Gradiometer Using Separated Diamond Quantum Magnetometers

sensors

Communication Gradiometer Using Separated Diamond Quantum Magnetometers

Yuta Masuyama 1,* , Katsumi Suzuki 2, Akira Hekizono 3, Mitsuyasu Iwanami 3, Mutsuko Hatano 1,2, Takayuki Iwasaki 2 and Takeshi Ohshima 1

1 Takasaki Advanced Radiation Research Institute, National Institutes for Quantum and Radiological Science and Technology, Takasaki, Gunma 370-1292, Japan; [email protected] (M.H.); [email protected] (T.O.) 2 Department of Electrical and Electronic Engineering, Tokyo Institute of Technology, Meguro, Tokyo 152-8552, Japan; [email protected] (K.S.); [email protected] (T.I.) 3 Department of Civil and Environmental Engineering, Tokyo Institute of Technology, Meguro, Tokyo 152-8552, Japan; [email protected] (A.H.); [email protected] (M.I.) * Correspondence: [email protected]

Abstract: The negatively charged nitrogen-vacancy (NV) center in diamonds is known as the spin defect and using its electron spin, magnetometry can be realized even at room temperature with extremely high sensitivity as well as a high dynamic range. However, a magnetically shielded enclosure is usually required to sense weak magnetic fields because environmental magnetic field noises can disturb high sensitivity measurements. Here, we fabricated a gradiometer with variable sensor length that works at room temperature using a pair of diamond samples containing negatively charged NV centers. Each diamond is attached to an optical fiber to enable free sensor placement. Without any magnetically shielding, our gradiometer realizes a magnetic noise spectrum comparable to that of a three-layer magnetically shielded enclosure, reducing the noises at the low-frequency range below 1 Hz as well as at the frequency of 50 Hz (power line frequency) and its harmonics. Citation: Masuyama, Y.; Suzuki, K.; These results indicate the potential of highly sensitive magnetic sensing by the gradiometer using the Hekizono, A.; Iwanami, M.; Hatano, NV center for applications in noisy environments such as outdoor and in vehicles. M.; Iwasaki, T.; Ohshima, T. Gradiometer Using Separated Diamond Quantum Magnetometers. Keywords: negatively charged nitrogen-vacancy (NV) center in diamond; magnetometry; quantum Sensors 2021, 21, 977. https:// sensing; gradiometer configuration; variable base length doi.org/10.3390/s21030977

Academic Editor: Guo-Hua Feng Received: 7 January 2021 1. Introduction Accepted: 27 January 2021 The negatively charged nitrogen-vacancy (NV) center in diamond is regarded as a Published: 2 February 2021 promising quantum sensor candidate by which sensing with extremely high sensitivity and high spatial resolution can be realized because of its excellent optical and spin properties, Publisher’s Note: MDPI stays neutral such as bright single-photon emission, spin-dependent luminescence intensity and long co- with regard to jurisdictional claims in herence time even at room temperature [1–3]. Since the sensitivity increases with increasing published maps and institutional affil- amounts of the NV center, an extremely weak magnetic field can be measured using the NV iations. center ensembles. It is also possible to resolve the nanometer level of the spatial resolution of the magnetic field using a single NV center. In addition, magnetic-field sensing can be carried out even in high magnetic field regions (more than ten Tesla) since signals do not saturate [4]. Thus, this indicates that we can realize magnetic field sensors with both Copyright: © 2021 by the authors. high sensitivity and wide dynamic range using the NV center. Moreover, quantum-sensing Licensee MDPI, Basel, Switzerland. based on the NV center can be applied to a wide variety of fields since diamond is sta- This article is an open access article ble against harsh environments [5–7] and is biocompatible [8–10]. In a previous study, distributed under the terms and Barry et al. detected magnetic fields from neuronal action potential of marine worms and conditions of the Creative Commons squid using an NV layer created near the surface of the diamond [11]. For a system of Attribution (CC BY) license (https:// applications, compact integrated magnetometers using the NV center demonstrated the creativecommons.org/licenses/by/ √ minimal detectable magnetic field of sub−10 nT/ Hz sensitivity over a 125 Hz bandwidth 4.0/).

