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Akirabha Chanuntranont, Kazuki Otani, Daiki Saito, Yuki Ueda, Masato Tsugawa, Shuntaro Usui, Yuto Miyake, [Tokuyuki Teraji](https://orcid.org/0000-0002-7731-0547), Shinobu Onoda, Takahiro Shinada, Hiroshi Kawarada, Takashi Tanii

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This is the Accepted Manuscript version of an article accepted for publication in Applied Physics Express .  IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it.  The Version of Record is available online at https://doi.org/10.35848/1882-0786/acede9 [Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/)

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[Enhancing photon collection from single shallow nitrogen-vacancy centers in diamond nanopillars for quantum heterodyne measurements](https://mdr.nims.go.jp/datasets/110fcdc6-27a5-4e8c-8a99-dc004328401e)

## Fulltext

Applied Physics ExpressEnhancing photon collection from single shallow nitrogen-vacancycenters in diamond nanopillars for quantum heterodyne measurementsAkirabha Chanuntranont 1 ∗ , Kazuki Otani 1, Daiki Saito 1, Yuki Ueda 1,Masato Tsugawa 1, Shuntaro Usui 1, Yuto Miyake 1, Tokuyuki Teraji 2,Shinobu Onoda 3, Takahiro Shinada 4, Hiroshi Kawarada 1, Takashi Tanii 1 †1 School of Fundamental Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo169-8555, Japan2 National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 304-0044, Japan3 National Institutes for Quantum Science and Technology, 1233 Watanuki, Takasaki, Gunma370-1292, Japan4 Center for Innovative Integrated Electronic Systems, Tohoku University, 468-1 Aramaki-aza-aoba,Aoba, Sendai, Miyagi 980-8572, JapanThe developments in quantum sensing protocols and nano-photonic waveguides are merged to improvethe performance of single nitrogen-vancancy (NV) centers in nuclear magnetic resonance (NMR) sens-ing. Nanopillars are designed with NV centers placed 5 nm below the top facet and fabricated through asimple procedure, suitable for mass production. Fluorescence intensities from these nanopillars are 3.5times greater than that of single shallow NV centers embedded in unstructured flat diamond. Quantumheterodyne measurements of an alternating magnetic field are performed with these nanopillars andevidence of improved peak clarity in the frequency spectrum is shown.Single nitrogen-vacancy (NV) centers in diamond are promising sensors for nano-1scale nuclear magnetic resonance (NMR) measurements.1–3) An electron trapped in a2diamond NV center lends itself to optical spin state initialization, fluorescent spin state3readout, and may be manipulated coherently even in ambient conditions.4) Particularly,4due to increased sensitivity from their close proximity to target spins, NV centers within55 nm of the diamond surface (shallow NV centers) can be used to detect the alternating6magnetic field (AMF) induced by nuclear spins placed on the diamond surface.5–9) In7general configurations, shallow diamond NV centers have a reported magnetic sensitiv-8ity in the order of ∼1 µT/√Hz · µm−2.10) This sensitivity allows the detection of single9atomic nuclei such as 13C, 1H and 19F placed on the diamond surface and is also suf-10∗The first, second and third authors contributed equally to this work†E-mail address: tanii@waseda.jp1/16Appl. Phys. Expressficient to measure the distance between the NV center and target nuclear spins with1atomic-scale accuracy.11,12)2While shallow single NV centers have proven to be highly sensitive in practice, two3factors limit their usefulness as nano-NMR sensors. First, the frequency resolution of4shallow NV centers remains limited. Typical AMF measurements with diamond NV5centers achieve frequency resolutions in the kHz regime, while frequency resolutions be-6low 10 Hz are required to identify the chemical structure around target nuclear spins by7resolving chemical shifts and J-coupling.12,13) In principle, higher frequency resolutions8can be obtained by prolonging the measurement duration, which is limited by the coher-9ence time of NV center electron spins. However, while electrons of NV centers located in10bulk diamond demonstrate long coherence times at ambient conditions, coherence times11are decreased considerably for shallow NV centers due to surface imperfections, such12as