Open Access
Add to BibSonomy
Abstract
The NV centers in a diamond were successfully created by the femtosecond laser single pulse. We also investigated the effect on the diamond lattice induced by the different laser pulse widths from both experimental and theoretical perspectives. Interestingly, in spite of the high thermal conductivity of a diamond, we found that there is a suitable pulse repetition rate of several tens kHz for the formation of NV center ensembles by the femtosecond laser pulse irradiation.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The negatively charged nitrogen-vacancy (NV−) center composed of impurity nitrogen adjacent to a vacancy in diamond is expected to apply to quantum technologies such as quantum computing [1], quantum cryptographic communication [2], and magnetic, electric field, temperature, and strain quantum sensing [3–5]. The NV− center has a good property of an electron spin, specifically, it has a long spin coherence time at even room temperature [6], which achieved the high T2 leading to the best sensitivities even now, and the spin can be controlled and detected optically. The NV center is formed by (1) incorporation of nitrogen during the synthesis process such as CVD [7] or (2) intentional process by electron beam irradiation or nitrogen ion implantation [8,9]. These methods have advantages in a quantum sensor application, however, some issues remain. For instance, the low spatial selectivity for method (1) is a problem to be solved. In addition, methods (2) need subsequent annealing to diffuse carbon vacancies and combine them with nitrogen impurities. Although, ion implantation methods have achieved resolution of lateral location of several nm [10], control of vertical position is difficult. As one possible solution to these issues, the femtosecond laser direct writing technique is attracting more attention for NV center formation. The remarkable advantage of the laser direct-writing method is to realize a flexible spatial arrangement of color centers in three dimensions. Bharadwaj et al. reported the integrated on-chip quantum device in diamond composed of laser-written waveguides with NV center ensembles [11]. Chen et al. reported the formation of vacancies (GR1 centers) associated with the neutral vacancy of the C atom (V°) by femtosecond laser pulse irradiation and subsequent vacancy diffusion by thermal annealing resulting in the single NV center formation [12]. They experimentally demonstrated the production of NV centers at desired locations with an accuracy within a few hundreds of nanometers in the image plane. They also reported the formation of highly reproducible NV centers without an annealing process [13]. They coaxially irradiated femtosecond laser pulses with a higher repetition rate as a heat source. More recently we have also demonstrated the efficient generation of NV center ensembles by optimizing the laser irradiation parameters such as the pulse width and the number of pulses [14,15]. We experimentally demonstrated that the laser pulse with shorter pulse width could generate more NV centers with a low probability of graphitization. Such pulse-width dependence can be due to the time variation of the electronic state leading to the difference in the force acting on the lattice. We have also revealed that a high-density NV center exceeding 1016 cm−3 inside a diamond can be achieved by femtosecond laser irradiation with adjusting the number of pulses and pulse energy, while considering the trend of NV concentration and graphitization. Interestingly, the annealing process was not required due to the continuous heating during the irradiation of an extremely large number of femtosecond laser pulses. Although the formation of the NV center ensemble on the surface [16] or inside [11] of a diamond by femtosecond laser irradiation has already been reported, the formation mechanism and timescale of the NV center formation are not fully understood.
In this study, we demonstrated the formation of NV− center by the single shot of femtosecond laser pulse without a successive annealing process. Furthermore, we investigated the effect on the diamond lattice induced by the different laser pulse widths from both experimental and theoretical perspectives. More interestingly, in spite of the high thermal conductivity of a diamond (∼103 W m−1 K−1 [17]), we found that there is a suitable pulse repetition rate of several tens kHz for the formation of NV− centers by the femtosecond laser pulse irradiation.
2. Experiments
A mode-locked regeneratively amplified Ti:sapphire laser system (Mira/RegA9000, Coherent) was used for NV center formation inside diamond samples. At first, we confirmed the effect of impurity nitrogen in the pristine diamond for the NV− center formation. Typically, high-pressure high-temperature (HPHT) type-Ib diamond includes higher impurity nitrogen concentration compared to chemical vapor deposition (CVD) type-IIa diamond. The previously reported NV− concentrations in various diamond samples were summarized in Fig. 1. In spite of different energy sources for NV− formation, roughly 10% of the impurity nitrogen in diamond is converted to NV− centers. In our experiments, we used a type-IIa CVD synthesis (100)-oriented diamond (N < 1 ppm) substrate.
