Abstract

In this paper, we analyse the prospects for using nitrogen-vacancy centre (NV) containing diamond as a laser gain material by measuring its key laser related parameters. Synthetic chemical vapour deposition grown diamond samples with an NV concentration of ~1 ppm have been selected because of their relatively high NV concentration and low background absorption in comparison to other samples available to us. For the samples measured, the luminescence lifetimes of the NV- and NV0 centres were measured to be 8 ± 1 ns and 20 ± 1 ns, respectively. The respective peak stimulated emission cross-sections were (3.6 ± 0.1) × 10−17 cm2 and (1.7 ± 0.1) × 10−17 cm2. These measurements were combined with absorption measurements to calculate the gain spectra for NV- and NV0 for differing inversion levels. Such calculations indicate that gains approaching those required for laser operation may be possible with one of the samples tested and for the NV- centre.

© 2017 Optical Society of America

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2017 (1)

J. Jeske, 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. Ohshima, 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).
[Crossref] [PubMed]

2016 (1)

J. Jeske, J. H. Cole, and A. D. Greentree, “Laser threshold magnetometry,” New J. Phys. 18(1), 013015 (2016).
[Crossref]

2015 (2)

R. J. Williams, J. Nold, M. Strecker, O. Kitzler, A. McKay, T. Schreiber, and R. P. Mildren, “Efficient Raman frequency conversion of high-power fiber lasers in diamond,” Laser Photonics Rev. 9(4), 405–411 (2015).
[Crossref]

J. Storteboom, P. Dolan, S. Castelletto, X. Li, and M. Gu, “Lifetime investigation of single nitrogen vacancy centres in nanodiamonds,” Opt. Express 23(9), 11327–11333 (2015).
[Crossref] [PubMed]

2014 (1)

Y. Chu, N. P. de Leon, B. J. Shields, B. Hausmann, R. Evans, E. Togan, M. J. Burek, M. Markham, A. Stacey, A. S. Zibrov, A. Yacoby, D. J. Twitchen, M. Loncar, H. Park, P. Maletinsky, and M. D. Lukin, “Coherent Optical Transitions in Implanted Nitrogen Vacancy Centers,” Nano Lett. 14(4), 1982–1986 (2014).
[Crossref] [PubMed]

2013 (4)

T. Yamamoto, T. Umeda, K. Watanabe, S. Onoda, M. L. Markham, D. J. Twitchen, B. Naydenov, L. P. McGuinness, T. Teraji, S. Koizumi, F. Dolde, H. Fedder, J. Honert, J. Wrachtrup, T. Ohshima, F. Jelezko, and J. Isoya, “Extending spin coherence times of diamond qubits by high-temperature annealing,” Phys. Rev. B 88(7), 075206 (2013).
[Crossref]

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), 1–45 (2013).
[Crossref]

D. Gatto Monticone, F. Quercioli, R. Mercatelli, S. Soria, S. Borini, T. Poli, M. Vannoni, E. Vittone, and P. Olivero, “Systematic study of defect-related quenching of NV luminescence in diamond with time-correlated single-photon counting spectroscopy,” Phys. Rev. B 88(15), 155201 (2013).
[Crossref]

N. Aslam, G. Waldherr, P. Neumann, F. Jelezko, and J. Wrachtrup, “Photo-induced ionization dynamics of the nitrogen vacancy defect in diamond investigated by single-shot charge state detection,” New J. Phys. 15(1), 013064 (2013).
[Crossref]

2012 (3)

G. Liaugaudas, G. Davies, K. Suhling, R. U. A. Khan, and D. J. F. Evans, “Luminescence lifetimes of neutral nitrogen-vacancy centres in synthetic diamond containing nitrogen,” J. Phys. Condens. Matter 24(43), 435503 (2012).
[Crossref] [PubMed]

V. G. Savitski, I. Friel, J. E. Hastie, M. D. Dawson, D. Burns, and A. J. Kemp, “Characterization of Single-Crystal Synthetic Diamond for Multi-Watt Continuous-Wave Raman Lasers,” IEEE J. Quantum Electron. 48(3), 328–337 (2012).
[Crossref]

K. Beha, A. Batalov, N. B. Manson, R. Bratschitsch, and A. Leitenstorfer, “Optimum Photoluminescence Excitation and Recharging Cycle of Single Nitrogen-Vacancy Centers in Ultrapure Diamond,” Phys. Rev. Lett. 109(9), 097404 (2012).
[Crossref] [PubMed]

