magnetometry with engineered nitrogen-vacancy spin ensembles in

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DC - magnetometry with engineered nitrogenvacancy spin ensembles in diamond Priyadharshini Balasubramanian, Christian Osterkamp, Yu Chen, Xiuliang Chen, Tokuyuki Teraji, E Wu, Boris Naydenov, and Fedor Jelezko Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.9b02993 • Publication Date (Web): 20 Aug 2019 Downloaded from pubs.acs.org on August 23, 2019

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DC-magnetometry with engineered nitrogen vacancy spin ensembles in diamond Priyadharshini Balasubramanian,

Chen,

‡

¶

Tokuyuki Teraji,

∗,†,k

Christian Osterkamp,

E Wu,

‡

†,§

Boris Naydenov,

†,k

Yu Chen,

‡,k

Xiuliang

†

and Fedor Jelezko

†Institute for Quantum Optics and

Center for Integrated Quantum Science and Technology (IQST) Ulm University, Albert Einstein Allee 11, Ulm 89081, Germany ‡State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai

200062, China

¶Wide Bandgap Materials Group, Research Center for Functional Materials, National

Institute for Material Science, 1-1, Namiki, Tsukuba, Ibaraki 305-0044, Japan

§Present address: Institute for Nanospectroscopy, Helmholtz-Zentrum Berlin für

Materialien und Energie (HZB), Kekuléstraÿe 5, Berlin 12489, Germany kContributed equally to this work E-mail: [email protected]

Abstract The exquisite optical and spin properties of nitrogen-vacancy(NV) centers in diamond have made them a promising platform for quantum sensing. The prospect of NV based sensors relies on the controlled production of these atomic-scale defects. Here we report on the fabrication of preferentially-oriented, shallow ensemble of NV centers and their applicability for sensing DC magnetic elds. For the present sample, the residual paramagnetic impurities are the dominant source of environmental noise, limiting 1

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the dephasing time (T∗2 ) of the NVs. By controlling the P1 spin-bath, we achieve a four-fold improvement in the T∗2 of the NV ensemble. Further, we show that combining spin-bath control and homonuclear decoupling sequence, cancel NV-NV interactions, and partially protect the sensors from a broader spin environment, thus extending the ensemble T∗2 up to 10 µs. With this decoupling protocol we measure an improved DC √

magnetic eld sensitivity of 1.2 nTµm3/2 / Hz. Using engineered NVs and decoupling protocols, we demonstrate the prospects of harnessing the full potential of NV based ensemble magnetometry.

Keywords nitrogen-vacancy center, preferential alignment,DC magnetic eld sensing, ensemble magnetometry Magnetic eld sensor that can probe static or low-frequency signals with high sensitivity and resolution is an indispensable tool with numerous application in physical and life sciences. Over the past few decades, quantum sensors based on solid-state qubits have emerged as a promising platform for developing sensitive magnetometers - a prime example being the negatively charged nitrogen-vacancy (NV) color center in diamond. The prominent features of NV center include long coherence times, 1 optical accessibility of spin states, 2 and ambient operating conditions. Furthermore, diamond is chemically inert and has low cytotoxicity, which makes NV sensors ideal for in vivo applications. 3 Recent demonstrations like probing the dynamics of neural networks, 4,5 magnetic imaging of living cells, 3,6,7 nanoscale NMR, 8 single protein detection, 9 and several others 10,11 have pioneered towards the applicability of NV based sensing technology. Magnetometry with an ensemble of NVs oer enhanced sensitivity, and numerous studies have explored the properties and prospects of high-density NV sensors. 12,13 The volume

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normalized sensitivity of an ensemble magnetometer is given as,

√ V √ η ≈ γC Nτ V

(1)

where γ is the gyromagnetic ratio, C the measurement contrast, N the number of sensors in the detection volume V and τ the eld interrogation time. The critical challenges for magnetometry in the high-density regime are the reduced measurement contrast (for singleaxis sensing Cens =

Csingle ), 4

and the short dephasing time of the sensor. While it is possible

to retain the maximal readout contrast with preferentially oriented NVs, the ultimate limit on the sensitivity is set by the available eld interrogation time (τ ). For DC eld sensing,