Sensors 2021, 21, 977. https://doi.org/10.3390/s21030977 https://www.mdpi.com/journal/sensors Sensors 2021, 21, 977 2 of 11

using a balanced detection method [12] and 1 µT in 1 ms integration time with the specific 3 construction volume of√ about 2.9 cm [13]. For the sensitivity improvements, the magnetic sensitivity of 0.9 pT/ Hz was achieved for an AC magnetic signal at 20 kHz [14] and magnetic signals in the frequency range between 10 Hz and 1 kHz [15]. As a result of these epoch-making demonstrations of magnetometry using the NV center, magnetoencephalography (MEG) [16], which requires highly sensitive magnetic sensors, is now one of the most challenging target applications using the NV center. Currently, a superconducting quantum interference device (SQUID) [17,18] and an alkali vapor cell [19,20] are used for highly sensitive magnetic-field sensing to detect extremely small signals such as MEG signals. However, magnetic shield boxes/rooms are usually needed to realize the magnetic-field sensing because environmental magnetic noise disturbs the sensitive sensors needed to detect small signals [21,22]. A gradiometer is a method to reduce the effect of the magnetic noise when there are not any magnetic shield boxes/rooms [21,23–25]. Using the gradiometer configuration that uses multiple magnetometers to measure the gradient magnetic field, it is possible to remove environmental magnetic noises because the differential signal at two detection positions cancels a spatially homogeneous magnetic field. For gradiometers√ using the NV center, Shin et al. reported that the sensitivity of 4.6 ± 0.3 nT/ Hz was achieved using the gradiometer technique with a base length of 300 µm [26]. Here, the “base length” is defined as the distance between the two detection points. It was also reported that several micrometer scale spatial resolutions of magnetic field variations of the order of 10 µT were demonstrated using diamond connected to a dual-core photonic crystal fiber for the gradiometer configuration [27]. Ideally, to detect small signals efficiently, the optimum base length should be selected depending on the distance between the measurement target and sensors, the sensor sensitivity, and the inhomogeneity of magnetic noise. In general, to improve the signal-to-noise ratio (SNR), the base length should be longer than the distance between the measuring object and sensors. However, in previous studies, two fixed detection points in a diamond chip were used for the gradiometers. Thus, the distance between each point was the length of the order of micrometers. On the other hand, when we apply the gradiometer methodology to MEG, the base length should be of the order of a centimeter or more. It is also worth mentioning that we can expand the NV center magnetometry not only inside of rooms but also outdoors if the NV center gradiometer method is developed. In this study, we fabricated the NV gradiometer with the variable base length using a configuration of optical fibers and a pair of diamonds separated from a diamond in which a high concentration of the NV centers was created by electron irradiation. The gradiometer demonstrated the high sensitivity of magnetic field measurement compatible with that in a magnetically shielded enclosure consisting of three-layer permalloy shield boxes. Furthermore, our gradiometer placed at 50 mm apart from the target detected a magnetic signal with a base length up to 100 mm, which is important for sensing a deep signal, such as the brain. Our results are a crucial step towards MEG working at room temperature without the requirement for magnetic shielding.

2. Materials and Methods A gradiometer cancels a homogeneous magnetic ﬁeld by subtracting the signal at sensor 2 from the signal at sensor 1 (Figure1a). A local magnetic signal that is the target signal decays quickly, whereas a noise coming from afar decays gradually. Thus, the gradiometer cancels the environmental magnetic noise that limits highly sensitive magnetic sensing. To realize sensing with high sensitivity, the base length is the important parameter for the gradiometer. Thus, the distance between the target and sensor 1, called “depth”, should be minimized for highly sensitive sensing, although the base length should be longer than the depth. For example, for sensing a deep brain signal, a base length of 50 mm or more is preferable. Sensors 2021, 21,Sensors x FOR 2021PEER, 21 REVIEW, 977 3 of 11 3 of 11

