Characterizing the magnetic noise power spectrum of dark spins in diamond

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 substitutional nitrogen (P1) centers in diamond that typically form the bath for nitrogen-vacancy (NV) centers. The Carr–Purcell–Meiboom–Gill (CPMG) dynamical decoupling experiments on the P1 centers were performed on a low [N] chemical vapor deposition (CVD) sample and a high [N] high-temperature, high-pressure (HPHT) 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msup> <mml:mi>ω</mml:mi> <mml:mrow> <mml:mn>0.7</mml:mn> <mml:mo>−</mml:mo> <mml:mn>1.0</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , and a prominent peak at the 13 C 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 13 C nuclear Larmor frequency. At 190 mT this is 2.04 MHz, 5.7 times higher than the CPMG modulation frequency ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>&lt;</mml:mo> </mml:mrow> <mml:mn>357</mml:mn> </mml:mrow> </mml:math> 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.