2011 (2)

S. Pezzagna, D. Rogalla, D. Wildanger, J. Meijer, and A. Zaitsev, “Creation and nature of optical centres in diamond for single-photon emission—overview and critical remarks,” New J. Phys. 13(3), 035024 (2011).
[Crossref]

I. Aharonovich, A. D. Greentree, and S. Prawer, “Diamond photonics,” Nat. Photonics 5(7), 397–405 (2011).
[Crossref]

2010 (1)

M. M. Biener, J. Biener, S. O. Kucheyev, Y. M. Wang, B. El-Dasher, N. E. Teslich, A. V. Hamza, H. Obloh, W. Mueller-Sebert, M. Wolfer, T. Fuchs, M. Grimm, A. Kriele, and C. Wild, “Controlled incorporation of mid-to-high Z transition metals in CVD diamond,” Diamond Related Materials 19(5-6), 643–647 (2010).
[Crossref]

2009 (5)

R. S. Balmer, J. R. Brandon, S. L. Clewes, H. K. Dhillon, J. M. Dodson, I. Friel, P. N. Inglis, T. D. Madgwick, M. L. Markham, T. P. Mollart, N. Perkins, G. A. Scarsbrook, D. J. Twitchen, A. J. Whitehead, J. J. Wilman, and S. M. Woollard, “Chemical vapour deposition synthetic diamond: materials, technology and applications,” J. Phys. Condens. Matter 21(36), 364221 (2009).
[Crossref] [PubMed]

I. Friel, S. L. Clewes, H. K. Dhillon, N. Perkins, D. J. Twitchen, and G. A. Scarsbrook, “Control of surface and bulk crystalline quality in single crystal diamond grown by chemical vapour deposition,” Diamond Related Materials 18(5-8), 808–815 (2009).
[Crossref]

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]

C. M. Breeding and J. E. Shigley, “The ‘type’ classification system of diamonds and its importance in gemology,” Gems & Gemology 45(2), 96–111 (2009).
[Crossref]

A. T. Collins and I. Kiflawi, “The annealing of radiation damage in type Ia diamond,” J. Phys. Condens. Matter 21(36), 364209 (2009).
[Crossref] [PubMed]

2008 (2)

A. J. Kemp, J. M. Hopkins, A. J. Maclean, N. Schulz, M. Rattunde, J. Wagner, and D. Burns, “Thermal Management in 2.3- μm Semiconductor Disk Lasers: A Finite Element Analysis,” IEEE J. Quantum Electron. 44(2), 125–135 (2008).
[Crossref]

A. Batalov, C. Zierl, T. Gaebel, P. Neumann, I. Y. Chan, G. Balasubramanian, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Temporal Coherence Of Photons Emitted by Single Nitrogen-Vacancy Defect Centers in Diamond Using Optical Rabi-Oscillations,” Phys. Rev. Lett. 100(7), 077401 (2008).
[Crossref] [PubMed]

2007 (4)

T.-S. Ahn, R. O. Al-Kaysi, A. M. Müller, K. M. Wentz, and C. J. Bardeen, “Self-absorption correction for solid-state photoluminescence quantum yields obtained from integrating sphere measurements,” Rev. Sci. Instrum. 78(8), 086105 (2007).
[Crossref] [PubMed]

N. B. Manson and R. L. McMurtrie, “Issues concerning the nitrogen-vacancy center in diamond,” J. Lumin. 127(1), 98–103 (2007).
[Crossref]

F. C. Waldermann, P. Olivero, J. Nunn, K. Surmacz, Z. Y. Wang, D. Jaksch, R. A. Taylor, I. A. Walmsley, M. Draganski, P. Reichart, A. D. Greentree, D. N. Jamieson, and S. Prawer, “Creating diamond color centers for quantum optical applications,” Diamond Related Materials 16(11), 1887–1895 (2007).
[Crossref]

T.-L. Wee, Y.-K. Tzeng, C.-C. Han, H.-C. Chang, W. Fann, J.-H. Hsu, K.-M. Chen, and Y.-C. Yu, “Two-photon Excited Fluorescence of Nitrogen-Vacancy Centers in Proton-Irradiated Type Ib Diamond,” J. Phys. Chem. A 111(38), 9379–9386 (2007).
[Crossref] [PubMed]