Fig. 1. Typical NV− concentrations as a function of the impurity nitrogen concentration. The NV− centers were created by various energy sources such as an electron, proton, or photon. Labels of data show the following references: 1 [18], 2 [19], 3 [20], 4 [21], 5 [15], 6 [22], 7 [23], 8 [18], 9 [11], and 10 [19], respectively. Dotted blue line is eye guide of [NV−] = 0.1×[N]. Dashed red line shows the optically detectable single NV− center (∼ 1012 cm-3).
The NV− centers induced by the femtosecond laser irradiation and the successive thermal annealing are considered to be formed by the following two steps: (i) creating vacancies by laser irradiation and (ii) capturing a mobile vacancy by substitutional nitrogen atoms. To test the formation of NV− centers during femtosecond laser pulse irradiation without subsequent thermal annealing, the few pulses of linearly polarized femtosecond laser were focused at 191 µm below the diamond sample surface through the objective lens (TU Plan Apo 50×, N.A. 0.80, Nikon). The laser irradiation conditions were as follows; repetition rate of 1 Hz, the pulse width of 110 fs, and pulse energy of 0.5 - 10 µJ.
For characterization of the concentration of formed NV− centers, photoluminescence (PL) mapping was carried out using a confocal microscope excited by 532 nm CW laser. The PL intensity maps ranging from 640 to 660 nm, which is derived from the phonon sideband of the NV−, were measured in planes parallel to the sample surface, including the femtosecond laser irradiated regions. The depth of focus for PL mapping was set to detect the maximum PL intensity in each femtosecond laser irradiated region. To subtract the influence of background derived from the NV− centers in a pristine diamond, the maximum PL intensity was normalized by that of a pristine diamond. The concentration of NV− ensembles was estimated by normalizing with the PL intensity of a single NV− center in the confocal volume V of the excited laser, ${n_{\textrm{NV}}} = I/({{I_{\textrm{single}}}V} )$, where I and ${I_{\textrm{single}}}$ are the PL intensity of the laser irradiated region and the single NV center, respectively [24]. The focal volume V was defined as the volume of the ellipsoid with each side’s length of the full width at half maximum of a Gaussian fit of PL intensity distribution of the single NV center [15].
To confirm the effect on NV center formation by the interpulse time, the laser experiments for NV center formation by changing the pulse repetition rate were also performed. The laser irradiation conditions were as follows; 800 nm, 60 fs, 100 or 200 nJ, and 2.5 × 105 pulses. The laser pulses were focused through the objective lens (TU Plan Apo 50× NA 0.80, Nikon) at a depth of 191 µm below the sample surface.
To understand the structural change of the photoexcited region in diamond, the X-ray microdiffraction measurements were performed at the BL13XU beamline in the SPring-8. The focused synchrotron radiation with the energy and the beam diameter of 10 keV and 200 nm was scanned on the area including the graphitized region to identify the NV center formation region using an X-ray photon counting detector. The beam diameter was estimated by the knife-edge method. The type-IIa diamond samples without surface modification were prepared by focusing of the femtosecond laser pulses in a direction perpendicular to (001) plane at a depth of 20 µm. The X-ray microdiffraction measurements of both non-graphitized (NV center formation region) and graphitized regions, which are irradiated by the femtosecond laser pulses (repetition rate of 1 kHz, the pulse width of 110 fs, and pulse energy of 70 nJ, 1000 pulses), were performed. Since the size of the NV center formation region was estimated to be a few microns by PL mapping, the X-ray microdiffraction has a sufficient spatial resolution to detect only the laser-processed region. The data were obtained around the (400) diffraction peak by scanning the focused synchrotron radiation including the laser-modified regions. The diffraction signals were detected by the ω-2θ scan, where ω and θ are the incidence angles on the sample surface and on the scattering planes, respectively. The reciprocal space maps (RSMs) were analyzed by extracting data in the laser-processed region. Details are described in the Supplemental document. We can estimate the in-plane and out-of-plane lattice coordinates of ${q_x}$ and ${q_z}$ from the $2\theta /\omega $ diffraction angle using the following equation:
where $\lambda $, $\omega $, and $\theta $ are wavelength of synchrotron radiation (= 1.24 Å), incident beam angle from sample surface, and half of the scattering angle $2\theta $, respectively.3. Time-dependent density-functional theory (TDDFT) simulation methods
Previously we have also assessed the effect of pulse width on NV center formation [14]. To understand the differences in pulse widths, we performed a TDDFT simulation [25]. In the simulation, we used an open-source TDDFT program package, Scalable ab initio Light-Matter simulator for Optics and Nanoscience (SALMON) [26]. For electron-ion interaction, a norm-conserving pseudopotential [27] is employed. For the exchange correlation potential, the adiabatic local density approximation (ALDA) with Perdew-Zunger functional [28] is adopted. A time step and a mean photon energy were to be Δt = 0.10 au (2.42 as) and 0.0570 au (3.7 × 1014 Hz), respectively. A cubic unit cell of 3.57 × 3.57 × 3.57 Å, which contains eight carbon atoms was used. The crystalline unit cell was divided into 16 × 16 × 16 uniform grids, resulting that the grid spacing was about 0.22 × 0.22 × 0.22 Å. We calculated the electronic excitation energy by changing the peak power density for the pulse width of 40 fs. Since it was difficult to calculate the electron dynamics for a longer timescale of 1 ps, we calculated and compared the difference in pulse width of 40 fs and 200 fs. We set the laser intensity for 40 fs and 200 fs so that the input laser pulse energy would be the same, and calculated the electron density. In addition, the force acting on an atom was calculated by the sum of the Coulomb force from electrons and other atoms, and the force by the macroscopic electric field [29].
4. Results and discussion
The PL intensity derived from NV− centers induced by several shots of femtosecond laser with different pulse energy is shown in Fig. 2(a). The maximum PL intensities (${I_{\textrm{max}}}$) of three different laser-processed regions with the same conditions and the averaged PL intensity (${I_{\textrm{bkg}}}$) of the pristine diamond on both sides 10 µm away from each laser-processed point were plotted. The normalized PL intensities by $({{I_{\textrm{max}}} - {I_{\textrm{bkg}}}} )/{I_{\textrm{bkg}}}$ are also plotted in Fig. 2(b). These figures clearly show the PL intensity is proportionally increased with increasing the number of pulses within this range. We estimated the concentration of NV− ensembles to be 2 × 1014 cm-3 for the 10 pulses with 2.0 µJ. Although the increasing rate of the normalized PL intensity with respect to the number of pulses was linear, the rate with respect to the pulse energy tended to saturate at 2.0 µJ. We confirmed the NV center formation by the femtosecond laser single-shot experiments without thermal treatment (Fig. 3). In all experiments, no apparent graphitization at the focal position and the surface of the diamond sample was observed. Although the increase in the PL intensity after the single pulse irradiation was low, the normalized PL intensities after subtracting ${I_{\textrm{bkg}}}$ from ${I_{\textrm{max}}}$ clearly increased with an increase in the pulse energy.
Fig. 2. (a) Plots of the PL intensity as a function of the irradiated femtosecond laser number of pulses. Symbols of ▾and – show the maximum PL intensities (${I_{\textrm{max}}}$) of three different laser-processed regions with the same conditions and the averaged PL intensities (${I_{\textrm{bkg}}}$) of the pristine diamond on both sides 10 µm away from each laser-processed point, respectively. (b) Plots of normalized PL intensity by $({{I_{\textrm{max}}} - {I_{\textrm{bkg}}}} )/{I_{\textrm{bkg}}}$.
Fig. 3. (a) Plots of the PL intensity for the single-shot experiments with various pulse energy. Symbols of ▴and – show the maximum PL intensities (${I_{\textrm{max}}}$) of three different laser-processed regions (#1, #2, and #3) with the same conditions and the averaged PL intensities (${I_{\textrm{bkg}}}$) of the pristine diamond on both sides 10 µm away from each laser-processed point, respectively. (b) Plots of normalized PL intensity by $({{I_{\textrm{max}}} - {I_{\textrm{bkg}}}} )/{I_{\textrm{bkg}}}$.
Figure 4 shows the PL intensity map and PL spectra before and after the femtosecond single pulse irradiated region. The increase in PL intensity was observed at the focal point of the femtosecond laser single pulse, and the PL spectrum clearly reveals that the increase in PL intensity is caused by the formation of NV centers. These results clearly indicate the NV centers were successfully photoinduced by the femtosecond single pulse irradiation without thermal annealing, unlike the Ref. of [12].