τ is limited to the dephasing time (T∗2 ) of the sensor, which places an upper bound on the maximum achievable sensitivity. Extensive research focuses on improving the sensor coherence through material engineering; however, the complexity of NV formation presents an inherent tradeo between the NV density and its coherence time, which is limited by the residual nitrogen impurities. Increasing the sensor density also limit the coherence time due to the inhomogeneous interactions between NVs. Protecting the sensor from these deleterious interactions is an essential step towards the development of broadband NV magnetometer with the highest sensitivity. The primary motivation of this work is to fabricate shallow, preferentially aligned ensemble of NV centers and explore its applicability in precision sensing technology. To this end, we study the limitation on the sensor dephasing time and investigate the dynamics between the sensor and the surrounding spin-bath. This information is crucial for both material engineering and designing sensing protocols for improved magnetometry. In this work, we enhance the ensemble sensitivity by improving its T∗2 using a combination of spin-bath control and homonuclear decoupling sequence. This decoupling technique mitigates the two most dominant dephasing mechanisms and substantially improve the coherence time of the NVs. The pulse sequence is also compatible with DC magnetometry, and we demonstrate

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Figure 1: (A) SIMS measurement showing the depth prole of the carbon (13 C) and nitrogen (14 N) content in the sample. From the data we determine the thickness of the NV layer to be ≈ 30 nm. (B) Confocal image showing a cross section of the diamond sample. The diamond layer studied in this work is fabricated using Plasma Enhanced Chemical Vapour Deposition technique (PECVD) in a home-built reactor. The sample is grown on top of a IIa type (111)-oriented diamond substrate (Element Six Ltd) which contains natural abundance of carbon-13 isotope (13 C ≈ 1.1%). For the overgrowth process, we use

13

C di-

minished methane gas (isotopic ratio ≈ 0.01%) with a nitrogen concentration of > 1019 cm−3 . The CVD conditions are optimized to produce a thin layer of dense as-grown NV centers, and the growth conditions are given in the supplementary material. 14 Since the nitrogen incorporation eciency is higher in a (111)-substrate, we expect a high density of nitrogen related defects in the overgrown layer, which is investigated using secondary ion mass spectrometry (SIMS) and confocal microscopy. In gure 1A, we show the SIMS measurement of the grown sample. The

13

13

C and

14

N density in the over-

C isotopic ratio gradually increases from 0.01% up to 1.1% (natural 4


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abundance) at a depth of ≈ 100 nm. As the growth process is performed in a atmosphere, the

13

12

C enriched

C isotope is probably introduced through plasma etching of the diamond

substrate. From this data, we estimate the thickness of the overgrown layer to be ≈ 100 nm. We note that the density of 14 N impurities also shows a steep variation within the overgrown layer with at least three times more 14 N conned to a depth of ≈ 30 nm. As the distribution of the NV centers depends on the

14

N density, we deduce the thickness of the NV rich layer

to be ≈ 30 nm. This value is especially relevant in the context of sensing external magnetic signals as the eld amplitude from the magnetic target decays with the distance. The density of the NV ensemble is determined from the photon counts measured with the confocal microscope. Figure 1B shows the cross-sectional confocal image of the sample recorded with a neutral density (ND) lter of optical density (OD) ≈ 1.5. From the rate of detected photons (≈ 180 x 106 cts/s), we estimate the presence of about 800 - 1000 NV centers in a sensing volume of 220 nm x 220 nm x 30 nm (≈ 3 − 4 ppm of NVs).(supplementary information) 0V

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(x 103 ) events

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0.9 0.8 0.7

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[1¯ 11]

[1¯ 11]

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[111]

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E field on π Laser

n

0.0 4200 4400 4600 4800 no. of photons / 100 ms

Figure 2: (A) ODMR spectrum at Bext ≈ 50 G, aligned along the [111] crystal direction. The dots represent the measured ODMR data with the double lorentzian t (solid line). The shaded region marks the expected position of the transition frequencies from other three NV direction. (B) The two possible orientations of the aligned NV centers (red with V and N , blue with N and V). (C) Single frequency pulsed ODMR scheme for measuring the Stark shift induced change in uorescence. (D) Histogram of measured photon counts with an external electric eld of voltages +20V and −20V. The red vertical line marks the photon counts measured without electric eld. NV centers incorporated during CVD growth on a (111)-substrate often show a high degree of preferential alignment along the [111] crystal direction. 1419 The orientational po5


