A. Creation of NV centers by a single laser pulse

We first examined the pulse number dependence of NV center creation. Figure 2(a) shows an optical micrograph of the diamond surface after fs-laser irradiation. In this experiment, diamond substrate No. 1 was used. The upper and lower sides show a series of circular- and linear-spot-irradiated regions for different input pulse numbers N. The laser fluence F was fixed at 5 J/cm2 for the circular spots and 26 J/cm2 for the linear spots. Due to laser-induced graphitization, the irradiated regions were more ablated and became darker with increasing N. Figures 2(b)–2(d) show confocal scans for circular spots for N = 1, 5, and 10 after the acid cleaning process. Each image has a bright circular region with a width of more than 25 µm. The region for N = 1 shows a higher PL intensity than the regions for N = 5 and 10. Figures 2(e)–2(g) show typical PL spectra obtained from the centers of the bright regions in Figs. 2(b)–2(d). The spectrum for N = 1 clearly shows spectral features associated with NV centers.5,37–425. M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C. L. Hollenberg, “The nitrogen-vacancy colour centre in diamond,” Phys. Rep. 528, 1 (2013). https://doi.org/10.1016/j.physrep.2013.02.00137. C. Schreyvogel, V. Polyakov, R. Wunderlich, J. Meijer, and C. E. Nebel “Active charge state control of single NV centres in diamond by in-plane Al-Schottky junction,” Sci. Rep. 5 12160 (2015). https://doi.org/10.1038/srep1216038. G. Davies, “Vibronic spectra in diamond,” J. Phys. C: Solid State Phys. 7, 3797 (1974). https://doi.org/10.1088/0022-3719/7/20/01939. A. Gruber, A. Dr̈benstedt, C. Tietz, L. Fleury, J. Wrachtrup, and C. von Borczyskowski, “Scanning confocal optical microscopy and magnetic resonance of single defect centers,” Science 276, 2012 (1997). https://doi.org/10.1126/science.276.5321.201240. S. Karaveli, O. Gaathon, A. Wolcott, R. Sakakibara, O. A. Shemesh, D. S. Peterka, E. S. Boyden, J. S. Owen, R. Yuste, and D. Englund, “Modulation of nitrogen vacancy charge state and fluorescence in nanodiamonds using electrochemical potential,” Proc. Natl. Acad. Sci. U. S. A. 113, 3938 (2016). https://doi.org/10.1073/pnas.150445111341. J. Jaske, D. W. M. Lau, X. Vidal, L. P. McGuinness, P. Reineck, B. C. Johnson, M. W. Doherty, J. C. McCallum, S. Onoda, F. Jelezko, T. Ohsima, T. Volz, J. H. Cole, B. C. Gibson, and A. D. Greentree, “Stimulated emission from nitrogen-vacancy centres in diamond,” Nat. Commun. 8, 14000 (2017). https://doi.org/10.1038/ncomms1400042. E. Fraczek, V. G. Savitski, M. Dale, B. G. Breeze, P. Diggle, M. Markham, A. Bennett, H. Dhillon, M. E. Newton, and A. J. Kemp, “Laser spectroscopy of NV−and NV0 colour centres in synthetic diamond,” Opt. Mater. Express 7, 2571 (2017). https://doi.org/10.1364/ome.7.002571 Compared with the spectrum for N = 1, the spectra for N = 5 and 10 have lower PL intensity, which indicates that the creation efficiency of the NV centers becomes low due to the increase of the laser ablation. Note the peaks at around 575 and 630 nm in the spectra that emerged regardless of the pulse number, and they are the Raman peaks from the diamond crystal.3737. C. Schreyvogel, V. Polyakov, R. Wunderlich, J. Meijer, and C. E. Nebel “Active charge state control of single NV centres in diamond by in-plane Al-Schottky junction,” Sci. Rep. 5 12160 (2015). https://doi.org/10.1038/srep12160Figures 2(h)–2(m) show images of linear-spot-irradiated regions for N = 1, 5, and 10, and PL spectra obtained near the centers of these irradiated regions. The results for the linear spots showed the same trend as those for the circular spots. Line-shaped regions that reflect the line spots were observed on the diamond surface. The region for N = 1 showed a high concentration of NV centers. From a Gaussian fit, the size of the irradiated region for N = 1 was estimated to be 51 × 4 µm2. This shows that for a focal spot line-scanned on a diamond surface, NV centers can be rapidly generated in a wide region without post-annealing.Creating NV centers with only a single laser pulse has not yet been reported. According to previous studies, the first pulse creates lattice vacancies (GR1 centers), and subsequent processes, such as thermal annealing16,1816. Y.