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arXiv:1802.03845 · Physical review. B./Physical review. B

T2 -limited sensing of static magnetic fields via fast rotation of quantum spins

A. A. Wood, A. G. Aeppli, Emmanuel Lilette, Yaakov Y. Fein, Alastair D. Stacey, Lloyd C. L. Hollenberg, Robert E Scholten, A. Martin

Published Nov 28, 2018• 26 citations
arXivHTMLPDF

Abstract

Diamond-based quantum magnetometers are more sensitive to oscillating (ac) magnetic fields than static (dc) fields because the crystal impurity-induced ensemble dephasing time ${T}_{2}^{*}$, the relevant sensing time for a dc field, is much shorter than the spin coherence time ${T}_{2}$, which determines the sensitivity to ac fields. Here we demonstrate measurement of dc magnetic fields using a physically rotating ensemble of nitrogen-vacancy centers at a precision ultimately limited by ${T}_{2}$ rather than ${T}_{2}^{*}$. The rotation period of the diamond is comparable to ${T}_{2}$ and the angle between the nitrogen-vacancy (NV) axis and the target magnetic field changes as a function of time, thus upconverting the static magnetic field to an oscillating field in the physically rotating frame. Using spin-echo interferometry of the rotating NV centers, we are able to perform measurements for over 100 times longer compared to a conventional Ramsey experiment. With modifications our scheme could realize dc sensitivities equivalent to demonstrated NV center ac magnetic field sensitivities of order $0.1\phantom{\rule{0.28em}{0ex}}\mathrm{nT}\phantom{\rule{0.16em}{0ex}}{\mathrm{Hz}}^{\ensuremath{-}1/2}$.