Figure 1. (a)Figure Schematic 1. (a) representation Schematic representation of the gradiometer of the gradiometer setup. A longersetup. A base longer length base than length the than depth the enabled us to selectively detectdepth the enabled target us signal. to selectively (b) A schematic detect the setup target of signal. the gradiometer (b) A schematic using setup the nitrogen-vacancy of the gradiometer (NV) centers in a pair of diamonds.using the nitrogen A dichroic-vacancy mirror ( selectivelyNV) centers reflected in a pair the of diamonds. laser beam A and dichroic transmitted mirror theselectively fluorescence re- from NV centers. The fluorescenceflected the laser from beam each diamondand transmitted (sensor the 1 and fluorescence sensor 2) was from detected NV centers. by the The respective fluorescence photodiode from connected to an oscilloscope.each diamond (sensor 1 and sensor 2) was detected by the respective photodiode connected to an oscilloscope. Figure1b shows a schematic setup of the gradiometer using two diamond quantum Figure 1bsensors shows that a schematic enabled ussetup to change of the gradiometer in a wide range using of thetwo base diamond length. quantum In each sensor, each sensors that enableddiamond us sample to change was in attached a wide range to an of optical the base fiber length. is mounted In each on sensor, a coplanar each waveguide diamond sampleantenna was that attached controls to thean NVoptical centers fiber homogeneously. is mounted on Thea coplanar antenna w hadaveguide a similar geometry antenna that ascontrols in a previous the NV centers study homogeneously. [28], but it was notThe aantenna resonator had type a similar for operatinggeometry spins in the as in a previousNV study centers [28], using but ait wide was not frequency a resonator range. type An for amplifier operating was spins connected in the NV to the coplanar- centers usingwaveguide a wide frequency antenna range. via a coaxial An amplifier cable to was amplify connected the continuous-wave to the coplanar from-wave- the microwave guide antenna(MW) via a source. coaxial The cable microwave to amplify with the 25continuous dBm was-wave frequency from modulatedthe microwave at 2 kHz with a (MW) source.frequency The microwave deviation with width 25 ofdBm 8 MHz. was frequency A 532 nm lasermodulated beam with at 2 300kHz mW with of a optical power frequency deviationthrough width the optical of 8 MHz. fiber A illuminated 532 nm laser both beam diamond with 300 samples mW of containingoptical power the NV centers. through the opticalFluorescence fiber illuminated from NV centers both diamond in a volume samples of 1.2 containing mm3 in each the diamond NV centers. was collected by Fluorescencea from photodetector NV centers (Thorlabs in a volume FDS100A2) of 1.2 mm through3 in each the diamond optical fiber, was andcollected photons by detected by a photodetectorphotodetectors (Thorlabs FDS100A2) were digitized through using the an optical oscilloscope fiber, and (Keysight photons Technologies detected by DSOS054A). photodetectorsA dichroicwere digitized mirror using and aan long oscilloscope pass filter (Keysight selectively Technologies passed through DSOS054A). the fluorescence at A dichroic mirrorwavelengths and a long above pass 600 nm.filter The selectively data sampling passed rate through and collection the fluorescence time were at 25 MS/s and wavelengths15 above s, respectively. 600 nm. The Then, data a sampling computer rate extracted and collection the modulated time wer frequencye 25 MS/sec component from and 15 sec, respectively.the fluorescence Then, signals a computer collected extracted by the the oscilloscope. modulated Finally,frequency the component signals subtracting the from the fluorescencesignals at signals sensor collected 2 from the by signals the oscilloscope. at sensor 1 Finally, were obtained. the signals The subtracting magnetic field strength the signals atwas sensor obtained 2 from from the the signals change at in s theensor optically 1 were detected obtained. magnetic The magnetic resonance field (ODMR) signal. strength was obtainedTypical fro ODMRm the signals change observed in the optically from sensors detected 1 and magnetic 2 are shown resonance in Figure 2. A bias (ODMR) signal.magnetic field of 2 mT was applied by a magnet during the measurement to separate the Typical magneticODMR signals sublevel. observed The ODMR from s signalsensors 1 showed and 2 are different shown intensities, in Figure 2 as. A shown bias in Figure2 magnetic fieldsince of 2 the mT NV was centers applied in diamondby a magnet have during four orientation the measurement axes and to can separate detect the only the compo- magnetic sublevel.nent of The the ODMR magnetic signals field showed parallel different to the orientation intensities, axis. as shown We used in theFigure strongest 2 ODMR since the NVsignals centers toin measurediamond the have magnetic four orientation field in this axes study, and can i.e., detect the most only left the side com- of the ODMR ponent of thesignals magne showntic field in parallelFigure 2to. theThe orientation line widths axis. of the We ODMR used the resonance strongest of ODMR Ch.1 and Ch.2 were signals to measure12.8 MHz the andmagnetic 13.1 MHz field within this a contrast study, i.e., of 1.7%the most and 1.8%,left side respectively. of the ODMR These diamonds signals shownhad in Figure similar 2 quantum. The line propertieswidths of the because ODMR an resonance electron irradiated of Ch.1 and diamond Ch.2 were sample was di- 12.8 MHz andvided 13.1 intoMHz two with parts, a contrast as explained of 1.7% below. and 1.8%, Since respectively. we used two These MW sources,diamonds the microwave had similar quantumfrequency properties could be adjusted because independentlyan electron irradiated at the steepest diamond point sample of each was ODMR di- spectrum of − vided into twothe parts, magnetic as explained sublevel below. ms = 1Since in the we following used two experiments. MW sources, Our the gradiometer microwave obtained the frequency coulddifference be adjusted between independently the magnetic at fieldthe steepest strength point at each of each sensor. ODMR The magnetic spectrum field strength

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of the magnetic sublevel ms = −1 in the following experiments. Our gradiometer obtained of the magnetic sublevel ms = −1 in the following experiments. Our gradiometer obtained the difference between the magnetic field strength at each sensor. The magnetic field the difference between the magnetic field strength at each sensor. The magnetic field strengalongth the along orientation the orientation axis was axis calculated was calculated from the from ﬂuorescent the fluorescent signal at thesignal steepest at the point steep- of strength along the orientation axis was calculated from the fluorescent signal at the steep- esteach point ODMR of each spectrum. ODMR Detailsspectrum. are Details described are indescribed Appendix inA Appendix. A. est point of each ODMR spectrum. Details are described in Appendix A.