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larization of as-grown NV center is explained in terms of step-wise growth process. 20,21 During the overgrowth process, nitrogen atoms are substituted in the surface rst, followed by the occasional association of lattice vacancy during subsequent deposition. This energetically favorable route promotes the preferential incorporation of the NV defects on a (111)-substrate. The alignment ratio of the NV centers in the overgrown layer is measured using the optically detected magnetic resonance (ODMR) technique. To spectrally isolate the preferred NV orientation, we apply a static magnetic eld of Bext ≈ 50 G parallel to the NV axis, which shows maximum Zeeman splitting between the ms ± 1 spin levels. The other three NV groups have the same projection of the eld, and hence, their transition frequencies overlap. The measured ODMR spectrum plotted in gure 2A conrms the preferential alignment (> 99%) of NV centers. This inference stems from the fact that the ODMR spectrum feature only two prominent resonance lines. The blue shaded region highlights the position of the expected transition frequency of other NV orientations. 22 Similarly, we record 30% spin readout contrast in all our pulsed experiments as well. To determine the orientation (N-V or V-N) of the aligned NV centers, we observe the electric eld induced change in the pulsed-ODMR spectrum. Typically, the NV centers are statistically oriented along two anti-parallel directions as shown in gure 2B, and the frequency shift depends on the angle (dened as φ) between the electric eld and the direction of the nearest carbon atom adjacent to the vacancy cite (f±1 ∝ ∓Cos(φ)). In the following experiment, we adapt a single frequency pulsed ODMR technique to detect the sign of the Stark shift through the change in photon counts. In gure 2C, we show the measurement scheme, and the experimental details are given in SI. The histogram of the measured photon counts for voltages +20V and −20V is plotted in gure 2D. In an ensemble with equal distribution of N-V and V-N orientations, only the absolute frequency change is detectable, which depends on the magnitude of the applied electric eld. However, we observe a clear shift in the photon counts on reversing the direction of the electric eld, strongly suggesting the preferential orientation of the NVs. This could again be attributed to the formation 6


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mechanism of the NV defects described in the previous section. A Similar experiment on preferentially aligned single NVs reports an orientation ratio of 74% V-N to 26% N-V. 16 Our result suggests that such a high degree of preferential orientation is also achievable on dense NV samples. π NV 2

π 2

τ

B

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τfixed

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T∗2 ≈ 210 ns

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Figure 3: (A) Ramsey sequence and the measured dephasing time of the spin ensemble. The data (dots) is t to the expression y0 + C exp[−(τ /T2∗ )p ] cos[2πf τ + φ] (solid line). (B) The pulse sequence for frequency swept DEER measurement and the corresponding spectrum recorded at Bext ≈ 666 G. The data shows ve distinct peaks which matches with the characteristic anisotropic hyperne splitting of the substitutional nitrogen (14 N) impurities. For convenience, the spin bath is grouped (labeled A to E) based on the hyperne interaction strength. The solid line shows the simulated 14 N spectrum with peak amplitudes reecting the abundance of each spectral group. (C) Measurement protocol for Spin Echo DOuble Resonance (SEDOR) experiment and the recorded SEDOR data with the t ∝ C exp[−(2τ ΓP1 )]. The transverse decay time of the sensor coherence (dephasing time,T∗2 ) is critical for DC magnetometry as this limits the maximum achievable sensitivity. We measure the dephasing time of the NV ensemble using the Ramsey sequence. The observed signal shown in gure 3A exhibits a mono-exponential decay with the characteristic time T∗2 ≈ 210 ns. This relatively short dephasing time could arise from the dipolar interaction between the NV centers and the surrounding paramagnetic spin-bath. More precisely, the dipolar interactions within the spin-bath cause random uctuations in the local environment of the NV spins, which leads to dephasing on a timescale T∗2 ∝ 1/(2π Γe−e ), where Γe−e ∝ 9.1 kHz/ppm is the interaction strength between electron spins. The measured ensemble dephasing time closely matches 7


π 2

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Bath

0.9 0.7

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freq sweep

Bath

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NV echo amplitude

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P|0i

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the value expected from a 14 N spin-bath of density ≈ 65 - 70 ppm. (From the SIMS data, we estimate the