2006 (2)

V. G. Vins and E. V. Pestryakov, “Color centers in diamond crystals: Their potential use in tunable and femtosecond lasers,” Diamond Related Materials 15(4-8), 569–571 (2006).
[Crossref]

T. Gaebel, M. Domhan, C. Wittmann, I. Popa, F. Jelezko, J. Rabeau, A. Greentree, S. Prawer, E. Trajkov, P. R. Hemmer, and J. Wrachtrup, “Photochromism in single nitrogen-vacancy defect in diamond,” Appl. Phys. B 82(2), 243–246 (2006).
[Crossref]

1999 (1)

G. Davies, “Current problems in diamond: towards a quantitative understanding,” Physica B 273–274, 15–23 (1999).
[Crossref]

1998 (1)

S. C. Lawson, D. Fisher, D. C. Hunt, and M. E. Newton, “On the existence of positively charged single-substitutional nitrogen in diamond,” J. Phys. Condens. Matter 10(27), 6171–6180 (1998).
[Crossref]

1997 (1)

H. Hanzawa, Y. Nisida, and T. Kato, “Measurement of decay time for the NV centre in Ib diamond with a picosecond laser pulse,” Diamond Related Materials 6(11), 1595–1598 (1997).
[Crossref]

1992 (1)

Y. Li, I. Duncan, and T. Morrow, “Absolute fluorescence quantum efficiency of titanium-doped sapphire at ambient temperature,” J. Lumin. 52(5-6), 275–276 (1992).
[Crossref]

1986 (2)

1985 (1)

1983 (1)

A. T. Collins, M. F. Thomaz, and M. I. B. Jorge, “Luminescence decay time of the 1.945 eV centre in type Ib diamond,” J. Phys. C Solid State Phys. 16(11), 2177–2181 (1983).
[Crossref]

1982 (1)

B. Aull and H. Jenssen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. 18(5), 925–930 (1982).
[Crossref]

1979 (1)

J. Walker, “Optical-Absorption and Luminescence in Diamond,” Rep. Prog. Phys. 42(10), 1605–1659 (1979).
[Crossref]

1976 (1)

G. Davies and M. F. Hamer, “Optical Studies of the 1.945 eV Vibronic Band in Diamond,” Proc. R. Soc. Lond. A Math. Phys. Sci. 348(1653), 285–298 (1976).
[Crossref]

1971 (1)

G. A. Crosby and J. N. Demas, “Measurement of photoluminescence quantum yields. Review,” J. Phys. Chem. 75(8), 991–1024 (1971).
[Crossref]

1959 (1)

W. V. Smith, P. P. Sorokin, I. L. Gelles, and G. J. Lasher, “Electron-Spin Resonance of Nitrogen Donors in Diamond,” Phys. Rev. 115(6), 1546–1552 (1959).
[Crossref]

1956 (1)

C. D. Clark, R. W. Ditchburn, and H. B. Dyer, “The Absorption Spectra of Natural and Irradiated Diamonds,” Proc. R. Soc. Lond. A Math. Phys. Sci. 234(1198), 363–381 (1956).
[Crossref]

Acosta, V. M.

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]

Aharonovich, I.

I. Aharonovich, A. D. Greentree, and S. Prawer, “Diamond photonics,” Nat. Photonics 5(7), 397–405 (2011).
[Crossref]

Ahn, T.-S.