dangling bonds and surface-modified phonons, in addition to paramagnetic sources13such as 13C and P1 centers in the diamond.14–16)14The second limiting factor is the low photon collection efficiency caused by the high15refractive index of diamond, which is approximately 2.42 at the air-diamond interface.16From a single NV center near the surface of unstructured (flat) diamond, we achieve on17average 40 kC/s. Once again, it is possible to compensate for the low photon collection18by prolonging the measurement duration, but this would require an intractably long19measurement duration and is not feasible considering the limited stability of our optical20equipment. To obtain good NMR measurement results in tractable time, photon counts21consistently above 100 kC/s are desired.22Potential solutions to these two problems have arisen in two independent strands23of research. One strand of research is focused on the development of quantum sensing24protocols. In this strand, multiple groups have developed a sensing protocol known25as quantum heterodyne (qdyne) which claims to overcome the limitation in frequency26resolution.17–19) As the name suggests, the method adapts the conventional heterodyne27method from signal processing to be used for quantum sensing with NV centers. In AMF28measurements, the Larmor precession of the NV center electron spin is modulated in29the presence of an AMF. In qdyne, this modulation is accumulated as a phase shift30of the electron spin using an XY8-k pulse sequence.20) Readout of the phase shift is31obtained by pulsed optically detected magnetic resonance (ODMR), where changes in32photon counts are expected to be proportional to the phase shift, hence the phase of the33AMF. Photon detection is performed at regular time intervals and the obtained photon342/16Appl. Phys. Expresscount time series is processed by a fast Fourier transform (FFT). As a result, qdyne1measurements produce peaks in the frequency regime at frequencies much lower than2that of the AMF. Each peak is then mapped to the frequency of the applied AMF using3the relationship between the two frequency regions. The reason that qdyne achieves a4high frequency resolution is that the number of samples can be increased arbitrarily5with a stable external clock, unrestricted by the coherence time of NV center electron6spins.17)7A second strand of research is focused on the development of nano-photonic waveg-8uides. These waveguides attempt to improve the photon collection efficiency from sin-9gle NV centers in diamond by exploiting characteristics ranging from enhancements10in mode couplings to optimization of the diamond surface to maximize critical angle11approaches.21–37) However, this strand of research is primarily focused on improving the12fluorescence characteristics of single NV centers in diamond with little regard to the13requirements of NMR sensing, such as charge stability, NV center depth and frequency14resolution.15In this paper, we merge these two strands of research and present results for an16AMF measurement, relevant to nano-NMR sensing. We propose a nanopillar design17optimized for a single NV center placed 5 nm below the diamond surface and present18a simple method for fabricating these nanopillars, suitable for mass production. The19photon counts and coherence time of NV center electron spins in these nanopillars are20compared with those in flat diamond. Finally, we perform qdyne AMF measurements21and compare the peak-to-floor-level fluctuation of the spectrum obtained from a single22NV center in a nanopillar to that from flat diamond.23The nanopillar dimensions were optimized for a single NV center placed 5 nm below24the diamond surface via a parameter grid-search using finite-difference time-domain25(FDTD) simulations (OptiFDTD, Optiwave Systems). In these simulations, the dia-26mond substrate is modelled after chemical-vapour-deposition (CVD) diamond, which is27an isotropic crystal with a refractive index of 2.4151 + i9.096 × 10−5. The NV center is28simulated as a point source emitting a 637 nm continuous wave with an Ey component.29The background mesh is simulated as air, with a refractive index of 1. As the control30model, flat diamond is simulated as a diamond slab of 0.5 µm thickness and 3 µm width.31The NV center is placed 5 nm below the