Fig. 4. PL maps of the NV− centers induced by the femtosecond laser single pulse with (a) 1 µJ, (b) 6 µJ or (c) 10 µJ. Scale bar shows 2 µm. (d) Typical PL spectra before and after the femtosecond laser single pulse irradiation in a type-IIa CVD synthesis (100)-oriented diamond.
The temperature ($\mathrm{\Delta }{T_1}$) at the focus after only one pulse irradiation was roughly estimated by the following equation [30]:
The RSMs before and after laser irradiation are shown in Fig. 5. Noted that we confirmed that the measured position for X-ray microdiffraction coincides with the position in which NV centers increase by PL mapping. Reciprocal space mapping gives the information of intensity distribution in the reciprocal space. Therefore, the RSMs are related to the variation of the lattice constant and tilt of the lattice plane. Compared to the unirradiated region, the broadening of ${q_x}$ distribution is remarkable after laser irradiation, indicating the lattice constant variations due to color center generation. Furthermore, for the graphitized region, broadening of not only ${q_x}$ but also ${q_z}$ distribution is also remarkable, indicating the lattice tilting is also changed.
Fig. 5. RSMs of (a) the pristine diamond, (b) the non-graphitized and (c) graphitized region. We confirmed that the measured position for X-ray microdiffraction coincides with the position in which NV− centers increase by PL mapping.
Let's start with the nonlinear response of the electronic excitation energy. Figure 6(a) indicates the slope for energy required for excitation as a function of the laser intensity changes at about 1012 W cm-2, suggesting that the nonlinearity becomes more remarkable near this laser intensity. Therefore, the nonlinear response of the electronic excitation energy for diamond will start at about 1012 W cm-2. Furthermore, from the calculation of the ionization rate for the diamond after photoexcitation, we found that the dominant ionization process changes from multiphoton ionization to tunneling ionization at the laser intensity of roughly 1013 W cm-2. Since the laser intensity at the focus can be estimated to be ∼ 1014 W cm-2 in our experiments at pulse energy of 1 µJ, the vacancies were formed by the contributions of nonlinear phenomena. The energy transfer from the femtosecond laser pulse to electrons occurs during femtoseconds. This energy received by the electrons is transferred to the motion of atoms on a longer time scale, causing damage to the material. As stated above, the temperature at the focus steeply decreases just after the photoexcitation. Consequently, the vacancy migrates and binds with substitutional nitrogen atom, during this rapid cooling time. It should be noted that the NV center can be formed within 250 fs after the excitation by femtosecond laser pulse according to the ab initio molecular dynamics simulation [33].
Fig. 6. (a) Plots of TDDFT calculation of the electronic excitation energy in a diamond as a function of the laser power density. The electric field E was applied parallel to the [001] direction in a diamond crystal structure and the pulse width was set to be 100 fs. Red and blue lines are the linear fit by the function of $y = a{x^b}$. The fitting parameter b corresponding to the number of photons is also shown. The simulation results of force on C atoms excited by the femtosecond pulse of (b) 40 fs, 5 × 1012 W cm-2, (c) 200 fs, 1 × 1012 W cm-2. Red arrows show the starting point when the force oscillations cannot follow the electric field.
And then, we evaluated the force on C atom [Fig. 6(b, c)]. For both cases of 40 fs and 200 fs, the force acting on C atom at (x, y, z) = (0, 0, 0) began to be disturbed during the passage of laser pulse, suggesting that the bonding state of C atoms was changed. The time during the electric field to remain to be applied after the bonding state begins to be disturbed becomes longer according to the longer pulse width. As the result, longer pulse width corresponds to a longer interaction time after electron excitation, leading to easy structural change such as phase transformation of graphitization.
