic ratio, supporting the assignment of X2 as nitrogen-related.
• Figure 3: (a) Model of the V-CH-V$^0$ complex corresponding to the identified MIT1 defect structure for X1. Gray atoms represent carbon, magenta for hydrogen, and dotted circles for vacancies. (b) Model of the N$^0_{\text{I}}$ complex corresponding to the WAR9 defect structure for X2. Nitrogen is represented by the larger blue atom.
• Figure 4: Universal control and coherence of the X1 hydrogen nuclear spin. (a) Applying the NEETR sequence (\ref{['fig:NDEER']}a) while on resonance with $\omega_{n+}$ for the X1 nuclear spin transition to achieve coherent control of the nuclear spin qubit (see quantum circuit of NEETR sequence above). The conditional HHCP steps implement an $i$SWAP between the NV and X electronic spins for a single hyperfine state. The selective nuclear spin drive achieves a controlled rotation for the nuclear spin state, conditioned on the electronic spin. Readout of the nuclear spin state is accomplished by repeating the $i$SWAP, mapping the change in X nuclear polarization to the electronic spin, which is then measured via the NV fluorescence. The signal shows several Rabi oscillations of the hydrogen nuclear spin with negligible decay. (b) Demonstrating full initialization of the hydrogen nuclear spin by performing sequential polarization transfer over the NV-X-Xn system. Both X1 hyperfine transitions are driven during HHCP for a complete NV-X $i$SWAP, and two conditional gates are applied to X1 for the electron-nuclear SWAP. We probe the nuclear spin polarization by measuring the DEER spectrum over the two hyperfine transitions. The amplitudes for each dip after the initialization sequence (purple) grow or shrink compared to the reference signal without initialization (red), confirming successful nuclear spin polarization with fidelity of 0.6(1) (Supplementary \ref{['sec:smFidelity']}). (c,d) Coherence measurements of the hydrogen nuclear spin qubit using the NEETR sequence with Ramsey and spin-echo evolution applied during the conditional $R(\theta)$ block (see insets). The last $\pi/2$-pulse has a modulated phase, with $\phi = 2\pi f_{\text{mod}}\tau$, to improve the estimate of the decay constant using a fit to an exponentially decaying cosine function. (c) Measuring the nuclear spin dephasing time with phase-modulated Ramsey at $f_{\text{mod}}= 20 \, \text{kHz}$, finding $T_2^{*} = 250(60) \,\mu\text{s}$. (d) Measuring the nuclear spin coherence time using phase-modulated spin-echo at $f_{\text{mod}} = 5 \,\text{kHz}$, finding $T_2 = 1.0(3)\, \text{ms}$.
• Figure S1: ZF-DEER characterization of other resonances (distinct from the X1 and X2 frequencies) indicating additional defects in the NV environment. (a) Measurement of the ZF-DEER spectrum (\ref{['fig:DEER']}b) at $\tau= 12 \,\mu\text{s}$ over three different averaging windows reveals several peaks with dynamic behavior. For each trace, we average for a minimum of approximately 10 hours to achieve sufficient SNR. The scans in blue and purple investigate the shifting resonances between 10-17 MHz, possibly due to a defect with a fluctuating charge state. The dashed lines indicate the resonances found in the main-text scan or from the additional scans shown here. Orange designates the X1 and X2 transitions. For the additional transitions, gray designates the peaks found only in the main-text scan, red for the static peak, and purple for the dynamic peaks. (b) We scan the interaction time in the ZF-DEER sequence with recoupling frequencies set to the resonances at the dashed lines (excluding the X1 and X2 transitions) to distinguish different defects based on their coupling strengths. Coupling strengths $d$ are estimated from fitting to an exponentially decaying cosine function. The traces at 15.2, 15.8, and 16.6 MHz have consistent coupling and appear within the same frequency scan in (a), suggesting they belong to the same defect.