-C. Chen, P. S. Salter, S. Knauer, L. Weng, A. C. Frangeskou, C. J. Stephen, S. N. Ishmael, P. R. Dolan, S. Johnson, B. L. Green, G. W. Morley, M. E. Newton, J. G. Rarity, M. J. Booth, and J. M. Smith, “Laser writing of coherent colour centres in diamond,” Nat. Photonics 11, 77 (2017). https://doi.org/10.1038/nphoton.2016.23418. C. J. Stephen, B. L. Green, Y. N. D. Lekhai, L. Weng, P. Hill, S. Johnson, A. C. Frangeskou, P. L. Diggle, Y. C. Chen, M. J. Strain, E. Gu, M. E. Newton, J. M. Smith, P. S. Salter, and G. W. Morley, “Deep three-dimensional solid-state qubit arrays with long-lived spin coherence,” Phys. Rev. Appl. 12, 064005 (2019). https://doi.org/10.1103/physrevapplied.12.064005 or illumination with a laser pulse train,17,34,3517. Y.-C. Chen, B. Griffiths, L. Weng, S. S. Nicley, S. N. Ishmael, Y. Lekhai, S. Johnson, C. J. Stephen, B. L. Green, G. W. Morley, M. E. Newton, M. J. Booth, P. S. Salter, and J. M. Smith, “Laser writing of individual nitrogen-vacancy defects in diamond with near-unity yield,” Optica 6, 662 (2019). https://doi.org/10.1364/optica.6.00066234. T. Kurita, Y. Shimotsuma, M. Fujiwara, M. Fujie, N. Mizuochi, M. Shimizu, and K. Miura, “Direct writing of high-density nitrogen-vacancy centers inside diamond by femtosecond laser irradiation,” Appl. Phys. Lett. 118, 214001 (2021). https://doi.org/10.1063/5.004995335. V. V. Kononenko, I. I. Vlasov, V. M. Gololobov, T. V. Kononenko, T. A. Semenov, A. A. Khomich, V. A. Shershulin, V. S. Krivobok, and V. I. Konov, “Nitrogen-vacancy defects in diamond produced by femtosecond laser nanoablation technique,” Appl. Phys. Lett. 111, 081101 (2017). https://doi.org/10.1063/1.4993751 create more vacancies or combine existing vacancies with substitutional nitrogen atoms. In the current work, however, the NV centers were created by single-pulse irradiation. This differs from previous experiments in that (1) the laser fluence was higher than the typical threshold for diamond graphitization (1–4 J/cm2, depending on several factors such as the pulse width, pulse number, and center wavelength),43–4743. Y. Liu, G. Chen, M. Song, X. Ci, B. Wu, E. Wu, and H. Zeng, “Fabrication of nitrogen vacancy color centers by femtosecond pulse laser illumination,” Opt. Express 21, 12843 (2013). https://doi.org/10.1364/oe.21.01284344. V. V. Kononenko, V. M. Gololobov, and V. I. Konov, “Latent laser-induced graphitization of diamond,” Appl. Phys. A 122, 258 (2016). https://doi.org/10.1007/s00339-016-9789-045. T. Kurita, N. Mineyuki, Y. Shimotsuma, M. Fujiwara, N. Mizuochi, M. Shimizu, and K. Miura, “Efficient generation of nitrogen-vacancy center inside diamond with shortening of laser pulse duration,” Appl. Phys. Lett. 113, 211102 (2018). https://doi.org/10.1063/1.505473046. P. Boerner, M. Hajri, N. Ackerl, and K. Wegener, “Experimental and theoretical investigation of ultrashort pulsed laser ablation of diamond,” J. Laser Appl. 31, 022202 (2019). https://doi.org/10.2351/1.509608847. B. Ali, H. Xu, D. Chetty, R. T. Sang, I. V. Litvinyuk, and M. Rybachuk, “Laser-induced graphitization of diamond under 30 fs laser pulse irradiation,” J. Phys. Chem. Lett. 13, 2679 (2022). https://doi.org/10.1021/acs.jpclett.2c00429 and (2) the laser pulse was loosely focused (NA ∼ 0.02) to obtain a large focal spot. Irradiating a single pulse onto a pristine diamond surface, both vacancy creation and N-V combination may occur together at a depth near the laser-ablated region. In contrast, multi-pulse irradiation will promote diamond graphitization and prevent the effective creation of NV centers due to the change in optical properties at the surface.44,4844. V. V. Kononenko, V. M. Gololobov, and V. I. Konov, “Latent laser-induced graphitization of diamond,” Appl. Phys. A 122, 258 (2016). https://doi.org/10.1007/s00339-016-9789-048. S. I. Kudryashov, A. A. Ionin, S. V. Makarov, N. N. Mel’Nik, L. V. Seleznev, and