14

N density in the NV rich layer to be ≈ 65 - 70 ppm which causes dephasing

on the timescale T∗2 ∝ 230ns.) To gather further information on the spin bath, we use the Spin Echo DOuble Resonance (SEDOR) sequence. 23 The scheme relies on observing the change in the spin-echo of the NVs, caused by the resonant manipulation of bath spins. Figure 3(B) shows the pulse sequence and the result of the frequency-swept SEDOR sequence. The recorded spectrum reveals the characteristic anisotropic hyperne spectrum of the substitutional nitrogen (14 N) impurities, commonly known as P1 centers. The solid line corresponds to the simulated P1 spectrum with a common linewidth of 5 MHz, and amplitude reecting the abundance of each spectral group. Note that the center peak (labeled C ) is composed of two P1 subgroups that appear indistinguishable in the power-broadened spectrum. Other impurities like NitrogenVacancy-Hydrogen defects (14 NVH) are also spectrally indistinguishable from the center transition of the P1 spectrum. 24 However, its abundance manifests in the amplitude of peak C, which we do not observe in the experiment. Based on the excellent agreement between the experimental and the simulated nitrogen spectrum, we conclude that the P1 impurities dominate the paramagnetic spin environment of the NVs. With the transition frequencies known, we measure the coupling strength between different P1 subgroups and NVs. In gure 3C, we show the pulse sequence and the measured signal of the SEDOR scheme, where the blue data set corresponds to the spin-echo of the NV ensemble. Compared to the spin echo signal, the sensors decay faster when a particular dephasing channel is switched on. The corresponding decay time is a sensitive measure of the ensemble averaged dipolar coupling strength between the sensors and the bath. 25 The extracted decoherence rate for dierent P1 groups are : ΓA = (1.01 ± 0.02) µs−1 , ΓB = (1.45

± 0.05) µs−1 , ΓC = (2.16 ± 0.07) µs−1 , ΓD = (1.96 ± 0.06) µs−1 , ΓE = (1.05 ± 0.02) µs−1 . The measured interaction strength resemble the relative abundance of each P1 subgroups. The estimation of the NV-P1 coupling strength is crucial for both understanding and decoupling 8


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Figure 4: (A) Measured dephasing rate is plotted as a function of P1 Rabi frequency ΩP1 . Spin-bath driving shows four-fold improvement in the T∗2 of NVs. (B) Combined homohetero- spin decoupling protocol. (C) The measured coherence of the NV ensemble with the WAHUHA cycling time of τc = 720 ns. The dephasing time of the sensor spins is extended upto T∗2 ≈ 10 µs. (D) Measured uorescence as a function of Bdc amplitude. Here, the eld interrogation time τtot = 4000 ns is composed of 4 WAHUHA sequence each with a cycling time of τc = 1000 ns. The right y-axis shows the measured uorescence (with ND lter of OD = 1 in the detection path) and the left y-axis shows the estimated uorescence (total uorescence accounting for the attenuation of the ND lter). The most eective scheme to suppress sensor-P1 interaction is by driving the P1 spins at a rate (ΩP1 ) exceeding its average coupling strength to the sensors (ΓNV-P1 ). 26 Upon satisfying the condition ΩP1 /ΓNV-P1 1, the hetero-spin dipolar interactions are incoherently averaged, thereby increasing the sensor's coherence time. In gure 4A, we study the decoupling ecacy of the P1 driving scheme, where we plot the measured ensemble dephasing rate against P1 Rabi frequency ΩP1 . Although dephasing time increase rapidly in the beginning, it saturates at T∗2 ≈ 850 ns for ΩP1 ≈ 5 MHz. A plausible explanation of this behavior is the emergence of other line broadening mechanisms that are not suppressed by P1 driving, which include the inuence of other dark paramagnetic spins,

13

C nuclear spins (T∗2 [NV−13 C (0.1%)] ≈ 10µs), 27

NV-NV interaction (T∗2 [NV−NV] ≈ 4µs), and charge dynamics. The coherence time of the NV ensemble measured with spin echo sequence is ≈ 2.6 µs. Note that the dephasing time measured with spin bath control almost approach the bare spin echo coherence time and the limitation in T∗2 could be attributed to the lower control delity of the central P1 transition. 9


Measured signal

the sensor-bath dynamics.