Figure 2. Typical optically detected magnetic resonance (ODMR) spectra of the spatially isolated Figure 2. Typical optically detected magnetic resonance (ODMR) spectra of the spatially isolated Figure 2. Typical optically detected magnetic resonance (ODMR) spectra of the spatially isolated didiamondamond samples samples of of s sensorensor 1 1 ( (Ch.Ch. 1 1)) and and s sensorensor 2 2 ( (Ch.Ch. 2 2).). The The detected detected fluorescence fluorescence at each detectordetec- diamond samples of sensor 1 (Ch. 1) and sensor 2 (Ch. 2). The detected fluorescence at each detec- toris aboutis about 0.2 0.2 mW. mW. The The ODMR ODMR signals signals (dips) (dips of the) of leftthe and left rightand right sides sides correspond correspond to magnetic to magnetic sublevels tor is about 0.2 mW. The ODMR signals (dips) of the left and right sides correspond to magnetic sublevelsms = −1 andms = +1,−1 and respectively, +1, respectively, for the NV for centerthe NV with center [111] with direction. [111] direction. The resonance The resonance of the other of threethe sublevels ms = −1 and +1, respectively, for the NV center with [111] direction. The resonance of the otherof the three four of orientation the four orientation axes is degenerate. axes is degenerate. Our microwave Our microwave circuit drives circuit the drives NV center the NV with center [111] other three of the four orientation axes is degenerate. Our microwave circuit drives the NV center withdirection [111] mostdirection effectively. most effectively. For each sensor, For each the sensor, noise voltage the noise of thevoltage ODMR of the measurement ODMR measure- is 0.057% of with [111] direction most effectively. For each sensor, the noise voltage of the ODMR measurement is 0.057% of the signal voltage of the fluorescence. ment is 0.057% ofthe the signal signal voltage voltage of of the the fluorescence. fluorescence. Next,Next, the the diamond diamond sample sample used used in in this this study study is is briefly briefly mentioned. mentioned. Our Our gradiometer gradiometer Next, the diamond sample used in this study is briefly mentioned. Our gradiometer usedused the the spatially spatially isolated isolated equal equal-quality-quality diamond diamond pair pair to to realize realize measurements measurements with with var- vari- used the spatially isolated equal-quality diamond pair to realize measurements with var- iableable detection points.points. FigureFigure3 3shows shows the the fabrication fabrication process process of theof the diamond diamond pair pair from from the iable detection points. Figure 3 shows the fabrication process of the diamond pair from thetype type Ib diamond, Ib diamond, which which contains contains a nitrogen a nitrogen concentration concentration of more of than more 10 19 thanatoms/cm 1019 at-3. the type Ib diamond, which contains a nitrogen concentration of more than 1019 at- oms/cmThe Ib diamond3. The Ib diamond was irradiated was irradiated with 2 MeV-electrons with 2 MeV- atelectrons a fluence at of a 1fluence× 1018 of/cm 1 ×2 10. To18 /cm avoid2. oms/cm3. The Ib diamond was irradiated with 2 MeV-electrons at a fluence of 1 × 1018 /cm2. Tothe avoid accumulation the accumulation of crystal of damage crystal damage and create and the create NV centersthe NV duringcenters irradiation,during irradiation, the elec- To avoid the accumulation of crystal damage and create◦ the NV centers during irradiation, thetron electron irradiation irradiation was carried was carried out at out 750 atC[ 75029 °C]. The[29]. gradiometer The gradiometer configuration configuration required re- the electron irradiation was carried out at 750 °C [29]. The gradiometer configuration re- quireddiamonds diamonds with equal-quality with equal-quality properties properties such as quantum such as quantum coherence coherence time, the number time, the of quired diamonds with equal-quality properties such as quantum coherence time, the numberthe NV of centers. the NV Therefore, centers. Therefore, the exposed the diamond exposed wasdiamond split into was two split pieces. into two pieces. number of the NV centers. Therefore, the exposed diamond was split into two pieces.