diamond surface. The fluorescence power, in32Watts, is measured as an area average at the end of the mesh 1 µm away from the33diamond surface. For the grid search, the nanopillar is modelled as a perfect diamond343/16Appl. Phys. Expresscylinder and we vary the cylinder diameter and length. The domain of the grid search1is diameter ∈ [10 nm, 300 nm] in steps of 10 nm and length ∈ [50 nm, 600 nm] in steps2of 50 nm. The nanopillars are placed on top of the previously described flat diamond3substrate. For each nanopillar, the NV center is placed 5 nm below the nanopillar’s top4facet and the fluorescence power is measured as an area average at the end of the mesh51 µm away from the top facet. For all simulations, the mesh parameters used are δx,6δy, δz =0.01 µm each, with δt = 1.66782047599076× 10−17 running for 30,000 timesteps.7Anisotropic perfect matched layer (APML) boundary conditions were used.8An example of results from the FDTD simulations are shown in Fig. 1 (a) and (b) for9an optimal nanopillar and flat diamond respectively. The optimal nanopillar has a width10of 200 nm and a length of 400 nm. The total simulation volumes used to produce the11results in Fig.1 (a) and (b) are x, y, z dimensions of 3 µm×3 µm×1.9 µm=17.1 µm3 and123 µm×3 µm×1.5 µm=13.5 µm3 respectively. These results suggest that the fluorescence13enhancement from nanopillars may be due to an optical cavity caused by differences14between the optical modes of the nanopillar and bulk diamond. The presence of an15optical cavity in the nanopillar can be seen in Fig. 1 (a) as light is reflected between16the top and bottom of the pillar, leading to enhanced photon collection through the17pillar apex. Meanwhile, Fig. 1 (b) shows that the air-diamond interface reflects most of18the photons emitted by the NV center back to the diamond bulk in measurements with19a flat diamond surface. In the optical cavity model, continued reflection between the20pillar’s top, air-diamond interface, and bottom, pillar-bulk interface, may induce an op-21tical resonance that enhances photon collection at the air-diamond interface. However,22further research will be necessary to further develop this model.23Nanopillars were fabricated on an approximately 20 µm thick, 99.95% 12C-enriched24homoepitaxial diamond film grown on a type-Ib high-pressure high-temperature (100)25single-crystalline diamond substrate. An overview of the fabrication process is provided26in Fig. 2 (a). The growth conditions for the high-quality homoepitaxial film are described27elsewhere.38,39) First, 15N ions were implanted into the film at an acceleration energy of282.5 keV with a fluence of 1.5 × 1011 cm−2. After cleaning the diamond substrate with a29hot mixed acid solution (HNO3 : H2SO4 = 1 : 3) at 200 ◦C for 30 min, thermal annealing30was performed at 1000 ◦C for 120 min in a 10% H2 forming gas atmosphere to create31NV centers and a hydrogen-terminated electroconductive surface. Next, the diamond32was spin coated on the NV side with PMGI (Microchem, PMGI SF 6S) and ZEP-520A33(ZEON, ZEP-520A) at 4000 rpm for 50 s with a slope of 10 s to form a double-layer resist344/16Appl. Phys. Expressfilm with thicknesses of 220 nm and 200 nm respectively. The diamond was then baked1at 225 ◦C for 5 minutes to harden the resist. After that, a regular array of nanoholes2was patterned onto the resist film (diameter, 200 nm; spacing, 2 µm) through electron3beam (EB) lithography. Thin Ti cylinders (diameter, 200 nm; thickness, 70 nm; spacing,42 µm) were then fabricated on the diamond surface through EB vapor deposition and5the resist was removed using a lift-off process. Finally, nanopillars were fabricated by6inductively coupled plasma (ICP)-reactive ion etching (O2, 30 SCCM, 1 Pa; ICP power,7700 W; Bias power 250 W) using the Ti cylinders as an etching mask. The diamond8was cleaned again with hot-mixed acid (HNO3 : H2SO4 = 1 : 3) at 200 ◦C for 30 min to9remove the Ti mask. Thermal annealing was performed at 465 ◦C for 8 h in an O2 gas10atmosphere to create an oxygen-terminated surface and enhance the charge stability of11shallow NV centers.12Pulsed ODMR measurements were performed using a home-built scanning confo-13cal fluorescence microscopy (CFM) system. A schematic of our pulsed ODMR setup14is shown in Fig. 2 (b). Our system is equipped with