1/T∗2 (MHz)

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The four pulse WAHUHA sequence depicted in gure 4B (pulse sequence applied on the NV spins) is one of the commonly used homonuclear (identical spins) decoupling sequence in solid-state NMR. The series of

π 2

pulses rotate the system Hamiltonian, cycling it equally

through all three spin components (i.e., along Sx , Sy , Sz spin operators), thereby suppressing the unwanted dipolar interactions. Other terms that are proportional to Sz operator in the system Hamiltonian (heteronuclear, hyperne, Zeeman interactions) are also scaled down by a factor of

√1 . 28 3

While the sequence partially protects the sensor from a broader spin envi-

ronment, it also limits the coupling to the relevant part of the spin Hamiltonian like Zeeman and chemical shift interactions. In the following sections, we explore the decoupling and sensing capabilities of the multi-pulse homohetero- spin decoupling sequence (WAHUHA + spin-bath control) presented in gure 4B. We measure the coherence time of the NV spin ensemble by combining the WAHUHA sequence and the P1 bath rotation. The multi-frequency π -pulse on the P1 bath (addressing each P1 transitions) is applied midway through the WAHUHA sequence. Repeating this basic unit twice achieves eective averaging of NV-P1 interactions (applied twice to account for the nite duration of the pulses). 29 This combined homohetero- spin decoupling sequence shows better sensor isolation and prolongs the dephasing time of the NV ensemble up to T∗2 ≈ 10µs (data shown in gure 4C). This value could potentially improve by suppressing pulse imperfections through robust control sequences using optimal control. The crucial advantage of the presented sequence is, it preserves static Zeeman interaction, and we analyze the performance of the combined homohetero spin decoupling sequence for DC magnetometry. To this end, we apply an external DC magnetic eld (Bdc ) and measure the uorescence change as a function of Bdc amplitude, which is plotted in gure √ 4C. From the data, we extract the DC magnetic eld sensitivity as ηWHH ≈ 31 nT/ Hz ( √ 3/2 ηV ≈ 1.2 nT µm / Hz). Taking the total uorescence into account (values given in WHH √ left x-axis of gure 4C), the estimated DC sensitivity is ηWHH,est ≈ 9 nT/ Hz (ηV WHH,est ≈

370 pT µm3/2 Hz−1/2 ). Note that the sensitivity without homo- or hetero-spin decoupling is 10


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√ √ 3/2 estimated as ηest ≈ 26 nT/ Hz (ηV / Hz). est ≈ 1 nT µm Although with the decoupling sequence, the eld interrogation time is signicantly enhanced (≈ 45X improvement over the bare NV ensemble dephasing time), the sensitivity is only slightly improved due to the intrinsic limitation of the decoupling scheme. The sensor is most sensitive to eld changes at the point of maximum slope, which in the case of Ramsey magnetometry is ∝ γN V τ C . Applying WAHUHA, project the Zeeman interaction equally onto all three spin axes, thus reducing the Zeeman strength and signal contrast by a factor of

√1 3

and

2 3

respectively. Thus improvement in sensitivity is only observed if the √

2

enhanced dephasing time T∗2,WHH T∗2 ( 3 2 3 ) . This scaling factor can be improved using proper initialization pulse to maximize the signal contrast. 2931 Further, with robust control pulses and improved isotopic purity, we expect the increase in T∗2 could compensate for the sensitivity reduction factor. In conclusion, we have fabricated a 30 nm thick diamond layer having a high density of NV centers (4 ppm) preferentially aligned along the (111) crystal axis. The dephasing time of the NVs is found to be T∗2 = 210 ns, where this values is limited by the interaction of the NV spins with the spin bath built of P1 centers. We show that by performing double resonance experiments on the NVs and P1 centers, T∗2 can be increased up to 850 ns. Moreover, by combing homonuclear dynamical decoupling pulses with a double resonance experiment, we reach T∗2 = 10 µs. Finally, we demonstrate that this new method can be used for √ DC eld sensing, where nd a sensitivity of 31 nT/ Hz and volume normalized sensitivity √ of 1.2 nTµm3/2 / Hz. This work presents the rst experimental realization of multi-pulse decoupling techniques compatible with Ramsey magnetometry and provides opportunities for DC sensing in the high sensor density limit.