D. V. Sinitsyn, “Femtosecond laser ablation of carbon: From spallation to formation of hot critical plasma,” AIP Conf. Proc. 1464, 244 (2012). https://doi.org/10.1063/1.4739878The concentration of NV centers at the highest PL intensity positions in the circular and linear spot irradiated regions for N = 1 [Figs. 2(b) and 2(h)] was estimated to be 1.5 × 1013 and 3.5 × 1013 cm−3, respectively. The typical concentration in a laser-irradiated region is ∼1 × 1013 cm−3. This concentration was calculated by comparison with the previously reported PL intensity for a single NV center in the effective focal volume VE.3434. T. Kurita, Y. Shimotsuma, M. Fujiwara, M. Fujie, N. Mizuochi, M. Shimizu, and K. Miura, “Direct writing of high-density nitrogen-vacancy centers inside diamond by femtosecond laser irradiation,” Appl. Phys. Lett. 118, 214001 (2021). https://doi.org/10.1063/5.0049953 Note, first, that this estimation depends on the detection efficiency and spatial resolution of the microscope. Second, generated NV centers were found only at the diamond surface within the axial resolution ZR of the system. Since the actual focal volume must be smaller than the effective focal volume, the actual NV center concentration will be higher than our estimation. Third, comparing the two images, the line-spot-irradiated region has a higher NV concentration than the circle-spot-irradiated region. The differences in the laser fluence as well as the shape of the focusing beam may influence NV center generation.

B. Laser fluence dependence

We next investigated the dependence on the fs-laser fluence. Figure 3(a) shows a series of circular-spot-irradiated regions for various fluences F ranging from 1.1 to 54 J/cm2 on diamond substrate No. 2. The pulse number N was fixed at 1 for each region. Figures 3(b)–3(l) show confocal images of the laser-irradiated regions, indicated by dotted circles in Fig. 3(a). In Fig. 3(b), for F = 1.1 J/cm2, there was no region with an increased PL intensity. However, higher-intensity regions for F > 1.8 J/cm2 are present in Figs. 3(c)–3(l). These results indicate that a threshold for NV center creation by single-pulse irradiation exists between F = 1.1 and 1.8 J/cm2. Our estimation is consistent with the typical graphitization threshold for a femtosecond laser pulse.43–4743. Y. Liu, G. Chen, M. Song, X. Ci, B. Wu, E. Wu, and H. Zeng, “Fabrication of nitrogen vacancy color centers by femtosecond pulse laser illumination,” Opt. Express 21, 12843 (2013). https://doi.org/10.1364/oe.21.01284344. V. V. Kononenko, V. M. Gololobov, and V. I. Konov, “Latent laser-induced graphitization of diamond,” Appl. Phys. A 122, 258 (2016). https://doi.org/10.1007/s00339-016-9789-045. T. Kurita, N. Mineyuki, Y. Shimotsuma, M. Fujiwara, N. Mizuochi, M. Shimizu, and K. Miura, “Efficient generation of nitrogen-vacancy center inside diamond with shortening of laser pulse duration,” Appl. Phys. Lett. 113, 211102 (2018). https://doi.org/10.1063/1.505473046. P. Boerner, M. Hajri, N. Ackerl, and K. Wegener, “Experimental and theoretical investigation of ultrashort pulsed laser ablation of diamond,” J. Laser Appl. 31, 022202 (2019). https://doi.org/10.2351/1.509608847. B. Ali, H. Xu, D. Chetty, R. T. Sang, I. V. Litvinyuk, and M. Rybachuk, “Laser-induced graphitization of diamond under 30 fs laser pulse irradiation,” J. Phys. Chem. Lett. 13, 2679 (2022). https://doi.org/10.1021/acs.jpclett.2c00429 In addition, when the fluence was increased, the region’s size also increased while the focal spot size [Fig. 3(m)] was maintained. Figure 3(n) shows the dependence of the fluence F on the diameter of the region. Here, the diameter was obtained by analyzing the edge position, which corresponds to the extremum of the first derivative for the radial direction of the PL intensity distribution. The diameter became larger than the fs-laser focal spot size (41 µm) at F = 9.6 J/cm2 and reached 100 µm at F = 54 J/cm2. In Fig. 3(n), we also show the increased NV concentration in each