a 532 nm-laser (Changchun New15Industries Optoelectronics Technology, MGL-III-532nm-300mW-1%), an acousto-optic16modulator (Gooch & Housego, AOMO 3350-120), a piezo stage (PI, NanoCube P-17611.3S) for objective scanning and a single-photon counting module (Laser Components,18COUNT-100C). An air objective lens (Olympus, MPLAPON 50×) and a long-pass fil-19ter (≥650 nm) were used in all fluorescence measurements. Microwaves (MWs) at the20resonant ODMR frequency (∼2 GHz) were generated by a radio frequency (RF) ana-21log signal generator (Keysight, E4428C) and pulsed by an RF circuit composed of a22phase shifter, two switches and a combiner (Mini-Circuits, ZX10Q-2-25-S+, ZASWA-232-50DR+ and ZX10-2-442-S+). The MW pulses were amplified by a power amplifier24(Mini-Circuits, ZHL-16W-43-S+) and applied to the NV center via a Cu wire antenna25(diameter, 20 µm) placed on the diamond substrate surface. The RF switching was con-26trolled by a data timing generator (Textronics, DTG5274). An Nd magnet supplied a27static magnetic field (∼30 mT), which was used to configure a two-level quantum sys-28tem consisting of NV center electron spin Ms = 0 and Ms = −1 sublevels. The photon29counting protocol was realized on a field-programmable gate array (FPGA) board (Dig-30ilent, Cora Z7-10) where a laboratory-designed hardware is implemented in hardware31description language (HDL) code. The data acquired by the FPGA was processed using32the Qudi software.40) Qdyne measurements were performed in intervals of 23.516 µs,33equivalent to the duration of an XY8-8 pulse sequence and some additional extra time.345/16Appl. Phys. ExpressRadio waves at 2 MHz were generated by an RF analog signal generator (Keysight,1N5181A), amplified by a power amplifier (Mini-Circuits, LZY-22+) and applied to the2NV center using a hand-wound coil (coil diameter, ∼38 mm; wire diameter, 0.40 mm;3coil turns, 50) surrounding the diamond substrate.4A scanning electron microscope (SEM) image of a fabricated nanopillar is shown in5Fig. 2 (c). The image is taken after removing the Ti mask. We note that the charge-up6effect is quite severe when procuring this image, even after surface termination with7hydrogen to create an electroconductive surface. Nevertheless, we are able to deter-8mine the diameter of the top facet, base and the pillar’s height to be 93 nm, 261 nm9and 260 nm respectively. The simple shape of the nanopillars makes them highly repro-10ducible in mass production. In a regular array of nanopillars, all nanopillars exhibit a11tapered shape with a flat top surface. The top and bottom diameters showed a standard12deviation of 8.6 nm and 7.2 nm, while the height showed a standard deviation of 4.4 nm.13The depth profile of NV centers created by 15N ion implantation at 2.5 keV was14reported to range from 2 nm to 11 nm with approximately 50% of the NV centers located15at a depth between 2 nm to 4 nm.16) It was observed that the Ti cylinders used as pillar16masks were not damaged by ICP-reactive ion etching, so we expect the NV centers17beneath the cap to be unaffected during etching. The NV center production yield and18number of NV centers per pillar was evaluated by previously reported methods.16) It19has been shown by Fukuda et al. through anti-bunching experiments that NV centers20produced by our method are distributed about the diamond surface following a Poisson21distribution characterized by the average number of NV centers per unit area, λ. In22our case, the NV center fabrication yield was found to be 5.91%, which results in23λ = 0.589. Note that this yield is significantly higher than that achieved by other24implantation techniques, which typically have yields of less than 1%.16) Furthermore,25an empirical count of NV centers per nanopillar was obtained to verify our method for26identifying nanopillars containing single NV centers. Single NV centers are identified by27a characteristic ODMR dip of approximately 15%. Using this method, we counted the28number of NV centers in each nanopillar and compare our results to the theoretically29obtained Poisson distribution. The comparison of our empirical counts with the Poisson30distribution is provided in Fig. 3. As can be seen in Fig. 3, approximately 30% of our31nanopillars contain single NV centers and our empirically obtained NV center