Figure 3. Fabrication process of the NV centers in diamond using electron beam irradiation. A Figure 3. Fabrication process of the NV centers in diamond using electron beam irradiation. A Figure 3. Fabrication processtype of Ib the diamond NV centers after electron in diamond beam using irradiation electron is beamdivided irradiation. into two and A typeattached Ib diamond to each optical after type Ib diamond after electron beam irradiation is divided into two and attached to each optical fiber. electron beamfiber. irradiation is divided into two and attached to each optical ﬁber.

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Sensors 2021, 21, 977 5 of 11 3. Results and Discussion 3.1. Cancellation of a Spatially Homogeneous Magnetic Field Noise 3. Results and Discussion To confirm the3.1. cancellation Cancellation ofof a the Spatially magnetic Homogeneous noise Magneticby the gradiometer, Field Noise the following experiment was carriedTo out. confirm First, the the cancellation spatially ofhomogeneous the magnetic noiseAC magnetic by the gradiometer, field of 20 the Hz following was induced by a solenoidexperiment coil was as carriedthe environmental out. First, the spatiallymagnetic homogeneous field noises AC (Figure magnetic 4a) field. The of 20 Hz magnetic field of 31was μT induced was generated by a solenoid by the coil solenoid as the environmental coil with a current magnetic of field2A. Then, noises (Figurethe 4a). in-homogeneous ACThe magnetic magnetic fieldfield of of 31 30µT Hz, was which generated was by used the solenoid as the targeted coil with asigna currentl, was of 2A. Then, the in-homogeneous AC magnetic field of 30 Hz, which was used as the targeted signal, induced by a copper wire beside sensor 1. The wire with a current of 1A generated a mag- was induced by a copper wire beside sensor 1. The wire with a current of 1A generated a netic field of 10 μT.magnetic Both AC field magnetic of 10 µT. fields Both AC were magnetic applied fields along were the applied orientation along the axis orientation of the axis of NV center (Figure the4b) NV. center (Figure4b).

Figure 4. (a) Gradiometer with the solenoid coil and the copper wire. The base length of the gradiometer was 27 mm. (b) DirectionFigure 4. of ( thea) Gradiometer magnetic fields with and the orientationsolenoid coil axis and of the the NV copper center. wire. The base length of the gradiometer was 27 mm. (b) Direction of the magnetic fields and the orientation axis of the NV center. Figure5 shows the time-domain signals of the detected magnetic field. The microwave Figure 5 showssources the time for sensor-domain 1 (Ch. signals 1) and sensorof the 2detected (Ch. 2) adjust magnetic the frequency field. The of the micro- microwave to wave sources for s2.71ensor and 1 2.7(Ch. GHz, 1) and respectively, sensor 2 which (Ch. were2) adjust the optimum the frequency points of of the the ODMR micro- spectrum of the m = −1 spin state for sensor 1 and sensor 2. Sensor 1 detected the small spatially wave to 2.71 and 2.7 GHz,s respectively, which were the optimum points of the ODMR inhomogeneous magnetic field signal modulating the large spatially homogeneous mag- spectrum of the mnetics = −1 field spin signal state (Figure for s5ensora, Ch. 1).1 and Sensor sensor 2 detected 2. Sensor only the 1 detected large spatially the homogeneoussmall spatially inhomogeneousmagnetic magnetic field signal field (Figure signal5a, modulating Ch. 2). The small the large spatially spatially inhomogeneous homogene- magnetic ous magnetic fieldfield signal signal (Figure remained 5a, Ch. in the 1) differential. Sensor 2 signaldetected due toonly the the cancellation large spatially of the large ho- spatially mogeneous magnetichomogeneous field signal magnetic (Figure field 5a, signal Ch. (Figure2). The5 a,small diff.). spatially inhomogeneous magnetic field signal remainedFourier-transform in the differential of the time-domain signal due signals to the indicated cancellation the ability of thethe cancellation large of the magnetic noise (Figure5b). The spatially homogeneous AC magnetic field of 20 Hz was spatially homogeneousreduced magnetic to less than field 1/50 signal in the ( differentialFigure 5a, signal. diff.). On the other hand, the in-homogeneous Fourier-transformAC magnetic of the time field-domain of 30 Hz signals was detected indicated by Ch.the 1,ab whereasility the nocancellation significant of peak was the magnetic noiseobserved (Figure for5b). Ch. The 2. Asspatially a result, homogeneous a peak at 30 Hz AC was magnetic observed infield the differentialof 20 Hz signal. was reduced to lessAt than 30 Hz, 1/50 the in subtracted the differential signal (Diff.) signal. was On about the 10% other smaller hand, than the Ch.1 in- becausehomoge- Ch. 2 also neous AC magneticdetected field of small 30 Hz amounts was detected of the component by Ch. 1, with whereas 30 Hz. no This significant indicated thatpeak the was shorter the observed for Ch. 2.base As a length, result, the a greaterpeak at the 30 loss Hz ofwas the observed difference in signal. the differential In the next section, signal. the At effect of base length on the loss is discussed. 30 Hz, the subtracted signal (Diff.) was about 10% smaller than Ch.1 because Ch. 2 also detected small amounts of the component with 30 Hz. This indicated that the shorter the base length, the greater the loss of the difference signal. In the next section, the effect of base length on the loss is discussed.