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T. Gaebel, M. Domhan, C. Wittmann, I. Popa, F. Jelezko, J. Rabeau, A. Greentree, S. Prawer, E. Trajkov, P. R. Hemmer, and J. Wrachtrup, “Photochromism in single nitrogen-vacancy defect in diamond,” Appl. Phys. B 82(2), 243–246 (2006).
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A. J. Kemp, J. M. Hopkins, A. J. Maclean, N. Schulz, M. Rattunde, J. Wagner, and D. Burns, “Thermal Management in 2.3- μm Semiconductor Disk Lasers: A Finite Element Analysis,” IEEE J. Quantum Electron. 44(2), 125–135 (2008).
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R. S. Balmer, J. R. Brandon, S. L. Clewes, H. K. Dhillon, J. M. Dodson, I. Friel, P. N. Inglis, T. D. Madgwick, M. L. Markham, T. P. Mollart, N. Perkins, G. A. Scarsbrook, D. J. Twitchen, A. J. Whitehead, J. J. Wilman, and S. M. Woollard, “Chemical vapour deposition synthetic diamond: materials, technology and applications,” J. Phys. Condens. Matter 21(36), 364221 (2009).
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T. Yamamoto, T. Umeda, K. Watanabe, S. Onoda, M. L. Markham, D. J. Twitchen, B. Naydenov, L. P. McGuinness, T. Teraji, S. Koizumi, F. Dolde, H. Fedder, J. Honert, J. Wrachtrup, T. Ohshima, F. Jelezko, and J. Isoya, “Extending spin coherence times of diamond qubits by high-temperature annealing,” Phys. Rev. B 88(7), 075206 (2013).
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F. C. Waldermann, P. Olivero, J. Nunn, K. Surmacz, Z. Y. Wang, D. Jaksch, R. A. Taylor, I. A. Walmsley, M. Draganski, P. Reichart, A. D. Greentree, D. N. Jamieson, and S. Prawer, “Creating diamond color centers for quantum optical applications,” Diamond Related Materials 16(11), 1887–1895 (2007).
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J. Jeske, 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. Ohshima, 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).
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V. G. Savitski, I. Friel, J. E. Hastie, M. D. Dawson, D. Burns, and A. J. Kemp, “Characterization of Single-Crystal Synthetic Diamond for Multi-Watt Continuous-Wave Raman Lasers,” IEEE J. Quantum Electron. 48(3), 328–337 (2012).
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A. J. Kemp, J. M. Hopkins, A. J. Maclean, N. Schulz, M. Rattunde, J. Wagner, and D. Burns, “Thermal Management in 2.3- μm Semiconductor Disk Lasers: A Finite Element Analysis,” IEEE J. Quantum Electron. 44(2), 125–135 (2008).
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S. C. Lawson, D. Fisher, D. C. Hunt, and M. E. Newton, “On the existence of positively charged single-substitutional nitrogen in diamond,” J. Phys. Condens. Matter 10(27), 6171–6180 (1998).
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Li, Y.

Y. Li, I. Duncan, and T. Morrow, “Absolute fluorescence quantum efficiency of titanium-doped sapphire at ambient temperature,” J. Lumin. 52(5-6), 275–276 (1992).
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Liaugaudas, G.

G. Liaugaudas, G. Davies, K. Suhling, R. U. A. Khan, and D. J. F. Evans, “Luminescence lifetimes of neutral nitrogen-vacancy centres in synthetic diamond containing nitrogen,” J. Phys. Condens. Matter 24(43), 435503 (2012).
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Y. Chu, N. P. de Leon, B. J. Shields, B. Hausmann, R. Evans, E. Togan, M. J. Burek, M. Markham, A. Stacey, A. S. Zibrov, A. Yacoby, D. J. Twitchen, M. Loncar, H. Park, P. Maletinsky, and M. D. Lukin, “Coherent Optical Transitions in Implanted Nitrogen Vacancy Centers,” Nano Lett. 14(4), 1982–1986 (2014).
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Y. Chu, N. P. de Leon, B. J. Shields, B. Hausmann, R. Evans, E. Togan, M. J. Burek, M. Markham, A. Stacey, A. S. Zibrov, A. Yacoby, D. J. Twitchen, M. Loncar, H. Park, P. Maletinsky, and M. D. Lukin, “Coherent Optical Transitions in Implanted Nitrogen Vacancy Centers,” Nano Lett. 14(4), 1982–1986 (2014).
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A. J. Kemp, J. M. Hopkins, A. J. Maclean, N. Schulz, M. Rattunde, J. Wagner, and D. Burns, “Thermal Management in 2.3- μm Semiconductor Disk Lasers: A Finite Element Analysis,” IEEE J. Quantum Electron. 44(2), 125–135 (2008).
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R. S. Balmer, J. R. Brandon, S. L. Clewes, H. K. Dhillon, J. M. Dodson, I. Friel, P. N. Inglis, T. D. Madgwick, M. L. Markham, T. P. Mollart, N. Perkins, G. A. Scarsbrook, D. J. Twitchen, A. J. Whitehead, J. J. Wilman, and S. M. Woollard, “Chemical vapour deposition synthetic diamond: materials, technology and applications,” J. Phys. Condens. Matter 21(36), 364221 (2009).
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Y. Chu, N. P. de Leon, B. J. Shields, B. Hausmann, R. Evans, E. Togan, M. J. Burek, M. Markham, A. Stacey, A. S. Zibrov, A. Yacoby, D. J. Twitchen, M. Loncar, H. Park, P. Maletinsky, and M. D. Lukin, “Coherent Optical Transitions in Implanted Nitrogen Vacancy Centers,” Nano Lett. 14(4), 1982–1986 (2014).
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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), 1–45 (2013).
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K. Beha, A. Batalov, N. B. Manson, R. Bratschitsch, and A. Leitenstorfer, “Optimum Photoluminescence Excitation and Recharging Cycle of Single Nitrogen-Vacancy Centers in Ultrapure Diamond,” Phys. Rev. Lett. 109(9), 097404 (2012).
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N. B. Manson and R. L. McMurtrie, “Issues concerning the nitrogen-vacancy center in diamond,” J. Lumin. 127(1), 98–103 (2007).
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Y. Chu, N. P. de Leon, B. J. Shields, B. Hausmann, R. Evans, E. Togan, M. J. Burek, M. Markham, A. Stacey, A. S. Zibrov, A. Yacoby, D. J. Twitchen, M. Loncar, H. Park, P. Maletinsky, and M. D. Lukin, “Coherent Optical Transitions in Implanted Nitrogen Vacancy Centers,” Nano Lett. 14(4), 1982–1986 (2014).
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Markham, M. L.