region. This concentration was obtained as follows: first, the background signal was subtracted from the photon count for each pixel in the region, where the background was defined as the average over 10 × 10 pixels on the right-top of each confocal image. Then, the photon count was averaged over the region of increased intensity. Finally, the count was divided by the effective focal volume. The NV concentration started to increase at F = 1.8 J/cm2 and gradually became relatively constant at F ∼ 10 J/cm2 while repeatedly rising and falling. A single pulse with sufficient fluence will generate NV centers on a diamond surface over a wide region.A single laser pulse with high fluence beyond the diamond graphitization threshold generates an NV-center-fabricated region over the focal spot size. Although the details of the mechanism are still under discussion, some possible factors, such as laser-produced plasma and induced shockwave, may relate to the NV centers’ creation. When a high-intense pulse is focused on a material surface, the surface is subject to photon-radiation pressure. The pressure Pp is estimated by Pp ∼ Ip/c = F/cwp, where Ip is the peak intensity, c is the speed of light, F is the fluence, and wp is the pulse width. For the laser pulse with F = 10 J/cm2 and wp = 35 fs (Ip = 3 × 1014 W/cm2), Pp impulsively reaches 10 GPa. Then, the laser pulse creates a high-dense plasma and laser ablation occurs.4949. B. Ali, I. V. Litvinyuk, and M. Rybachuk, “Femtosecond laser micromachining of diamond: Current research status, applications and challenge,” Carbon 179, 209 (2021). https://doi.org/10.1016/j.carbon.2021.04.025 During the process, the diamond also experiences high recoiled pressure by laser-ablated defects Pr. According to the study of femtosecond-laser-driven shockwave for Al film5050. R. Evans, A. D. Badger, F. Falliès, M. Mahdieh, T. A. Hall, P. Audebert, J.-P. Geindre, J.-C. Gauthier, A. Mysyrowicz, G. Grillon, and A. Antonetti, “Time- and space-resolved optical probing of femtosecond-laser-driven shock waves in aluminum,” Phys. Rev. Lett. 77, 3359 (1996). https://doi.org/10.1103/physrevlett.77.3359 and Si materials,5151. M. Tsujino, T. Sano, O. Sakata, N. Ozaki, S. Kimura, S. Takeda, M. Okoshi, N. Inoue, R. Kodama, K. F. Kobayashi, and A. Hirose, “Synthesis of submicron metastable phase of silicon using femtosecond laser-driven shock wave,” J. Appl. Phys. 110, 126103 (2011). https://doi.org/10.1063/1.3673591 Pr is an order of 10–100 GPa for Ip ∼ 1014–1015 W/cm2. The diamond will also be subject to high pressure. Depending on the laser fluence, the plasma distribution and shockwave propagation induced by such high pressure may assist the N-V formation at the laser-irradiated region. In the current study, plasma formation will occur not only at the diamond surface but also in the air region just above the surface. The maximum intensity reached 1.5 × 1015 W/cm2 (F = 54 J/cm2) at the focal position. According to the Coulomb-barrier suppression theory,5252. S. Augst, D. D. Meyerhofer, D. Strickland, and S. L. Chin, “Laser ionization of noble gases by Coulomb-barrier suppression,” J. Opt. Soc. Am. B 8, 858 (1991). https://doi.org/10.1364/josab.8.000858 the ionization thresholds for ambient molecules (O2 and N2) can be calculated as 8.4 × 1013 and 2.4 × 1014 W/cm2, respectively.52,5352. S. Augst, D. D. Meyerhofer, D. Strickland, and S. L. Chin, “Laser ionization of noble gases by Coulomb-barrier suppression,” J. Opt. Soc. Am. B 8, 858 (1991). https://doi.org/10.1364/josab.8.00085853. X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A 66, 033402 (2002). https://doi.org/10.1103/physreva.66.033402 Hence, the air molecules just above the diamond surface will also be ionized by the intense laser field and induce a plasma state.54,5554. P. Sprangle, J. R. Peñano, and B. Hafizi, “Propagation of intense short laser pulses in the atmosphere,” Phys. Rev. E 66, 046418 (2002). https://doi.org/10.1103/PhysRevE.66.04641855. B. Rethfeld, K. Sokolowski-Tinten, D. von der Linde, and S. I. Anisimov, “Timescales in the response of materials to femtosecond laser excitation,” Appl. Phys. A 79, 767 (2004). https://doi.org/10.1007/s00339-004-2805-9 The laser-induced plasma in the air also expands with supersonic velocity and drives shockwaves, which may relate to the NV creation.