counts32agrees closely with the theoretical distribution, with a sum of squared errors of 3.8×10−3.33Thus, we can successfully identify nanopillars with single NV centers. Using this process,346/16Appl. Phys. Expresswe choose only a nanopillar with a single NV center to conduct our measurements.1CFM images comparing the fluorescence profile of a shallow single NV center ob-2tained from a nanopillar and unstructured flat diamond are shown in Fig. 4 (a) and3(b) respectively. Visually, it can be seen from Fig. 4 that the single NV center in the4nanopillar is much brighter than in flat diamond, while maintaining a similar dispersion5profile. The average photon count detected from the nanopillar was measured to be 1806kC/s, while flat diamond only achieved 90 kC/s. The background fluorescence of the7nanopillar and flat diamond were measured to be 40 kC/s and 50 kC/s respectively.8Correcting for the background fluorescence, the fluorescence contribution of the sin-9gle NV center in nanopillar and flat diamond are 140 kC/s and 40 kC/s respectively.10Thus, the photon collection rate of the NV center in the nanopillar is 3.5 times higher11than that in flat diamond and our requirement that photon counts must be consistently12greater than 100 kC/s is satisfied.13Hahn echo measurements were performed to compare the electron spin coherence14times T2 of an NV center in a nanopillar after oxygen termination to that in flat di-15amond. The measured T2 of a single NV center electron spin in a nanopillar is 5.7 µs,16which is comparable to that in flat diamond at 4.5 µs. This coherence time has been17proven to fulfill the requirement for detection of 1H and 19F spins placed on the dia-18mond surface.16) This result confirms that the charge characteristics of shallow single19NV centers in oxygen-terminated nanopillars satisfies the requirements for nano-NMR20measurements.21To test the effectiveness of a single NV center in an oxygen-terminated nanopillar for22nano-NMR, qdyne measurements were performed. Each measurement was performed23for 600 s, resulting in approximately 2.55 × 107 samples. The goal of the measurement24is to detect an AMF with a frequency of 2 MHz, supplied by an RF analog signal25generator. The power of the AMF applied to the NV center is estimated to be 6.10 µT,26calculated from the current flowing through the coil. The spectra obtained using a27single NV center in a nanopillar and flat diamond are shown in Fig. 5 (a) and (b)28respectively. In each of the figures, simulated theoretical spectra are also shown. As29can be seen from the spectra, there is a small discrepancy between the measured peak30frequency and the original AMF frequency, which may be caused by a discrepancy31between the clock of the RF analog signal generator and the data timing generator. It32can also be seen from Fig. 5 that the enhanced photon collection from the nanopillar33directly contributes to obtaining a clear spectral peak. The experimentally obtained347/16Appl. Phys. Expresspeak amplitude obtained with the nanopillar is 0.368, more than double that of the flat1diamond at 0.178. Meanwhile, the floor level fluctuation (standard deviation from the2averaged baseline) obtained with the nanopillar is 0.0417 and that of the flat diamond is30.0406, which is a negligibly small difference. The simulated ideal frequency spectra were4obtained through Monte Carlo simulations. The number of photons detected at each5sampling point were drawn from a Poisson distribution parameterized by the photon6collection rate and AMF frequency. As can be seen in Fig. 5, there is a 64% deviation7between the simulated and measured peak amplitude of the nanopillar spectrum and8a 36% deviation for the flat diamond spectrum. These deviations were confirmed to9be owing mainly to the thermal drift of the laser optics and partially to background10fluorescence and stray light.11In conclusion, we have presented a nanopillar design in the context of nano-NMR12sensing with an NV center placed within 5 nm of the top facet. We have provided a sim-13ple fabrication procedure that yields highly reproducible nanopillars, suitable for mass14production. With our fabricated nanopillars, we have shown a 3.5 times improvement15in photon collection from the nanopillar resulting in an average photon count of 14016kC/s