T. Yamamoto, T. Umeda, K. Watanabe, S. Onoda, M. L. Markham, D. J. Twitchen, B. Naydenov, L. P. McGuinness, T. Teraji, S. Koizumi, F. Dolde, H. Fedder, J. Honert, J. Wrachtrup, T. Ohshima, F. Jelezko, and J. Isoya, “Extending spin coherence times of diamond qubits by high-temperature annealing,” Phys. Rev. B 88(7), 075206 (2013).
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R. S. Balmer, J. R. Brandon, S. L. Clewes, H. K. Dhillon, J. M. Dodson, I. Friel, P. N. Inglis, T. D. Madgwick, M. L. Markham, T. P. Mollart, N. Perkins, G. A. Scarsbrook, D. J. Twitchen, A. J. Whitehead, J. J. Wilman, and S. M. Woollard, “Chemical vapour deposition synthetic diamond: materials, technology and applications,” J. Phys. Condens. Matter 21(36), 364221 (2009).
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J. Jeske, 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. Ohshima, 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).
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J. Jeske, 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. Ohshima, 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).
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T. Yamamoto, T. Umeda, K. Watanabe, S. Onoda, M. L. Markham, D. J. Twitchen, B. Naydenov, L. P. McGuinness, T. Teraji, S. Koizumi, F. Dolde, H. Fedder, J. Honert, J. Wrachtrup, T. Ohshima, F. Jelezko, and J. Isoya, “Extending spin coherence times of diamond qubits by high-temperature annealing,” Phys. Rev. B 88(7), 075206 (2013).
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R. J. Williams, J. Nold, M. Strecker, O. Kitzler, A. McKay, T. Schreiber, and R. P. Mildren, “Efficient Raman frequency conversion of high-power fiber lasers in diamond,” Laser Photonics Rev. 9(4), 405–411 (2015).
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N. B. Manson and R. L. McMurtrie, “Issues concerning the nitrogen-vacancy center in diamond,” J. Lumin. 127(1), 98–103 (2007).
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R. J. Williams, J. Nold, M. Strecker, O. Kitzler, A. McKay, T. Schreiber, and R. P. Mildren, “Efficient Raman frequency conversion of high-power fiber lasers in diamond,” Laser Photonics Rev. 9(4), 405–411 (2015).
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Mollart, T. P.

R. S. Balmer, J. R. Brandon, S. L. Clewes, H. K. Dhillon, J. M. Dodson, I. Friel, P. N. Inglis, T. D. Madgwick, M. L. Markham, T. P. Mollart, N. Perkins, G. A. Scarsbrook, D. J. Twitchen, A. J. Whitehead, J. J. Wilman, and S. M. Woollard, “Chemical vapour deposition synthetic diamond: materials, technology and applications,” J. Phys. Condens. Matter 21(36), 364221 (2009).
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Morrow, T.