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Figure 5. ((aa)) Time Time-domain-domain signals signals at at s sensorensor 1 1(Ch.1 (Ch.1),), sensor sensor 2 2(Ch.2 (Ch.2)) and and subtracted subtracted signal signal (Diff. (Diff.).). The detected wave wave for for Ch. Ch. 2 2 is is almost almost a asingle single frequency frequency wave wave because because the the copper copper wire wire applying applying a magnetica magnetic field ﬁeld of of30 30Hz Hz is far is farfrom from sensor sensor 2. On 2. the On other the other hand, hand, since sincesensor sensor 1 detects 1 detects both 20 both and 20 30and Hz 30 magnetic Hz magnetic fields, ﬁelds, the detected the detected wave wave at Ch.1 at Ch.1is a com is abination combination of the of sin the wave. sin wave. (b) Fourier (b) Fourier-- transform of thethe time-domaintime-domain signalssignals fromfrom Ch.1 Ch.1 (solid (solid red red line), line) Ch., Ch. 2 2 (dashed-dotted (dashed-dotted green green line) line and) anddiff (dasheddiff (dashed blue blue line). line).

3.2. Base Base Length Dependence As above above-mentioned,-mentioned, the the distance distance of of the the base base length length to tothe the targ targetet depth depth is a iskey a keypa- rameterparameter for for magnetometry magnetometry (noise (noise cancelation cancelation)) by by gradiometer. gradiometer. We We measured measured the base length dependence dependence of of the the acquired acquired signal. signal. One One sensor sensor of of the the gradiometer gradiometer was was placed placed at 50 at mm50 mm apart apart from from the thetarget target magnet magnet assuming assuming the target the target object object is in a is deep in a part deep of part the ofbody, the suchbody, as such in the as inbrain. the brain. By varying By varying the position the position of the of other the other sensor, sensor, i.e., the i.e., base the base length, length, we measuredwe measured the thedifferential differential signal signal level. level. The The results results of of Figure Figure 66 clearly demonstrated thatthat the differential signalsignal dramatically dramatically increased increased with with increasing increasing base base length, length, and and the the saturation satura- tionwas was observed observed at a baseat a base length length above above 50 mm. 50 mm. This This result result indicates indicates that thethat gradiometer the gradiometer with withvariable variable base lengthbase length demonstrated demonstrated in this in study this isstudy useful is touseful sense to a sense target a with target deep with regions. deep regions.To obtain To large obtain signals large of signals the gradiometer, of the gradiometer, the base length the base should length be should longer thanbe longer the depth. than theOn depth. the other On hand, the other to cancel hand, the to magneticcancel thenoise, magnetic sensor noise, 1 and sensor sensor 1 and 2 should sensor detect 2 should the detectsame level. the same Therefore, level. Therefore, the base length the base should length be set should appropriately, be set appropriately, considering theconsidering distance between the measurement target and the noise source. In this respect, the gradiometer

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the distance between the measurement target and the noise source. In this respect, the gradiometer usingusing the the optical optical fiber ﬁber has anan advantageadvantage since since the the base base length length can can be be easily easily changed without changed withoutthe the adjustment adjustment of the of the optical optical path. path.

Figure 6. (aFigure) Setup 6. for (a) measuringSetup for measuring the base lengththe base dependence. length dependence. Sensor 1Sensor and sensor 1 and sensor 2 are connected 2 are connected to optical ﬁbers independently,to optical allowing fibers to change independently, the base lengthallowing freely. to change (b) Calculated the base differentiallength freely. signal (b) Calculated level using differen- the gradiometer as a function of thetial basesignal length. level using the gradiometer as a function of the base length.

