ISSN 0253-2778

CN 34-1054/N

Open AccessOpen Access JUSTC Physics 11 May 2022

High-sensitivity double-quantum magnetometry in diamond via quantum control

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https://doi.org/10.52396/JUSTC-2021-0249
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  • Author Bio:

    Yang Dong received his PhD degree in Physics from University of Science and Technology of China (USTC). He is currently a Research Associate at Department of Optical Engineering, USTC. His major research interests focus on the quantum sensing and quantum coherent operation with a solid spin in diamond

  • Corresponding author: E-mail: dongy13@ustc.edu.cn
  • Received Date: 25 November 2021
  • Accepted Date: 18 January 2022
  • Available Online: 11 May 2022
  • High-fidelity quantum operation of qubits plays an important role in magnetometry based on nitrogen-vacancy (NV) centers in diamonds. However, the nontrivial spin-spin coupling of the NV center decreases signal contrast and sensitivity. Here, we overcome this limitation by exploiting the amplitude modulation of microwaves, which allows us to perfectly detect magnetic signals at low fields. Compared with the traditional double-quantum sensing protocol, the full contrast of the detection signal was recovered, and the sensitivity was enhanced three times in the experiment. Our method is applicable to a wide range of sensing tasks, such as temperature, strain, and electric field.

      Implement double-quantum magnetometry in diamond with high-fidelity quantum control.

    High-fidelity quantum operation of qubits plays an important role in magnetometry based on nitrogen-vacancy (NV) centers in diamonds. However, the nontrivial spin-spin coupling of the NV center decreases signal contrast and sensitivity. Here, we overcome this limitation by exploiting the amplitude modulation of microwaves, which allows us to perfectly detect magnetic signals at low fields. Compared with the traditional double-quantum sensing protocol, the full contrast of the detection signal was recovered, and the sensitivity was enhanced three times in the experiment. Our method is applicable to a wide range of sensing tasks, such as temperature, strain, and electric field.

    • We demonstrate a simple method to synchronously manipulating electron spin of NV center coupling with the nuclear spin in its maximal mixed state by microwave MW amplitude modulation technology.
    • The maximum contrast of double-quantum (DQ) magnetometry is realized and the DC magnetic field detection sensitivity is improved over a wide range of bias magnetic field.
    • Working in the regime of very low Zeeman splitting, the detection sensitivity is enhanced approximately three times and yield high sensitivity (~200 nT/ Hz) for DC magnetic field detection with DQ pulse sequences, which is prefer to detect nuclear spin signals at zero- and low-field Nano-NMR with NV centers.