Y. Li, I. Duncan, and T. Morrow, “Absolute fluorescence quantum efficiency of titanium-doped sapphire at ambient temperature,” J. Lumin. 52(5-6), 275–276 (1992).
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Mueller-Sebert, W.

M. M. Biener, J. Biener, S. O. Kucheyev, Y. M. Wang, B. El-Dasher, N. E. Teslich, A. V. Hamza, H. Obloh, W. Mueller-Sebert, M. Wolfer, T. Fuchs, M. Grimm, A. Kriele, and C. Wild, “Controlled incorporation of mid-to-high Z transition metals in CVD diamond,” Diamond Related Materials 19(5-6), 643–647 (2010).
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F. C. Waldermann, P. Olivero, J. Nunn, K. Surmacz, Z. Y. Wang, D. Jaksch, R. A. Taylor, I. A. Walmsley, M. Draganski, P. Reichart, A. D. Greentree, D. N. Jamieson, and S. Prawer, “Creating diamond color centers for quantum optical applications,” Diamond Related Materials 16(11), 1887–1895 (2007).
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M. M. Biener, J. Biener, S. O. Kucheyev, Y. M. Wang, B. El-Dasher, N. E. Teslich, A. V. Hamza, H. Obloh, W. Mueller-Sebert, M. Wolfer, T. Fuchs, M. Grimm, A. Kriele, and C. Wild, “Controlled incorporation of mid-to-high Z transition metals in CVD diamond,” Diamond Related Materials 19(5-6), 643–647 (2010).
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T. Gaebel, M. Domhan, C. Wittmann, I. Popa, F. Jelezko, J. Rabeau, A. Greentree, S. Prawer, E. Trajkov, P. R. Hemmer, and J. Wrachtrup, “Photochromism in single nitrogen-vacancy defect in diamond,” Appl. Phys. B 82(2), 243–246 (2006).
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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).
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Y. Chu, N. P. de Leon, B. J. Shields, B. Hausmann, R. Evans, E. Togan, M. J. Burek, M. Markham, A. Stacey, A. S. Zibrov, A. Yacoby, D. J. Twitchen, M. Loncar, H. Park, P. Maletinsky, and M. D. Lukin, “Coherent Optical Transitions in Implanted Nitrogen Vacancy Centers,” Nano Lett. 14(4), 1982–1986 (2014).
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[Crossref] [PubMed]

I. Friel, S. L. Clewes, H. K. Dhillon, N. Perkins, D. J. Twitchen, and G. A. Scarsbrook, “Control of surface and bulk crystalline quality in single crystal diamond grown by chemical vapour deposition,” Diamond Related Materials 18(5-8), 808–815 (2009).
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D. Gatto Monticone, F. Quercioli, R. Mercatelli, S. Soria, S. Borini, T. Poli, M. Vannoni, E. Vittone, and P. Olivero, “Systematic study of defect-related quenching of NV luminescence in diamond with time-correlated single-photon counting spectroscopy,” Phys. Rev. B 88(15), 155201 (2013).
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V. G. Vins and E. V. Pestryakov, “Color centers in diamond crystals: Their potential use in tunable and femtosecond lasers,” Diamond Related Materials 15(4-8), 569–571 (2006).
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D. Gatto Monticone, F. Quercioli, R. Mercatelli, S. Soria, S. Borini, T. Poli, M. Vannoni, E. Vittone, and P. Olivero, “Systematic study of defect-related quenching of NV luminescence in diamond with time-correlated single-photon counting spectroscopy,” Phys. Rev. B 88(15), 155201 (2013).
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J. Jeske, 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. Ohshima, 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).
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A. J. Kemp, J. M. Hopkins, A. J. Maclean, N. Schulz, M. Rattunde, J. Wagner, and D. Burns, “Thermal Management in 2.3- μm Semiconductor Disk Lasers: A Finite Element Analysis,” IEEE J. Quantum Electron. 44(2), 125–135 (2008).
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F. C. Waldermann, P. Olivero, J. Nunn, K. Surmacz, Z. Y. Wang, D. Jaksch, R. A. Taylor, I. A. Walmsley, M. Draganski, P. Reichart, A. D. Greentree, D. N. Jamieson, and S. Prawer, “Creating diamond color centers for quantum optical applications,” Diamond Related Materials 16(11), 1887–1895 (2007).
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N. Aslam, G. Waldherr, P. Neumann, F. Jelezko, and J. Wrachtrup, “Photo-induced ionization dynamics of the nitrogen vacancy defect in diamond investigated by single-shot charge state detection,” New J. Phys. 15(1), 013064 (2013).
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M. M. Biener, J. Biener, S. O. Kucheyev, Y. M. Wang, B. El-Dasher, N. E. Teslich, A. V. Hamza, H. Obloh, W. Mueller-Sebert, M. Wolfer, T. Fuchs, M. Grimm, A. Kriele, and C. Wild, “Controlled incorporation of mid-to-high Z transition metals in CVD diamond,” Diamond Related Materials 19(5-6), 643–647 (2010).
[Crossref]

Wang, Z. Y.