3.3. Comparison3.3. Between Comparison Gradiometor between and Gradiometor Magnetically and Shielded Magnetically Enclosure Shielded. Enclosure The effectivenessThe of effectiveness the noise cancelation of the noise is cancelationshown in Figure is shown 7. We in compared Figure7. We the compared the environmentalenvironmental magnetic noise magnetic between noisethe gradiometer, between the a gradiometer, single sensor a in single a magnetically sensor in a magnetically shielded enclosure,shielded and enclosure,the single sensor and the without single any sensor magnetic without shielding any magnetic (Figure 7a shielding). The (Figure7a). magnetically shieldedThe magnetically enclosure shieldedconsisted enclosure of three-layer consisted permalloy of three-layer shield boxes permalloy that had shield boxes that a shielding performancehad a shielding of more performance than 60 dB of morefor fluctuating than 60 dB magnetic for fluctuating fields magneticabove 1 Hz fields above 1 Hz (Figure 7b). In (Figurethe case7b). of no In themagnetic case of shielding no magnetic nor shieldinggradiometer, nor the gradiometer, magnetic noise the magnetic was noise was found, which found,limited which the highly limited sensitive the highly magnetic sensitive sensing magnetic (Figure sensing 7c (Figure). The 7frequencyc). The frequency peaks peaks correspondedcorresponded to the frequency to the frequency of the utility of the utilityfrequency, frequency, i.e., 50 i.e., Hz, 50 and Hz, its and harmon- its harmonics. One of ics. One of the themagneti magneticc noises noises at low at lowfrequency frequency came came from from the trains the trains running running beside beside our our building. building. In theIn case the caseof using of using the thegradiometer, gradiometer, the the noise noise floor floor was was 34 34 nT, nT, which which was was com- comparable to that parable to thatobserved observed in in the the magnetically magnetically shielded shielded enclosure. enclosure. The The gradiometer gradiometer canceled canceled magnetic noises magnetic noisesat at the the frequency frequency of of the the utility utility frequency frequency andand itsits harmonics. Moreover, Moreover, the the gradiometer gradiometer reducedreduced magnetic noised noised to to the the same same level level as that as that in the in magnetically the magnetically shielded enclosure. shielded enclosureFor the. For frequency the frequency below below 1 Hz, 1 the Hz, noise the noiselevel of level the of magnetically the magnetically shielded enclosure shielded enclosure(W/shield) (W/shield and) gradiometer and gradiometer (W/difference) (W/difference was remarkably) was remarkably reduced reduced compared to the only compared to thesensor only 1 sensor without 1 thewithout magnetically the magnetically shielded enclosureshielded enclosure (W/O difference, (W/O differ- W/O shield). Thus, ence, W/O shieldthe). gradiometer Thus, the gradiometer successfully successfully removed the removed magnetic the noise magnetic at the samenoise level at the as the magnetic same level as theenclosure. magnetic However, enclosure. the However, noise floor the noise above floor 10 Hzabove was 10 the Hz samewas the for same all three methods because of the limitation of the sensor sensitivity. For further sensitivity improvement, one for all three methods because of the limitation of the sensor sensitivity. For further sensi- of the limiting factors was the fluctuation of the resonance frequency of the NV center due tivity improvement, one of the limiting factors was the fluctuation of the resonance fre- to thermal drift. The double quantum method that used two spin states m = ±1 cancels quency of the NV center due to thermal drift. The double quantum method that used twoS this fluctuation [15,30,31]. We intend to apply the double quantum method as a further spin states mS = ±1 cancels this fluctuation [15,30,31]. We intend to apply the double quan- investigation. Moreover, the magnetically shielded enclosure was not good at removing tum method as a further investigation. Moreover, the magnetically shielded enclosure low-frequency magnetic noise. Therefore, it was worth mentioning that the gradiometer was not good at removing low-frequency magnetic noise. Therefore, it was worth men- had more capability to remove noises in low-frequency regions when the quality of the NV tioning that the gradiometer had more capability to remove noises in low-frequency re- center was improved. gions when the quality of the NV center was improved.

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Figure 7. (a) Setup for measuring the magnetic noise frequency spectrum of the environment. (W/O difference, W/O shield) Figure 7. (a) Setup for measuring the magnetic noise frequency spectrum of the environment. (W/O difference, W/O shield) Only sensor 1 without any magnetic shielding nor using the gradiometer. (W/difference) The gradiometer with the base Only sensor 1 without any magnetic shielding nor using the gradiometer. (W/difference) The gradiometer with the base length of 50 mm. ( (W/W/ shield shield)) On Onlyly sensor sensor 1 1 in in the the three three-layer-layer magnetically magnetically shielded shielded enclosure. enclosure. ( (bb)) Three Three-layer-layer magnetically magnetically shielded enclosure. The The size size of of 70 cm is for magnetic sensing of small animalsanimals insideinside thethe enclosure.enclosure. (c) Magnetic noise frequency spectrum. The peaks between between 50 50 an andd 350 Hz Hz are are from from the the commercial commercial power power supply supply ( (5050 Hz Hz)) and and its its harmonics. harmonics. These magnetic noises propagated in space because the signal at 50 Hz and its harmonics disappear in a magnetically shielded enclosure (W/shield).(W/shield).

