Mesoscopic Spin Coherence in a Disordered Dark Electron Spin Ensemble

Abstract

Harnessing dipolar spin environments as controllable quantum resources is a central challenge in solid-state quantum technologies. Here, we report the observation of a coherent mesoscopic spin state in a disordered ensemble of substitutional nitrogen (P1) centers in diamond. An iterative Hartmann-Hahn protocol transfers polarization from dense nitrogen-vacancy (NV) centers to a P1 ensemble, yielding a 740-fold enhancement over room-temperature thermal equilibrium as revealed by differential readout. The resulting mesoscopic P1 spin ensemble exhibits collective Rabi oscillations and long-lived spin-lock and Hahn-echo coherences. We identify a crossover in the saturation polarization arising from the competition between coherent driving and local disorder, providing a quantitative measure of the system's intrinsic disorder. These results establish a foundation for utilizing dark electron spin ensembles as robust resources for quantum sensing and quantum many-body simulation.

Figures (4)

• Figure 1: NV-P1 hybrid electron spin system and polarization transfer protocol. (a) Atomic structures of the NV (left) and P1 (right) centers. Spheres represent carbon atoms (gray), nitrogen atoms (blue), and vacancies (light gray). The P1 JT axis is highlighted in red. Blue and orange arrows denote NV and P1 electron spins, respectively. (b) HH condition. Two spin species with distinct resonance frequencies $\omega_\text{NV}$ and $\omega_\text{P1}$ are resonantly driven at Rabi frequencies $\Omega_\text{NV}$ and $\Omega_\text{P1}$, respectively. In the dressed-state basis $\{|+\rangle_d, |-\rangle_d\}$, the energy splittings are matched when $\Omega_\text{NV} = \Omega_\text{P1}$. (c) P1 electron spin resonance spectrum measured via DEER. The hyperfine interaction and JT distortion result in five visible spectral subgroups with population fractions of $\{1,3,4,3,1\}/12$. We address a P1 subgroup with a population fraction of 3/12 (indicated by an arrow) for polarization transfer measurements. The solid red line represents a multi-Lorentzian fit. (d) Measurement of the HH resonance condition. NV SL contrast is plotted as a function of the P1 Rabi frequency $\Omega_\text{P1}$, with $\Omega_\text{NV}=3.95$ MHz. The solid line represents a Lorentzian fit. (e) Iterative polarization transfer protocol. The sequence comprises optical NV initialization followed by interaction with the P1 ensemble under the HH condition. This cycle is repeated to accumulate polarization in the P1 ensemble. Error bars represent s.e.m.
• Figure 2: Polarization transfer pulse sequences and polarization dynamics. (a) Detailed pulse sequences. Light (dark) colors represent microwave pulses along the $x$ ($y$) axis. The polarization transfer stage involves 5 μs of DSL under the HH condition and 5 μs of laser illumination. In the subsequent readout stage, the signal is obtained by sweeping the duration $t$ of the second DSL sequence. For the NV (blue), the final $\pi/2$ pulse employs phase cycling ($\pm$) for common-mode noise rejection. For the P1 (orange), the pulses in the dotted box prepare the P1 bath polarization parallel ($\uparrow\uparrow$) or antiparallel ($\uparrow\downarrow$) to the NV. In the absence of these pulses, the sequence measures the reference bare NV SL. (b) Normalized SL signal $C$ for parallel and antiparallel configurations ($\Omega=6.40$ MHz). Data are shown for the thermal state ($N=0$, black) and after iterative transfer ($N=32$, red). Dashed lines indicate stretched exponential fits. (c) Signal difference $\Delta C$ versus SL duration $t$ for varying cycle numbers $N$. Dashed lines are exponential fits. Error bars represent s.e.m.
• Figure 3: Coherent control and relaxation dynamics of the polarized P1 ensemble. (a) Collective Rabi oscillations of the P1 bath measured after $N=16$ transfer cycles. The solid red line represents a fit to a damped cosine function. (b) FFT spectra of the Rabi signal. A distinct frequency component appears for the polarized state ($N=16$, black), whereas no signature is visible for the thermal state ($N=0$, gray). (c) Rotating-frame spin relaxation time ($T_{1\rho}$) measured via SL. (d) Measured Hahn-echo spin dephasing time ($T_2$). Dashed red lines in (c) and (d) are fits to exponential decays. Error bars represent s.e.m.
• Figure 4: Competition between coherent driving and disorder. (a) Quasi-equilibrium amplitude $A$ versus cycle number $N$ for various P1 Rabi frequencies $\Omega$. The signal saturates as the polarization transfer rate balances with dissipation. Dashed lines are exponential fits. (b) Dependence of the saturation amplitude $A_{\text{sat}}$ on $\Omega$. The signal enhancement at higher Rabi frequencies indicates that strong driving suppresses the local disorder, thereby facilitating spin transport across the ensemble. The red dashed line is a fit to the phenomenological model described in the text. Error bars indicate fitting uncertainties.