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  • [1]
    Degen C L, Reinhard F, Cappellaro P. Quantum sensing. Rev. Mod. Phys., 2017, 89: 035002. doi: 10.1103/RevModPhys.89.035002
    [2]
    Barry J F, Schloss J M, Bauch E, et al. Sensitivity optimization for NV-diamond magnetometry. Rev. Mod. Phys., 2020, 92: 015004. doi: 10.1103/RevModPhys.92.015004
    [3]
    Chen X, Zou C, Gong Z, et al. Subdiffraction optical manipulation of the charge state of nitrogen vacancy center in diamond. Light Sci. Appl., 2015, 4: e230. doi: 10.1038/lsa.2015.3
    [4]
    Chen X D, Wang E H, Shan L K, et al. Focusing the electromagnetic field to 10−6λ for ultra-high enhancement of field-matter interaction. Nat. Commun., 2021, 12: 6389. doi: 10.1038/s41467-021-26662-5
    [5]
    Dong Y, Du B, Zhang S C, et al. Solid quantum sensor based on nitrogen-vacancy center in diamond. Acta. Phys. Sin., 2018, 67: 160301. doi: 10.7498/aps.67.20180788
    [6]
    Fang K, Acosta V M, Santori C, et al. High-sensitivity magnetometry based on quantum beats in diamond nitrogen-vacancy centers. Phys. Rev. Lett., 2013, 110: 130802. doi: 10.1103/PhysRevLett.110.130802
    [7]
    Mamin H J, Sherwood M H, Kim M, et al. Multipulse double-quantum magnetometry with near-surface nitrogen-vacancy centers. Phys. Rev. Lett., 2014, 113: 030803. doi: 10.1103/PhysRevLett.113.030803
    [8]
    Bauch E, Hart C A, Schloss J M, et al. Ultralong dephasing times in solid-state spin ensembles via quantum control. Phys. Rev. X, 2018, 8: 031025. doi: 10.1103/PhysRevX.8.031025
    [9]
    Maze J R, Stanwix P L, Hodges J S, et al. Nanoscale magnetic sensing with an individual electronic spin in diamond. Nature, 2008, 455: 644–647. doi: 10.1038/nature07279
    [10]
    Balasubramanian G, Chan I Y, Kolesov R, et al. Nanoscale imaging magnetometry with diamond spins under ambient conditions. Nature, 2008, 455: 648–651. doi: 10.1038/nature07278
    [11]
    Dong Y, Zheng Y, Li S, et al. Non-Markovianity-assisted high-fidelity Deutsch–Jozsa algorithm in diamond. npj Quantum Inf., 2018, 4: 3. doi: 10.1038/s41534-017-0053-z
    [12]
    Dong Y, Zhang S C, Lin H B, et al. Quantifying the performance of multi-pulse quantum sensing. Phys. Rev. B, 2021, 103: 104104. doi: 10.1103/PhysRevB.103.104104
    [13]
    Li C H, Dong Y, Xu J Y, et al. Enhancing the sensitivity of a single electron spin sensor by multi-frequency control. Appl. Phys. Lett., 2018, 113: 072401. doi: 10.1063/1.5042796
    [14]
    Kong F, Zhao P J, Ye X Y, et al. Nanoscale zero-field electron spin resonance spectroscopy. Nat. Commun., 2018, 9: 1563. doi: 10.1038/s41467-018-03969-4
    [15]
    Jiang M, Frutos R P, Wu T, et al. Magnetic gradiometer for the detection of zero- to ultralow-field nuclear magnetic resonance. Phys. Rev. Appl., 2019, 11: 024005. doi: 10.1103/PhysRevApplied.11.024005
    [16]
    Xu N Y, Tian Y, Chen B, et al. Dynamically polarizing spin register of N-V centers in diamond using chopped laser pulses. Phys. Rev. Appl., 2019, 12: 024055. doi: 10.1103/PhysRevApplied.12.024055
    [17]
    Zhao B W, Dong Y, Zhang S C, et al. Improving the NV generation efficiency by electron irradiation. Chin. Opt. Lett., 2020, 18: 080201. doi: 10.3788/COL202018.080201
    [18]
    Dong Y, Zhang S C, Zheng Y, et al. Experimental implementation of universal holonomic quantum computation on solid-state spins with optimal control. Phys. Rev. Appl., 2021, 16: 024060. doi: 10.1103/PhysRevApplied.16.024060
    [19]
    Cerrillo J, Casado S O, Prior J. Low field nano-NMR via three-level system control. Phys. Rev. Lett., 2021, 126: 220402. doi: 10.1103/PhysRevLett.126.220402
    [20]
    Dong Y, Chen X D, Guo G C, et al. Reviving the precision of multiple entangled probes in an open system by simple π-pulse sequences. Phys. Rev. A, 2016, 94: 052322. doi: 10.1103/PhysRevA.94.052322
    [21]
    Dong Y, Xu J Y, Zhang S C, et al. Composite-pulse enhanced room-temperature diamond magnetometry. Funct. Diamond, 2021, 1: 125–134. doi: 10.1080/26941112.2021.1898792
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    Figure  1.  Coherent operation of a single NV center in diamond. (a) Pulsed ODMR spectrum of a single $ ^{{\text{14}}}{\text{NV}} $ center at a bias magnetic field of 21 Gauss. A single resonant spectral line splits into three lines with intervals of 2.16 MHz because of the unpolarized $ ^{{\text{14}}}{\text{N}} $ nuclear spin hyperfine coupling with nitrogen NV electron spin. (b-c) Rabi oscillation of electron spin for the transition $ \left| {0,0} \right\rangle \leftrightarrow \left| {1,0} \right\rangle $ with different MW power. For low MW power, the Rabi oscillation can be fitted with a simple cosine function. When the MW power is increased three times, the frequency of Rabi oscillation cannot be easily determined for experimental results. The laser power at 532 nm is 0.7 mW in our experiment.