from a single NV center, which satisfies our requirement for tractable nano-NMR17measurements. We have also shown that the single NV in our fabricated nanopillars18have sufficiently long T2 for nano-NMR measurements. Finally, we have demonstrated19the effectiveness of our nanopillars in nano-NMR measurements by obtaining a 2 times20improvement in the peak amplitude obtained through qdyne AMF measurements, with21no significant increase in baseline fluctuations. With these demonstrations, we have ef-22fectively merged the developments in quantum sensing protocols with the developments23in nano-photonic structures.24While these are large improvements over NV sensing performance in flat diamond,25there is still a considerable discrepancy between our measured enhancement and the26theoretical value calculated through simulations. We believe some major sources of27these discrepancies to be sub-optimal nanopillar shape, as an artifact of the etching28process, as well as laser optics thermal drift and background fluorescence effects. In29future works, we will continue to improve our fabrication process, optical setup and30measurement protocol to control these sources of error. Furthermore, the T2 of shallow31single NV centers in nanopillars are still too short to detect many nuclear species of32interest. Increasing these T2 times remain an avenue of future research.338/16Appl. Phys. ExpressAcknowledgment1This work was supported by Japan Society for the Promotion of Science (JSPS) KAK-2ENHI Grant Number JP22H01921, JP18H03766 and JP23H00169, and partly by Ad-3vanced Research Infrastructure for Materials and Nanotechnology in Japan (ARIM)4and Design & Engineering by Joint Inverse Innovation for Materials Architecture5(DEJI2MA) of the Ministry of Education, Culture, Sports, Science and Technology6(MEXT). We also acknowledge the support of MEXT Q-LEAP (JPMXS0118068379),7JST CREST (JPMJCR1773), JST Moonshot R&D (JPMJMS2062), MIC R&D for con-8struction of a global quantum cryptography network (JPMI00316), JSPS KAKENHI9(No. 20H02187 and 20H05661).109/16Appl. Phys. ExpressReferences11) J. R. Maze, P. L. Stanwix, J. S. Hodges, S. Hong, J. M. Taylor, P. Cappellaro,2L. Jiang, M. V. Gurudev Dutt, E. Togan, A. S. Zibrov, A. Yacoby,3R. L. Walsworth, and M. D. Lukin, Nature 455 644 (2008).42) V. S. Perunicic, L. T. Hall, D. A. Simpson, C. D. Hill, and L. C. L. Hollenberg,5Phys. Rev. B 89 054432 (2014).63) L. M. Pham, S. J. DeVience, F. Casola, I. Lovchinsky, A. O. Sushkov, E. Bersin,7J. Lee, E. Urbach, P. Cappellaro, H. Park, A. Yacoby, M. Lukin,8and R. L. Walsworth, Phys. Rev. B 93 045425 (2016).94) R. Schirhagl, K. Chang, M. Loretz, C. L. Degen, Annu. Rev. Phys. Chem. 651083-105 (2014).115) N, Aharon, I. Schwartz, and A, Retzker, Phys. Rev. Lett. 122 120403 (2019).126) G. Balasubramanian, P. 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A 212 11 2365-2384 (2015).2139) T. Teraji, J. Appl. Phys. 118 115304 (2015).2240) J. M. Binder, A. Stark, N. Tomek, J. Scheuer, F. Frank, K. D. Jahnke, C. Müller,23S. Schmitt, M. H. Metsch, T. Unden, T. Gehring, A. Huck, U. L. Andersen,24L. J. Rogers, and F. Jelezko, SoftwareX 6 85-90 (2017).2512/16Appl. Phys. ExpressFig. 1. FDTD simulations showing the side fluorescence profile of a shallow single NV center in (a)a diamond nanopillar and (b) unstructured flat diamond.13/16Appl. Phys. ExpressFig. 2. (a) Schematic of the nanopillar fabrication process. (left) A double layer resist film isspin-coated after creating shallow NV centers in the diamond. (center) Titanium is deposited afterthe double layer resist film was patterned. (right) A nanopillar is fabricated by O2-plasma etching.(b) Sample setup for the pulsed ODMR measurements. (c) SEM image (bird’s eye view) of ananopillar after the Ti mask was removed by hot mixed acid cleaning.14/16Appl. Phys. ExpressFig. 3. Comparison between theoretical NV center Poisson distribution (orange line) withempirically counted number of NV centers (blue bars).Fig. 4. CFM images showing the top fluorescence profile of a shallow single NV center in (a) adiamond nanopillar and (b) unstructured flat diamond.15/16Appl. Phys. ExpressFig. 5. Frequency spectrum obtained by qdyne measurements and simulation for a shallow singleNV center in (a) a diamond nanopillar and (b) unstructured flat diamond.16/16