Due to the high thermal conductivity of a diamond, the interpulse time of the femtosecond laser pulses does not seemingly affect NV center formation. Furthermore, there is no apparent absorption at around 800 nm by optical centers in a diamond by radiation damage and annealing [34]. To confirm the effect on NV center formation by the interpulse time, we observed the normalized PL intensities from NV center induced by the femtosecond laser pulses with various repetition rates (Fig. 7). In the experiments, the number of irradiation pulses were set the same as 2.5 × 105 pulses by changing the irradiation time. According to the increase in the pulse repetition rate, the normalized PL intensity derived from NV center was initially increased and then saturated, finally slightly decreased, suggesting that the formation of NV centers depends on the pulse repetition rate. A slight decrease in the NV center for both 100 and 200 nJ was observed at around 100 kHz, i.e. the interpulse time of 10 µs. More interestingly, such a tendency to increase and decrease NV center by the pulse repetition rate did not change after the thermal treatment at 1000°C for 1h. The behavior of decrease in the NV center for the higher pulse repetition rate than about 100 kHz may be interpreted in terms of the competition between the formation and annihilation of the NV centers. There is a possibility that the formation of an NV center reduces the thermal conductivity compared to that of the pristine diamond, leading to effective thermal accumulation in the case of a higher pulse repetition rate. Indeed, a decrease in the NV center with increasing in the annealing time was reported for electron irradiated diamond under 1073 K annealing, which is explained by the recombination of interstitial carbon and NV center [35]. Furthermore, the formation of (N−V−N)° (H3 center) and annihilation of NV center were also reported by high-temperature annealing (>1573 K) of N ion implanted diamond, which is explained by diffusion of N atom [36]. On the other hand, the reason why decreasing in the NV center below several tens kHz is unexplained. To test the difference in means of the results from three separate experiments, the statistical method of one-way analysis of variance was performed and obtained the P-value which is the upper probability of the test statistic in the F-distribution. The P-values of 0.00615 and 0.00041 for 100 nJ and 200 nJ, respectively, were smaller than 0.05, indicating a significant difference between the conditions of pulse repetition rate. To understand this phenomenon, the dynamics of defect formation induced by laser irradiation should be investigated.
Fig. 7. Plots of normalized PL intensity by $({{I_{\textrm{max}}} - {I_{\textrm{bkg}}}} )/{I_{\textrm{bkg}}}$ as a function of pulse repetition rate. The results of femtosecond laser irradiation with 200 nJ followed by the annealing at 1273 K for 1hr are also shown.
5. Conclusions
In this paper, we demonstrated the formation of NV center in a diamond by the femtosecond laser single pulse irradiation without thermal treatment. We have also revealed that the efficiency in the NV center formation depends on the irradiated laser pulse width from both experimental and theoretical perspectives. Interestingly, the formation of the NV center also depended on the pulse repetition rate in spite of the same pulse energy and the number of pulses. Since the remarkable benefit of such femtosecond laser direct-writing method is to realize flexible spatial arrangement of NV center in three-dimension, this technique has a potential to open the new frontier to develop the quantum applications.
Funding
Ministry of Education, Culture, Sports, Science and Technology Q-LEAP (JPMXS0118067395); Japan Society for the Promotion of Science (20H02656).
Acknowledgments