C. Creation of NV centers in a millimeter-sized region

The results shown in Fig. 3 inspired us to create NV centers in a millimeter-sized region for single-shot irradiation. In Fig. 3(l), we showed the results for laser pulse irradiation with a spot diameter 2w (= 2wx = 2wy) of 41 µm and a fluence F of 54 J/cm2. The pulse energy E corresponds to 0.36 mJ, derived from a simple Gaussian distribution F = E/(πw2/2). After upgrading the CPA system, our current maximum pulse energy reached 500 mJ.3636. S. Inoue, S. Sakabe, Y. Nakamiya, and M. Hashida, “Jitter-free 40-fs 375-keV electron pulses directly accelerated by an intense laser beam and their application to direct observation of laser pulse propagation in a vacuum,” Sci. Rep. 10, 20387 (2020). https://doi.org/10.1038/s41598-020-77236-2 Applying the maximum energy gives a laser pulse with a larger focal spot and a higher fluence. Figure 4 shows the relation between 2w and F for a given E. For example, for F fixed at 54 J/cm2, 2w increases from 41 to 1540 µm when E is increased from 0.36 to 500 mJ (from the blue-filled circle to the red-unfilled circle in Fig. 4). In addition, with sufficient laser fluence, the region containing NV centers is larger than the spot diameter, as shown in Fig. 3(n). Therefore, single-shot laser irradiation can create NV centers in a region with a diameter larger than 1.5 mm. Reducing the fluence while keeping the pulse energy fixed will increase the spot diameter. For the next example, we consider a laser pulse with F = 9.6 J/cm2 and 2w = 41 µm (giving E = 0.064 mJ). Under these conditions, the NV-center-created region became almost as wide as the focal spot. If the fluence F is fixed at 9.6 J/cm2, the beam diameter increases to 2w = 3640 µm at E = 500 mJ (from the blue-filled square to the red-unfilled square). When the fluence is larger than the estimated threshold for NV creation (in this case, F = 1.1–1.8 J/cm2, indicated by the gray bar), a single laser pulse with a sufficiently large spot diameter will generate NV centers over a millimeter-sized region.Based on the above-mentioned discussion, we prepared a laser pulse of several hundred mJ. However, we must change experimental conditions to use such a high-energy pulse. When a high-energy pulse goes through the air atmosphere, it interacts with air molecules via non-linear optical processes, deteriorating the pulse quality. We must carry out such a high-energy experiment in a vacuum (∼5 × 10−2 Pa) [Fig. 5(a)]. In addition, to obtain the high energy while suppressing the laser damage to the optics, the beam diameter was expanded to 50 mm. If the parabolic mirror with f = 165 mm focuses this laser beam, the NA becomes 0.15. The left side of Fig. 5(b) shows the beam profile at the focal position. The spot size diameter (2wx, 2wy) became (5.7, 4.8 µm). Since the ideal spot size is calculated to be about 7 µm (in the case of the Airy disk diameter 2w of the diffraction-limited spot at a uniformly-illuminated beam, 2w = 1.22λ/NA), our laser beam was well-focused. Then we observed the beam profile at the defocused position. For example, the right side of Fig. 5(b) shows the profile at the position about 5 mm behind the focus. We confirmed the defocused spot diameter was about 1.5 mm, enough size to perform the irradiation experiments.In the actual irradiation experiment, we applied pulse energy E = 166 mJ and defocused spot diameter 2w = 1.13 mm (the defocused position was set to 3.7 mm). Here, the diameter was confirmed by the irradiation mark on an aluminum plate before conducting the diamond irradiation experiments. The upper side of Fig. 5(c) shows the micrograph after the single pulse irradiation on diamond substrate No. 3. The irradiated region pattern reflects the laser intensity