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Abstract The coherence times of solid-state spin qubits are often limited by the presence of a spin bath. Characterizing the spectrum of the local magnetic field fluctuations of the bath is key to understanding spin qubit decoherence. Here we use pulsed electron paramagnetic resonance (pEPR) based noise spectroscopy to measure the magnetic noise power spectra for ensembles of P1 (substitutional nitrogen) centers in diamond that typically form the bath for NV (nitrogen-vacancy) centers. The Carr-Purcell-Meiboom-Gill (CPMG) dynamical decoupling experiments on the P1 centers were performed on a low [N] CVD (chemical vapor deposition) sample and a high [N] HPHT (high-temperature, high-pressure) sample at 89 mT. We characterize the NV centers of the latter sample using the same 2.5 GHz pEPR spectrometer. All power spectra show two distinct features, a broad component that is observed to scale as approximately 1/ω^{0.7-1.0}, and a prominent peak at the 13C Larmor frequency. The behavior of the broad component is consistent with an inhomogeneous distribution of Lorentzian spectra due to clustering of P1 centers, which has recently been shown to be prevalent in HPHT diamond. We develop techniques utilizing harmonics of the CPMG filter function to improve characterization of high-frequency signals, which we demonstrate on the 13C nuclear Larmor frequency. At 190 mT this is 2.04 MHz, 5.7 times higher than the CPMG modulation frequency (<357 kHz, hardware-limited). Understanding the properties of the bath allow us to either exploit it as a quantum resource or optimize decoupling performance, while also informing sample fabrication technologies. The techniques are applicable to ac magnetometry for nanoscale nuclear magnetic resonance and chemical sensing. 

Understanding the spatial distribution of the P1 centers is crucial for diamond-based sensors and quantum devices. P1 centers serve as polarization sources for dynamic nuclear polarization (DNP) quantum sensing and play a significant role in the relaxation of nitrogen vacancy (NV) centers. Additionally, the distribution of NV centers correlates with the distribution of P1 centers, as NV centers are formed through the conversion of P1 centers. We utilized DNP and pulsed electron paramagnetic resonance (EPR) techniques that revealed strong clustering of a significant population of P1 centers that exhibit exchange coupling and produce asymmetric line shapes. The 13C DNP frequency profile at a high magnetic field revealed a pattern that requires an asymmetric EPR line shape of the P1 clusters with electron–electron (e–e) coupling strengths exceeding the 13C nuclear Larmor frequency. EPR and DNP characterization at high magnetic fields was necessary to resolve energy contributions from different e–e couplings. We employed a two-frequency pump–probe pulsed electron double resonance technique to show cross-talk between the isolated and clustered P1 centers. This finding implies that the clustered P1 centers affect all of the P1 populations. Direct observation of clustered P1 centers and their asymmetric line shape offers a novel and crucial insight into understanding magnetic noise sources for quantum information applications of diamonds and for designing diamond-based polarizing agents with optimized DNP efficiency for 13C and other nuclear spins of analytes. We propose that room temperature 13C DNP at a high field, achievable through straightforward modifications to existing solution-state NMR systems, is a potent tool for evaluating and controlling diamond defects.