    Figure  2.  Rabi oscillation with shaped MW pulse. (a) MW sequence scheme of amplitude modulation. The gray region denotes carrier frequency (${\omega = }{{f}_{\text{2}}}$). The blue dash line denotes the modulation function $A(t) = {\varOmega _0}\left[ {2{\rm cos}(\Delta t) + 1} \right]$,where ${\varOmega _0} = 0.558$ MHz. (b) Rabi oscillation of NV center driving by the amplitude modulation of the MW pulse. The time scale for the $\pi$ gate is 920 ns.

    Figure  3.  Ramsey sensing results. (a) Pulse sequence for the Ramsey sensing protocol. A DC magnetic field is applied along the NV center axis. (b–c) Ramsey fringes of the NV center driven with or without amplitude modulation of MW pulse. Here, the MW pulse addresses the target transition $ \left| {0,0} \right\rangle \leftrightarrow \left| {1,0} \right\rangle $. The duration time of the $\pi/2$ gate is 460 ns. By fitting experimental results with theory, the coherent time for both cases is $ T_2^* \approx 4 $ ${\text{μs}}$. However, the signal contrast of our sharp sequence is improved approximately three times compared with the traditional method. The Rabi frequency for the traditional Ramsey is set as ${\varOmega _0} = 0.558$ MHz.

    Figure  4.  DQ Ramsey sensing protocol and results. (a) Pulse sequence for the DQ Ramsey sensing protocol. Compared with the SQ Ramsey sequence, the $\pi$ gate (denoted with orange) needs to be applied after preparing the electron spin into a superposition state $ \left( {\left| 0 \right\rangle + \left| 1 \right\rangle } \right)/\sqrt 2 $. The frequency of the $\pi$ gate is in resonance with the transition $ \left| {0,0} \right\rangle \leftrightarrow \left| { - 1,0} \right\rangle $. Then, the probe state $ \left( {\left| { - 1} \right\rangle + \left| 1 \right\rangle } \right)/\sqrt 2 $ for the detection of the DC magnetic field is obtained. (b) DQ Ramsey sensing results as a function of sensing time (τ) and DC magnetic-field change. (c) DQ Ramsey results with fixed amplitude of DC magnetic field, which corresponds to the blue dashed line in Fig. 4 (b). The coherence time for DQ Ramsey is $ T_{2,DQ}^* \approx 2 $ ${\text{μs}}$. (d) DQ Ramsey results (denoted by red dots) as a function of the amplitude of DC magnetic field with fixed sensing time (τ=1 ${\text{μs}}$) for out shaped MW pulse. The blue square corresponds to the rectangular MW pulse. (e) Measured sensitivity of a single NV spin magnetometer over a range of sensing time after repeating $ N = 1.5 \times {10^6} $ times.