distribution, as shown on right side of Fig. 5(b). The region diameter of 1.08 mm, judging from the microscope scale bar, was consistent with the above-estimated diameter. Although the intensity distribution was neither uniform nor Gaussian, we estimated the fluence F of 33 J/cm2 according to the same procedure discussed in Fig. 4 (the green-filled diamond). The estimated fluence was much higher than the graphitization threshold and enough for the high-fluence experiment. The lower side of Fig. 5(c) shows the micrograph after boiling acid treatment. Although some shaded pattern remained, almost all of the laser-induced defects were removed.Figure 5(d) shows a series of confocal images at several regions on substrate No. 3. While the substrate is 2 mm square, the region that can sweep at one time is only 100 µm square. It is not practical to measure the entire substrate. Hence, we measured only 35 images to evaluate the size of the PL-increased region and the difference between the irradiated and non-irradiated regions. We first measured one of the four corners as a reference position. Then we measured several images for other regions by changing the lateral position using the two-axis micrometer attached to the sample stage. Here, the mirrored and tilted image of Fig. 5(c) is also overlapped in the background to clarify to compare the confocal image position with the laser-irradiated region. Judging from the boundary shape of the PL-increased region, the size of the PL-increased region was consistent with that of the laser-irradiated region. In addition, no particular PL increase was observed outside the laser-irradiated region. Figure 5(e) is an image of the area A shown in Fig. 5(d). We can confirm a part of the boundary area of the PL-increased region. Figure 5(f) shows the PL spectra measured at points A-1 to A-3, indicated in Fig. 5(e). Points A-1 and A-2 were selected in the unirradiated region. Point A-1 showed a typical spectrum on the pristine diamond surface and did not include the NV center’s signal. In some cases, we found NV centers’ signal like the A-2’s PL spectrum. Point A-3 was inside the irradiated region. The A-3’s spectrum shows a strong NV centers’ signal, about one-order higher than the A-2’s spectrum. Figure 5(g) is a close-up of area B in Fig. 5(d), showing the vicinity of the center in the irradiated region. Although the PL intensity did not uniformly distribute, the entire intensity became much higher than that of the unirradiated region. The distribution may reflect several factors, such as the laser profile, the local structure of the diamond surface, and local nitrogen distribution. We also confirmed PL spectra at several points (B-1 to B-3)  as shown in Fig 5(f), and all the data showed strong signals from NV centers. For example, the PL intensity at point B-3 is more than ten times larger than that of a single NV center, and the corresponding concentration is at least >5 × 1013 cm−3. Combined with the results of spin coherence time measurements discussed in Sec. , we conclude that a single-shot femtosecond laser pulse created NV centers in a millimeter-sized region.In this experiment, the estimated laser fluence was higher than 10 J/cm2, which suggests the PL-increased region may expand compared with the laser-irradiated region, as shown in Fig. 3(l). Nevertheless, the size of the PL-increased region almost coincided with that of the laser-irradiated region. One of the differences in the experimental conditions between Figs. 3 and 5 is whether the sample-surrounding environment is in an air atmosphere or a vacuum. As mentioned in Sec. , the presence of a laser-induced plasma shock wave caused by air breakdown may affect the creation of NV centers’ around the laser-irradiated region. As another possible reason, an air atmosphere may affect the propagation direction of a shock wave induced on a diamond surface. In any case, the creation of NV centers was realized in a vacuum. We are continuing our investigations into controlling the NV center density and the region’s size.