We thank Dr. K. Sumitani, Y. Imai, and S. Kimura from Japan Synchrotron Radiation Research Institute (JASRI) / SPring-8 for their help with X-ray microdiffraction measurements. The synchrotron radiation experiments were performed at the BL13XU of SPring-8 with the approval of the JASRI (Proposal No. 2019A1060). The computation in this research was performed by supercomputer Oakforest-PACS at JCAHPC through the Multidisciplinary Cooperative Research Program in CCS, the University of Tsukuba. This work was partially supported by JSPS KAKENHI Grant No. 20H02656. Also, we thank MEXT Q-LEAP (JPMXS0118067395) and the Spintronics Research Network of Japan.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. W. Pfaff, B. J. Hensen, H. Bernien, S. B. van Dam, M. S. Blok, T. H. Taminiau, M. J. Tiggelman, R. N. Schouten, M. Markham, and D. J. Twitchen, “Unconditional quantum teleportation between distant solid-state quantum bits,” Science 345(6196), 532–535 (2014). [CrossRef]
2. F. Rozpedek, R. Yehia, K. Goodenough, M. Ruf, P. C. Humphreys, R. Hanson, S. Wehner, and D. Elkouss, “Near-term quantum-repeater experiments with nitrogen-vacancy centers: Overcoming the limitations of direct transmission,” Phys. Rev. A 99(5), 052330 (2019). [CrossRef]
3. J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, “High-sensitivity diamond magnetometer with nanoscale resolution,” Nat. Phys. 4(10), 810–816 (2008). [CrossRef]
4. J. Cai, F. Jelezko, and M. B. Plenio, “Hybrid sensors based on colour centres in diamond and piezoactive layers,” Nat. Commun. 5(1), 4065 (2014). [CrossRef]
5. D. M. Toyli, D. J. Christle, A. Alkauskas, B. B. Buckley, C. G. Van de Walle, and D. D. Awschalom, “Measurement and control of single nitrogen-vacancy center spins above 600 K,” Phys. Rev. X 2(3), 031001 (2012). [CrossRef]
6. 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(1), 3766 (2019). [CrossRef]
7. T. Fukui, Y. Doi, T. Miyazaki, Y. Miyamoto, H. Kato, T. Matsumoto, T. Makino, S. Yamasaki, R. Morimoto, N. Tokuda, M. Hatano, Y. Sakagawa, H. Morishita, T. Tashima, S. Miwa, Y. Suzuki, and N. Mizuochi, “Perfect selective alignment of nitrogen-vacancy centers in diamond,” Appl. Phys. Express 7(5), 055201 (2014). [CrossRef]
8. C. A. McLellan, B. A. Myers, S. Kraemer, K. Ohno, D. D. Awschalom, and A. C. Bleszynski Jayich, “Patterned formation of highly coherent nitrogen-vacancy centers using a focused electron irradiation technique,” Nano Lett. 16(4), 2450–2454 (2016). [CrossRef]
9. A. Haque and S. Sumaiya, “An overview on the formation and processing of nitrogen-vacancy photonic centers in diamond by ion implantation,” J. Manuf. Mater. Process. 1(1), 6 (2017). [CrossRef]
10. M. Haruyama, S. Onoda, T. Higuchi, W. Kada, A. Chiba, Y. Hirano, T. Teraji, R. Igarashi, S. Kawai, H. Kawarada, Y. Ishii, R. Fukuda, T. Tanii, J. Isoya, T. Ohshima, and O. Hanaizumi, “Triple nitrogen-vacancy centre fabrication by C5N4Hn ion implantation,” Nat. Commun. 10(1), 2664 (2019). [CrossRef]
11. V. Bharadwaj, O. Jedrkiewicz, J. P. Hadden, B. Sotillo, M. R. Vázquez, P. Dentella, T. T. Fernandez, A. Chiappini, A. N. Giakoumaki, T. L. Phu, M. Bollani, M. Ferrari, R. Ramponi, P. E. Barclay, and S. M. Eaton, “Femtosecond laser written photonic and microfluidic circuits in diamond,” JPhys Photonics 1(2), 022001 (2019). [CrossRef]
12. 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(2), 77–80 (2017). [CrossRef]
13. 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(5), 662–667 (2019). [CrossRef]
14. 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(21), 211102 (2018). [CrossRef]
15. 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(21), 214001 (2021). [CrossRef]
16. 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(8), 081101 (2017). [CrossRef]
17. A. A. Balandin, “Thermal properties of graphene and nanostructured carbon materials,” Nat. Mater. 10(8), 569–581 (2011). [CrossRef]
18. V. M. Acosta, E. Bauch, M. P. Ledbetter, C. Santori, K.-M. C. Fu, P. E. Barclay, R. G. Beausoleil, H. Linget, J. F. Roch, F. Treussart, S. Chemerisov, W. Gawlik, and D. Budker, “Diamonds with a high density of nitrogen-vacancy centers for magnetometry applications,” Phys. Rev. B 80(11), 115202 (2009). [CrossRef]
19. D. Farfurnik, N. Alfasi, S. Masis, Y. Kauffmann, E. Farchi, Y. Romach, Y. Hovav, E. Buks, and N. Bar-Gill, “Enhanced concentrations of nitrogen-vacancy centers in diamond through TEM irradiation,” Appl. Phys. Lett. 111(12), 123101 (2017). [CrossRef]