4. Conclusions Conclusions We demonstrated demonstrated the the gradiometer gradiometer with with variable variable base base length length using using a pair a of pair diamonds of dia- mondscontaining containing the NV the center NV and center evaluated and evaluated the gradiometer the gradiometer conﬁguration configuration and performance. and performance.An applied An spatially applied homogeneousspatially homogeneous magnetic magnetic ﬁeld was field reduced was reduced to less than to less 1/50 than in 1/50 the indifferential the differential signal. signal. As a result, As a aresult, signal a atsignal 10 µ Tat with 10 μT a frequency with a frequency of 30 Hz of was 30 detectedHz was detectedin the magnetic in the magnetic noise at 31noiseµT withat 31 aμT frequency with a frequency of 20 Hz byof the20 Hz gradiometer. by the gradiometer. Using the Usinggradiometer, the gradiometer, the background the background magnetic noisemagnetic was reducednoise was to reduced the same to level the same as that level in the as thatmagnetically in the magnetically shielded enclosure shielded enclosure in the frequency in the frequency range below range 1 Hz.below In addition,1 Hz. In addition, the gra- thediometer gradiometer removed removed the magnetic the magnetic noise of noise the commercial of the commercial power supply power frequencies supply frequencies of 50 Hz ofand 50 its Hz harmonics. and its harmonics. Thus, the Thus, result the suggests result thatsuggests the NV that center the NV gradiometer center gradiometer can be applied can

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to high-sensitive magnetometry even without any magnetically shielded enclosure, such as outdoor application for exploration of natural resources and monitoring the consciousness of car drivers. Since the gradiometer adopts the optical fiber system, the gradiometer is suit- able for constructing a portable system, not only the flexibility of the base length depending on the measurement target and magnetic field environment. To realize gradiometer applications, further investigations to improve the magnetic sensitivity are necessary. We intend to create the NV center ensembles with high-quality, e.g., high concentration NV with long spin coherence time, high ODMR contrast, etc., by optimizing electron irradiation and thermal treatment conditions. In addition, to realize a field-portable diamond NV gradiometer with extremely high sensitivity, we will optimize the design of the gradiometer, including the improvement of the spin manipulation sequence.

Author Contributions: Y.M. and K.S. contributed equally to this work. The project was planned by Y.M., T.I. and M.H.; Y.M. designed experiments with K.S. and A.H.; Electron irradiation was carried out by T.O.; The paper was written by Y.M. and K.S. with contributions from T.O., T.I., M.I. and M.H. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by MEXT Quantum Leap Flagship Program (MEXT Q-LEAP) Grant Number JPMXS0118067395. YM acknowledges the support of JSPS KAKENHI (20K14392), QST President’s Strategic Grant (Exploratory Research). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data that support the findings of this study are available within this article and also from the corresponding author on request basis. Conflicts of Interest: The authors declare no conflict of interest, any personal circumstances or interest that may be perceived as inappropriately influencing the representation or interpretation of reported research results. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Appendix A Magnetic sensing by the NV center is achieved by measuring the resonance frequency of magnetic resonance. The shift of the resonance frequency of the NV center by the magnetic ﬁeld B parallel to the orientation axis of the NV center is:

ν± = D ± gµB B/h, (A1)

where zero-field-splitting parameter D ≈ 2.87 GHz, gµB/h = 28 GHz/T is the gyromagnetic ratio of the electronic spin (Figure A1). Since the intensity of fluorescence reflects the magnetic level of the NV center, the magnetic resonance spectrum is obtained optically. Measuring the quantum state by light achieves a highly sensitive measurement because the energy of light is sufficiently higher than that of the environment. Compared to a SQUID pickup coil gradiometer, our gradiometer used a different method to cancel the homogeneous magnetic signal. In the case of the SQUID pickup coil, the constitution of the pickup coils was designed to obtain the subtracted signal by canceling the current from each pickup coil [32]. While the NV center had a high dynamic range, the subtracted signal was calculated by the computer after performing the magnetic measurement. Sensors 2021, 21, x FOR PEER REVIEW 10 of 11 Sensors 2021, 21, 977 10 of 11

Figure A1. Energy-level diagram of the negatively charged NV center in diamond. The two magnetic

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