D. Electron-spin coherence time

The electron-spin coherence time T2 and free induction decay (FID) time T2* are directly related to the required sensitivity for AC and DC quantum sensing applications.4,6,26–284. L. Rondin, J.-P. Tetienne, T. Hingant, J.-F. Roch, P. Maletinsky, and V. Jacques, “Magnetometry with nitrogen-vacancy defects in diamond,” Rep. Prog. Phys. 77, 056503 (2014). https://doi.org/10.1088/0034-4885/77/5/0565036. E. D. Herbschleb, H. Kato, Y. Maruyama, T. Danjo, T. Makino, S. Yamasaki, I. Ohki, K. Hayashi, H. Morishita, M. Fujiwara, and N. Mizuochi, “Ultra-long coherence times amongst room temperature solid-state spins,” Nat. Commun. 10, 3766 (2019). https://doi.org/10.1038/s41467-019-11776-826. S. Choi, J. Choi, R. Landig, G. Kucsko, H. Zhou, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, V. Khemani, C. von Keyserlingk, N. Y. Yao, E. Demler, and M. D. Lukin, “Observation of discrete time-crystalline order in a disordered dipolar many-body system,” Nature 543, 221 (2017). https://doi.org/10.1038/nature2142627. E. V. Levine, M. J. Turner, P. Kehayias, C. A. Hart, N. Langellier, R. Trubko, D. R. Glenn, R. R. Fu, and R. L. Walsworth, “Principles and techniques of the quantum diamond microscope,” Nanophotonics 8, 1945 (2019). https://doi.org/10.1515/nanoph-2019-020928. E. Bauch, S. Singh, J. Lee, C. A. Hart, J. M. Schloss, M. J. Turner, J. F. Barry, L. M. Pham, N. Bar-Gill, S. F. Yelin, and R. L. Walsworth, “Decoherence of ensembles of nitrogen-vacancy centers in diamond,” Phys. Rev. B 102, 134210 (2020). https://doi.org/10.1103/physrevb.102.134210 We finally measured T2 and T2* at the fs-laser-irradiated regions using a spin-echo sequence and a Ramsey sequence. To measure T2 and T2*, we applied microwave irradiation to the NV centers using a Cu wire with a diameter of 30 µm placed over the diamond substrate [Fig. 6(a), left side]. A static magnetic field B0 was applied along one of four possible N-V axes using a permanent magnet. The right side of Fig. 6(a) shows a close-up confocal image of area C, in the vicinity of the center of the laser-irradiated region and close to (µm) the Cu wire [area C is also shown in Fig. 5(d)]. Figure 6(b) shows the optically-detected magnetic resonance (ODMR) spectrum measured at point C-1 in area C. Four peaks split by the Zeeman effect due to the static field are observed. The peak at 2566 (3190) MHz corresponds to the transition between the electron spin states |ms = 0⟩ and |ms = −1⟩ (|ms = +1⟩ for the NV centers along the static field.2727. E. V. Levine, M. J. Turner, P. Kehayias, C. A. Hart, N. Langellier, R. Trubko, D. R. Glenn, R. R. Fu, and R. L. Walsworth, “Principles and techniques of the quantum diamond microscope,” Nanophotonics 8, 1945 (2019). https://doi.org/10.1515/nanoph-2019-0209 The B0 was about 11.1 mT, estimated by using the Zeeman shifts of the two peaks (624 MHz = 2γB0, where γ = 28.0 MHz/mT is the electron gyromagnetic ratio). Using the NV centers with |ms = 0⟩ ↔ |ms = −1⟩ transition (indicated by black arrow), Rabi oscillation of the electron spins