20. J. Botsoa, T. Sauvage, M.-P. Adam, P. Desgardin, E. Leoni, B. Courtois, F. Treussart, and M.-F. Barthe, “Optimal conditions for NV− center formation in type-1b diamond studied using photoluminescence and positron annihilation spectroscopies,” Phys. Rev. B 84(12), 125209 (2011). [CrossRef]
21. J. Choi, S. Choi, G. Kucsko, P. C. Maurer, B. J. Shields, H. Sumiya, S. Onoda, J. Isoya, E. Demler, F. Jelezko, N. Y. Yao, and M. D. Lukin, “Depolarization dynamics in a strongly interacting solid-state spin ensemble,” Phys. Rev. Lett. 118(9), 093601 (2017). [CrossRef]
22. H. Zheng, J. Xu, G. Z. Iwata, T. Lenz, J. Michl, B. Yavkin, K. Nakamura, H. Sumiya, T. Ohshima, J. Isoya, J. Wrachtrup, A. Wickenbrock, and D. Budker, “Zero-field magnetometry based on nitrogen-vacancy ensembles in diamond,” Phys. Rev. Appl. 11(6), 064068 (2019). [CrossRef]
23. J. F. Barry, M. J. Turner, J. M. Schloss, D. R. Glenn, Y. Song, M. D. Lukin, H. Park, and R. L. Walsworth, “Optical magnetic detection of single-neuron action potentials using quantum defects in diamond,” Proc. Natl. Acad. Sci. U. S. A. 113(49), 14133–14138 (2016). [CrossRef]
24. K. Hayashi, Y. Matsuzaki, T. Ashida, S. Onoda, H. Abe, T. Ohshima, M. Hatano, T. Taniguchi, H. Morishita, M. Fujiwara, and N. Mizuochi, “Experimental and theoretical analysis of noise strength and environmental correlation time for ensembles of nitrogen-vacancy centers in diamond,” J. Phys. Soc. Jpn. 89(5), 054708 (2020). [CrossRef]
25. M. Uemoto, S. Kurata, N. Kawaguchi, and K. Yabana, “First-principles study of ultrafast and nonlinear optical properties of graphite thin films,” Phys. Rev. B 103(8), 085433 (2021). [CrossRef]
26. M. Noda, S. A. Sato, Y. Hirokawa, M. Uemoto, T. Takeuchi, S. Yamada, A. Yamada, Y. Shinohara, M. Yamaguchi, K. Iida, I. Floss, T. Otobe, K. M. Lee, K. Ishimura, T. Boku, G. F. Bertsch, K. Nobusada, and K. Yabana, “SALMON: Scalable ab-initio light-matter simulator for optics and nanoscience,” Comput. Phys. Commun. 235, 356–365 (2019). [CrossRef]
27. N. Troullier and J. L. Martins, “Efficient pseudopotentials for plane-wave calculations,” Phys. Rev. B 43(3), 1993–2006 (1991). [CrossRef]
28. J. P. Perdew and A. Zunger, “Self-interaction correction to density-functional approximations for many-electron systems,” Phys. Rev. B 23(10), 5048–5079 (1981). [CrossRef]
29. A. Yamada and K. Yabana, “Multiscale time-dependent density functional theory for a unified description of ultrafast dynamics: Pulsed light, electron, and lattice motions in crystalline solids,” Phys. Rev. B 99(24), 245103 (2019). [CrossRef]
30. M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, “Mechanism of heat-modification inside a glass after irradiation with high-repetition rate femtosecond laser pulses,” J. Appl. Phys. 108(7), 073533 (2010). [CrossRef]
31. V. I. Volga, L. M. Buchnev, N. V. Markelov, and B. K. Dymov, “Enthalpy and heat capacity of diamonds over a wide range of temperatures,” Sint. Almazy 3, 9–11 (1976).
32. G. Davies, “The effect of nitrogen impurity on the annealing of radiation damage in diamond,” J. Phys. C: Solid State Phys. 5(17), 2534–2542 (1972). [CrossRef]
33. M. Kempkes, T. Zier, K. Singer, and M. E. Garcia, “Ultrafast nonthermal NV center formation in diamond,” Carbon 174, 524–530 (2021). [CrossRef]
34. A. T. Collins, “Optical centres produced in diamond by radiation damage,” New Diam. Front. C. Tec. 17(2), 47–61 (2007).
35. C. Zhang, H. Yuan, N. Zhang, L. X. Xu, B. Li, G. D. Cheng, Y. Wang, Q. Gui, and J. C. Fang, “Dependence of high density nitrogen-vacancy center ensemble coherence on electron irradiation doses and annealing time,” J. Phys. D: Appl. Phys. 50(50), 505104 (2017). [CrossRef]
36. T. Lühmann, N. Raatz, R. John, M. Lesik, J. Rödiger, M. Portail, D. Wildanger, F. Kleißler, K. Nordlund, A. Zaitsev, J.-F. Roch, A. Tallaire, J. Meijer, and S. Pezzagna, “Screening and engineering of colour centres in diamond,” J. Phys. D: Appl. Phys. 51(48), 483002 (2018). [CrossRef]