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Acknowledgement The authors thank Matthew Markham, Senior Scientist at Element Six for providing the (111) - diamond substrate and Dr. Yan Liu for fruitful discussions. This work has been supported by DFG, Volkswagenstiftung, EU (STREP Project DIADEMS, ERC Synergy Grant BioQ), and IQST. Y.C. thank the support of The Graduate School of East China Normal University, Shanghai, China. T.T. acknowledges the support of JSPS KAKENHI (no. 26220903 and 16H06326), JST CREST (no. JPMJCR1773) and MEXT Q-LEAP(Quantum metrology & sensing), Japan. E.W. acknowledges funding from Shanghai International Cooperation Project (no. 16520710600). B.N. thank the Bundesministerium für Bildung und Forschung (BMBF) for the ARCHES award.

Supporting Information Available A detailed description of the CVD growth conditions, the experimental setup and measurement schemes including determination of NV center orientation, coherence time and bath spin density of the fabricated NV enriched layer can be found in the supplementary information.

References (1) Balasubramanian, G.; Neumann, P.; Twitchen, D.; Markham, M.; Kolesov, R.; Mizuochi, N.; Isoya, J.; Achard, J.; Beck, J.; Tissler, J.; Jacques, V.; Hemmer, P. R.; Jelezko, F.; Wrachtrup, J. Ultralong spin coherence time in isotopically engineered diamond. Nature Materials 2009, 8, 383387. (2) Gruber, A.; Dra, A.; Tietz, C.; Fleury, L.; Wrachtrup, J.; Borczyskowski, C. V. Scanning Confocal Optical Microscopy and Magnetic Resonance on Single Defect Centers. 2012,

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(3) McGuinness, L. P.; Yan, Y.; Stacey, A.; Simpson, D. A.; Hall, L. T.; Maclaurin, D.; Prawer, S.; Mulvaney, P.; Wrachtrup, J.; Caruso, F.; Scholten, R. E.; Hollenberg, L. C. L. Quantum measurement and orientation tracking of uorescent nanodiamonds inside living cells. Nature Nanotechnology 2011, 6, 358 EP . (4) Hall, L. T.; Beart, G. C.; Thomas, E. A.; Simpson, D. A.; McGuinness, L. P.; Cole, J. H.; Manton, J. H.; Scholten, R. E.; Jelezko, F.; Wrachtrup, J.; Petrou, S.; Hollenberg, L. C. High spatial and temporal resolution wide-eld imaging of neuron activity using quantum NV-diamond. Scientic Reports 2012, 2, 19. (5) Barry, J. F.; Turner, M. J.; Schloss, J. M.; Glenn, D. R.; Song, Y.; Lukin, M. D.; Park, H.; Walsworth, R. L. Optical magnetic detection of single-neuron action potentials using quantum defects in diamond. Proceedings of the National Academy of Sciences

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Walsworth, R. L.; Park, H.; Lukin, M. D. Nuclear magnetic resonance detection and spectroscopy of single proteins using quantum logic. Science 2016, 351, 836841. (10) Balasubramanian, G.; Chan, I. Y.; Kolesov, R.; Al-Hmoud, M.; Tisler, J.; Shin, C.; Kim, C.; Wojcik, A.; Hemmer, P. R.; Krueger, A.; Hanke, T.; Leitenstorfer, A.; Bratschitsch, R.; Jelezko, F.; Wrachtrup, J. Nanoscale imaging magnetometry with diamond spins under ambient conditions. Nature 2008, 455, 648651. (11) Maze, J. R.; Stanwix, P. L.; Hodges, J. S.; Hong, S.; Taylor, J. M.; Cappellaro, P.; Jiang, L.; Dutt, M. V. G.; Togan, E.; Zibrov, A. S.; Yacoby, A.; Walsworth, R. L.; Lukin, M. D. Nanoscale magnetic sensing with an individual electronic spin in diamond.

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z (µm)

5

> 99% prefrential alignment

3 1

30%

[111]

2.7

[1¯11]

[1¯ 11]

[¯1¯11]

[¯ 1¯ 11]

[¯111]

[¯ 111]

2.8 2.9 Frequency (GHz)

[111]

Measured signal

0.9

0.7

DC magnetometry

x (µm)

1.0

0.8

M Cts/s

Graphical TOC Entry

fluorescence

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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3.0

5.4 5.2 5.0 4.8

3 √ 2 ηV dc 1.2 nTµm / Hz

4.6 0

17

2

4

6

8 10 Bdc (µT)


12

14

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magnetometry with engineered nitrogen-vacancy spin ensembles in

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