DOI
10.1103/physrevb.98.174114

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Diamond-based quantum magnetometers are more sensitive to oscillating (ac) magnetic fields than static (dc) fields because the crystal impurity-induced ensemble dephasing time T2∗{T}_{2}^{*}T2∗​, the relevant sensing time for a dc field, is much shorter than the spin coherence time T2{T}_{2}T2​, which determines the sensitivity to ac fields. Here we demonstrate measurement of dc magnetic fields using a physically rotating ensemble of nitrogen-vacancy centers at a precision ultimately limited by T2{T}_{2}T2​ rather than T2∗{T}_{2}^{*}T2∗​. The rotation period of the diamond is comparable to T2{T}_{2}T2​ and the angle between the nitrogen-vacancy (NV) axis and the target magnetic field changes as a function of time, thus upconverting the static magnetic field to an oscillating field in the physically rotating frame. Using spin-echo interferometry of the rotating NV centers, we are able to perform measurements for over 100 times longer compared to a conventional Ramsey experiment. With modifications our scheme could realize dc sensitivities equivalent to demonstrated NV center ac magnetic field sensitivities of order 0.1nTHz\ensuremath−1/20.1\phantom{\rule{0.28em}{0ex}}\mathrm{nT}\phantom{\rule{0.16em}{0ex}}{\mathrm{Hz}}^{\ensuremath{-}1/2}0.1nTHz\ensuremath−1/2.
Magnetic sensors are typically much more sensitive to oscillating (AC) magnetic fields than static (DC) fields, due to the presence of more noise at lower frequency, typically scaling with a 1/f1/f1/f dependence. For quantum magnetometers, this characteristic noise is reflected in the ensemble dephasing time T2∗T_2^*T2∗​, the relevant sensing time for a DC field, being much lower than the spin coherence time T2T_2T2​, which determines the sensitivity to AC fields. Here, we demonstrate measurement of DC magnetic fields using a physically rotating ensemble of nitrogen-vacancy centres at a precision limited by the electron spin coherence time, T2T_2T2​. We rotate the host diamond with a period comparable to T2T_2T2​, such that the angle between the NV axis and the magnetic field to be detected changes as a function of time, upconverting the static magnetic field to an oscillating field in the physically rotating frame. Using spin-echo interferometry, we observe an order of magnitude improvement in DC magnetometer response compared to a conventional Ramsey experiments. Enhancements to our scheme could realise DC sensitivities equivalent to demonstrated AC magnetic field sensitivities with NV centres.
We demonstrate quantum sensing of dc magnetic fields that exceeds the sensitivity of conventional ${T}_{2}^{\ensuremath{\ast}}$-limited dc magnetometry by more than an order of magnitude. We use nitrogen-vacancy centers in a diamond rotating at periods comparable to the spin coherence time, and characterize the dependence of magnetic sensitivity on measurement time and rotation speed. Our method up-converts only the dc field of interest and preserves the quantum coherence of the sensor. These results definitively improve the sensitivity of a quantum magnetometer to dc fields, demonstrating that sensitivity below the ${T}_{2}^{\ensuremath{\ast}}$ limit is possible and can be applied to any diamond magnetometer where ${T}_{2}\ensuremath{\gg}{T}_{2}^{\ensuremath{\ast}}$ to yield an order-of-magnitude sensitivity improvement.
Quantum sensing with solid-state spins offers the promise of high spatial resolution, bandwidth, and dynamic range at sensitivities comparable to more mature quantum sensing technologies, such as atomic vapor cells and superconducting devices. However, despite comparable theoretical sensitivity limits, the performance of bulk solid-state quantum sensors has so far lagged behind these more mature alternatives. A recent review [Barry et al., Rev. Mod. Phys. 92, 015004 (2020)] suggests several paths to improve performance of magnetometers employing nitrogen-vacancy defects in diamond, the most-studied solid-state quantum sensing platform. Implementing several suggested techniques, we demonstrate the most sensitive nitrogen-vacancy-based bulk magnetometer reported to date. Our approach combines tailored diamond growth to achieve low strain and long intrinsic dephasing times, the use of double-quantum Ramsey and Hahn-echo magnetometry sequences for broadband and narrowband magnetometry, respectively, and P1 driving to further extend dephasing time. Notably, the device does not include a flux concentrator, preserving the fixed response of the nitrogen vacancies to magnetic field. The magnetometer realizes a minimum sensitivity of 460fTs1/2460\phantom{\rule{0.2em}{0ex}}\mathrm{fT}\phantom{\rule{0.2em}{0ex}}{\mathrm{s}}^{1/2}460fTs1/2 in a broadband dc-sensitive mode and 210fTs1/2210\phantom{\rule{0.2em}{0ex}}\mathrm{fT}\phantom{\rule{0.2em}{0ex}}{\mathrm{s}}^{1/2}210fTs1/2 in a narrowband ac mode. We describe the experimental setup in detail and highlight potential paths for future improvement.
Ultimate sensitivity for quantum magnetometry using nitrogen-vacancy (NV) centers in a diamond is limited by a number of NV centers and coherence time. Microwave irradiation with a high and homogeneous power density for a large detection volume is necessary to achieve a highly sensitive magnetometer. Here, we demonstrate a microwave resonator to enhance the power density of the microwave field and an optical system with a detection volume of 1.4 × 10−3 mm3. The strong microwave field enables us to achieve 48 ns Rabi oscillation which is sufficiently faster than the phase relaxation time of NV centers. This system combined with a decoupling pulse sequence, XY16, extends the spin coherence time (T2) up to 27 times longer than that with a spin echo method. Consequently, we obtained an AC magnetic field sensitivity of 10.8 pt/Hz using the dynamical decoupling pulse sequence.
A controlled qubit in a rotating frame opens new opportunities to probe fundamental quantum physics, such as geometric phases in physically rotating frames, and can potentially enhance detection of magnetic fields. Realising a single qubit that can be measured and controlled during physical rotation is experimentally challenging. In this work, we demonstrate quantum control of a single nitrogen-vacancy (NV) centre within a diamond rotated at 200,000rpm, a rotational period comparable to the NV spin coherence time T2T_2T2​. We stroboscopically image individual NV centres that execute rapid circular motion in addition to rotation, and demonstrate preparation, control and readout of the qubit quantum state with lasers and microwaves. Using spin-echo interferometry of the rotating qubit, we are able to detect modulation of the NV Zeeman shift arising from the rotating NV axis and an external DC magnetic field. Our work establishes single NV qubits in diamond as quantum sensors in the physically rotating frame, and paves the way for the realisation of single-qubit diamond-based rotation sensors.
Abstract Nitrogen-vacancy (NV) center ensembles in diamond are one of the most promising solid-state quantum platforms for various sensing applications. Achieving ultimate sensitivity requires simultaneously long spin dephasing times ( T2∗{T}_{2}^{* }T2∗​ T 2 * ) and high NV center concentrations. In this work, we propose a systematic measurement approach to quantify the electron spin dephasing in NV center ensembles and analyze the contributions of various sources to the dephasing time, including NV-NV interactions, strain and electric field distributions, 13 C nuclear spins, and P1 electron spins. Our method is validated using a series of high-performance diamond samples, providing a comprehensive understanding of dephasing mechanisms and revealing correlations between NV concentration and different dephasing sources. Building on these insights, we outline strategies to further enhance the achievable sensitivity for DC magnetic field measurements.