    [1]
    Degen C L, Reinhard F, Cappellaro P. Quantum sensing. Rev. Mod. Phys., 2017, 89: 035002. doi: 10.1103/RevModPhys.89.035002
    [2]
    Barry J F, Schloss J M, Bauch E, et al. Sensitivity optimization for NV-diamond magnetometry. Rev. Mod. Phys., 2020, 92: 015004. doi: 10.1103/RevModPhys.92.015004
    [3]
    Chen X, Zou C, Gong Z, et al. Subdiffraction optical manipulation of the charge state of nitrogen vacancy center in diamond. Light Sci. Appl., 2015, 4: e230. doi: 10.1038/lsa.2015.3
    [4]
    Chen X D, Wang E H, Shan L K, et al. Focusing the electromagnetic field to 10−6λ for ultra-high enhancement of field-matter interaction. Nat. Commun., 2021, 12: 6389. doi: 10.1038/s41467-021-26662-5
    [5]
    Dong Y, Du B, Zhang S C, et al. Solid quantum sensor based on nitrogen-vacancy center in diamond. Acta. Phys. Sin., 2018, 67: 160301. doi: 10.7498/aps.67.20180788
    [6]
    Fang K, Acosta V M, Santori C, et al. High-sensitivity magnetometry based on quantum beats in diamond nitrogen-vacancy centers. Phys. Rev. Lett., 2013, 110: 130802. doi: 10.1103/PhysRevLett.110.130802
    [7]
    Mamin H J, Sherwood M H, Kim M, et al. Multipulse double-quantum magnetometry with near-surface nitrogen-vacancy centers. Phys. Rev. Lett., 2014, 113: 030803. doi: 10.1103/PhysRevLett.113.030803
    [8]
    Bauch E, Hart C A, Schloss J M, et al. Ultralong dephasing times in solid-state spin ensembles via quantum control. Phys. Rev. X, 2018, 8: 031025. doi: 10.1103/PhysRevX.8.031025
    [9]
    Maze J R, Stanwix P L, Hodges J S, et al. Nanoscale magnetic sensing with an individual electronic spin in diamond. Nature, 2008, 455: 644–647. doi: 10.1038/nature07279
    [10]
    Balasubramanian G, Chan I Y, Kolesov R, et al. Nanoscale imaging magnetometry with diamond spins under ambient conditions. Nature, 2008, 455: 648–651. doi: 10.1038/nature07278
    [11]
    Dong Y, Zheng Y, Li S, et al. Non-Markovianity-assisted high-fidelity Deutsch–Jozsa algorithm in diamond. npj Quantum Inf., 2018, 4: 3. doi: 10.1038/s41534-017-0053-z
    [12]
    Dong Y, Zhang S C, Lin H B, et al. Quantifying the performance of multi-pulse quantum sensing. Phys. Rev. B, 2021, 103: 104104. doi: 10.1103/PhysRevB.103.104104
    [13]
    Li C H, Dong Y, Xu J Y, et al. Enhancing the sensitivity of a single electron spin sensor by multi-frequency control. Appl. Phys. Lett., 2018, 113: 072401. doi: 10.1063/1.5042796
    [14]
    Kong F, Zhao P J, Ye X Y, et al. Nanoscale zero-field electron spin resonance spectroscopy. Nat. Commun., 2018, 9: 1563. doi: 10.1038/s41467-018-03969-4
    [15]
    Jiang M, Frutos R P, Wu T, et al. Magnetic gradiometer for the detection of zero- to ultralow-field nuclear magnetic resonance. Phys. Rev. Appl., 2019, 11: 024005. doi: 10.1103/PhysRevApplied.11.024005
    [16]
    Xu N Y, Tian Y, Chen B, et al. Dynamically polarizing spin register of N-V centers in diamond using chopped laser pulses. Phys. Rev. Appl., 2019, 12: 024055. doi: 10.1103/PhysRevApplied.12.024055
    [17]
    Zhao B W, Dong Y, Zhang S C, et al. Improving the NV generation efficiency by electron irradiation. Chin. Opt. Lett., 2020, 18: 080201. doi: 10.3788/COL202018.080201
    [18]
    Dong Y, Zhang S C, Zheng Y, et al. Experimental implementation of universal holonomic quantum computation on solid-state spins with optimal control. Phys. Rev. Appl., 2021, 16: 024060. doi: 10.1103/PhysRevApplied.16.024060
    [19]
    Cerrillo J, Casado S O, Prior J. Low field nano-NMR via three-level system control. Phys. Rev. Lett., 2021, 126: 220402. doi: 10.1103/PhysRevLett.126.220402
    [20]
    Dong Y, Chen X D, Guo G C, et al. Reviving the precision of multiple entangled probes in an open system by simple π-pulse sequences. Phys. Rev. A, 2016, 94: 052322. doi: 10.1103/PhysRevA.94.052322
    [21]
    Dong Y, Xu J Y, Zhang S C, et al. Composite-pulse enhanced room-temperature diamond magnetometry. Funct. Diamond, 2021, 1: 125–134. doi: 10.1080/26941112.2021.1898792

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