was observed to determine the lengths of the π and π/2 pulses [Fig. 6(c)]. Then, we measured spin-echo signals and obtained T2 [Fig. 6(d)]. To remove common-mode noise, the measured S0 (rotational axis of the second π/2 pulse parallel to that of the first π/2 pulse) and S1 (antiparallel) were subtracted and normalized as (S0 − S1)/(S0 + S1).6,566. E. D. Herbschleb, H. Kato, Y. Maruyama, T. Danjo, T. Makino, S. Yamasaki, I. Ohki, K. Hayashi, H. Morishita, M. Fujiwara, and N. Mizuochi, “Ultra-long coherence times amongst room temperature solid-state spins,” Nat. Commun. 10, 3766 (2019). https://doi.org/10.1038/s41467-019-11776-856. N. Bar-Gill, L. M. Pham, A. Jarmola, D. Budker, and R. L. Walsworth, “Solid-state electronic spin coherence time approaching one second,” Nat.Commun. 4, 1743 (2013). https://doi.org/10.1038/ncomms2771 Then, T2 was obtained by fitting to an exponential decay function (∝exp−(2τ/T2)n), where 2τ is the time between the first and second π/2 pulses. We measured T2 at three different points in this region, and the average value was 1.2 µs. We also measured T2 at three points in the laser-irradiated region with F = 9.6 J/cm2 [Fig. 3(g)] and the pristine (non-laser-irradiated) region, and the average T2 became 1.0 and 1.2 µs, respectively. According to previous studies, T2 for an ensemble of NV centers scales with the nitrogen concentration [N].2828. E. Bauch, S. Singh, J. Lee, C. A. Hart, J. M. Schloss, M. J. Turner, J. F. Barry, L. M. Pham, N. Bar-Gill, S. F. Yelin, and R. L. Walsworth, “Decoherence of ensembles of nitrogen-vacancy centers in diamond,” Phys. Rev. B 102, 134210 (2020). https://doi.org/10.1103/physrevb.102.134210 Based on the nitrogen content of our sample ([N] ∼ 100 ppm), the expected T2 was 1–2 µs. Our results are consistent with the results of previous research, indicating that P1 centers (substitutional nitrogen atoms) deteriorate the spin coherence of the NV centers. We also measured T2* by Ramsey sequence at the laser-irradiated region [Fig. 6(e)].2828. E. Bauch, S. Singh, J. Lee, C. A. Hart, J. M. Schloss, M. J. Turner, J. F. Barry, L. M. Pham, N. Bar-Gill, S. F. Yelin, and R. L. Walsworth, “Decoherence of ensembles of nitrogen-vacancy centers in diamond,” Phys. Rev. B 102, 134210 (2020). https://doi.org/10.1103/physrevb.102.134210 The T2* was determined by fitting the FID signal to an exponential decay function (∝exp−(τ/T2*)n), where τ is the time between the first and second π/2 pulses. The average value at three different points was 45 ns, which is also consistent with the expected T2* (∼100 ns at [N] ∼ 100 ppm).2828. E. Bauch, S. Singh, J. Lee, C. A. Hart, J. M. Schloss, M. J. Turner, J. F. Barry, L. M. Pham, N. Bar-Gill, S. F. Yelin, and R. L. Walsworth, “Decoherence of ensembles of nitrogen-vacancy centers in diamond,” Phys. Rev. B 102, 134210 (2020). https://doi.org/10.1103/physrevb.102.134210 These results indicate that the laser ablation and subsequent surface treatment will not influence the lengths of T2 and T2*. This is beneficial for quantum applications with high sensitivity.