F. C. Waldermann, P. Olivero, J. Nunn, K. Surmacz, Z. Y. Wang, D. Jaksch, R. A. Taylor, I. A. Walmsley, M. Draganski, P. Reichart, A. D. Greentree, D. N. Jamieson, and S. Prawer, “Creating diamond color centers for quantum optical applications,” Diamond Related Materials 16(11), 1887–1895 (2007).
[Crossref]

Watanabe, K.

T. Yamamoto, T. Umeda, K. Watanabe, S. Onoda, M. L. Markham, D. J. Twitchen, B. Naydenov, L. P. McGuinness, T. Teraji, S. Koizumi, F. Dolde, H. Fedder, J. Honert, J. Wrachtrup, T. Ohshima, F. Jelezko, and J. Isoya, “Extending spin coherence times of diamond qubits by high-temperature annealing,” Phys. Rev. B 88(7), 075206 (2013).
[Crossref]

Wee, T.-L.

T.-L. Wee, Y.-K. Tzeng, C.-C. Han, H.-C. Chang, W. Fann, J.-H. Hsu, K.-M. Chen, and Y.-C. Yu, “Two-photon Excited Fluorescence of Nitrogen-Vacancy Centers in Proton-Irradiated Type Ib Diamond,” J. Phys. Chem. A 111(38), 9379–9386 (2007).
[Crossref] [PubMed]

Wentz, K. M.

T.-S. Ahn, R. O. Al-Kaysi, A. M. Müller, K. M. Wentz, and C. J. Bardeen, “Self-absorption correction for solid-state photoluminescence quantum yields obtained from integrating sphere measurements,” Rev. Sci. Instrum. 78(8), 086105 (2007).
[Crossref] [PubMed]

Whitehead, A. J.

R. S. Balmer, J. R. Brandon, S. L. Clewes, H. K. Dhillon, J. M. Dodson, I. Friel, P. N. Inglis, T. D. Madgwick, M. L. Markham, T. P. Mollart, N. Perkins, G. A. Scarsbrook, D. J. Twitchen, A. J. Whitehead, J. J. Wilman, and S. M. Woollard, “Chemical vapour deposition synthetic diamond: materials, technology and applications,” J. Phys. Condens. Matter 21(36), 364221 (2009).
[Crossref] [PubMed]

Wild, C.

M. M. Biener, J. Biener, S. O. Kucheyev, Y. M. Wang, B. El-Dasher, N. E. Teslich, A. V. Hamza, H. Obloh, W. Mueller-Sebert, M. Wolfer, T. Fuchs, M. Grimm, A. Kriele, and C. Wild, “Controlled incorporation of mid-to-high Z transition metals in CVD diamond,” Diamond Related Materials 19(5-6), 643–647 (2010).
[Crossref]

Wildanger, D.

S. Pezzagna, D. Rogalla, D. Wildanger, J. Meijer, and A. Zaitsev, “Creation and nature of optical centres in diamond for single-photon emission—overview and critical remarks,” New J. Phys. 13(3), 035024 (2011).
[Crossref]

Williams, R. J.

R. J. Williams, J. Nold, M. Strecker, O. Kitzler, A. McKay, T. Schreiber, and R. P. Mildren, “Efficient Raman frequency conversion of high-power fiber lasers in diamond,” Laser Photonics Rev. 9(4), 405–411 (2015).
[Crossref]

Wilman, J. J.

R. S. Balmer, J. R. Brandon, S. L. Clewes, H. K. Dhillon, J. M. Dodson, I. Friel, P. N. Inglis, T. D. Madgwick, M. L. Markham, T. P. Mollart, N. Perkins, G. A. Scarsbrook, D. J. Twitchen, A. J. Whitehead, J. J. Wilman, and S. M. Woollard, “Chemical vapour deposition synthetic diamond: materials, technology and applications,” J. Phys. Condens. Matter 21(36), 364221 (2009).
[Crossref] [PubMed]

Wittmann, C.

T. Gaebel, M. Domhan, C. Wittmann, I. Popa, F. Jelezko, J. Rabeau, A. Greentree, S. Prawer, E. Trajkov, P. R. Hemmer, and J. Wrachtrup, “Photochromism in single nitrogen-vacancy defect in diamond,” Appl. Phys. B 82(2), 243–246 (2006).
[Crossref]

Wolfer, M.

M. M. Biener, J. Biener, S. O. Kucheyev, Y. M. Wang, B. El-Dasher, N. E. Teslich, A. V. Hamza, H. Obloh, W. Mueller-Sebert, M. Wolfer, T. Fuchs, M. Grimm, A. Kriele, and C. Wild, “Controlled incorporation of mid-to-high Z transition metals in CVD diamond,” Diamond Related Materials 19(5-6), 643–647 (2010).
[Crossref]

Woollard, S. M.

R. S. Balmer, J. R. Brandon, S. L. Clewes, H. K. Dhillon, J. M. Dodson, I. Friel, P. N. Inglis, T. D. Madgwick, M. L. Markham, T. P. Mollart, N. Perkins, G. A. Scarsbrook, D. J. Twitchen, A. J. Whitehead, J. J. Wilman, and S. M. Woollard, “Chemical vapour deposition synthetic diamond: materials, technology and applications,” J. Phys. Condens. Matter 21(36), 364221 (2009).
[Crossref] [PubMed]

Wrachtrup, J.

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), 1–45 (2013).
[Crossref]

T. Yamamoto, T. Umeda, K. Watanabe, S. Onoda, M. L. Markham, D. J. Twitchen, B. Naydenov, L. P. McGuinness, T. Teraji, S. Koizumi, F. Dolde, H. Fedder, J. Honert, J. Wrachtrup, T. Ohshima, F. Jelezko, and J. Isoya, “Extending spin coherence times of diamond qubits by high-temperature annealing,” Phys. Rev. B 88(7), 075206 (2013).
[Crossref]

N. Aslam, G. Waldherr, P. Neumann, F. Jelezko, and J. Wrachtrup, “Photo-induced ionization dynamics of the nitrogen vacancy defect in diamond investigated by single-shot charge state detection,” New J. Phys. 15(1), 013064 (2013).
[Crossref]

A. Batalov, C. Zierl, T. Gaebel, P. Neumann, I. Y. Chan, G. Balasubramanian, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Temporal Coherence Of Photons Emitted by Single Nitrogen-Vacancy Defect Centers in Diamond Using Optical Rabi-Oscillations,” Phys. Rev. Lett. 100(7), 077401 (2008).
[Crossref] [PubMed]

T. Gaebel, M. Domhan, C. Wittmann, I. Popa, F. Jelezko, J. Rabeau, A. Greentree, S. Prawer, E. Trajkov, P. R. Hemmer, and J. Wrachtrup, “Photochromism in single nitrogen-vacancy defect in diamond,” Appl. Phys. B 82(2), 243–246 (2006).
[Crossref]

F. Jelezko and J. Wrachtrup, “Single defect centres in diamond: A review,” Phys. Status Solidi203(13), 3207–3225 (2006) (a).
[Crossref]

Yacoby, A.

Y. Chu, N. P. de Leon, B. J. Shields, B. Hausmann, R. Evans, E. Togan, M. J. Burek, M. Markham, A. Stacey, A. S. Zibrov, A. Yacoby, D. J. Twitchen, M. Loncar, H. Park, P. Maletinsky, and M. D. Lukin, “Coherent Optical Transitions in Implanted Nitrogen Vacancy Centers,” Nano Lett. 14(4), 1982–1986 (2014).
[Crossref] [PubMed]

Yamamoto, T.

T. Yamamoto, T. Umeda, K. Watanabe, S. Onoda, M. L. Markham, D. J. Twitchen, B. Naydenov, L. P. McGuinness, T. Teraji, S. Koizumi, F. Dolde, H. Fedder, J. Honert, J. Wrachtrup, T. Ohshima, F. Jelezko, and J. Isoya, “Extending spin coherence times of diamond qubits by high-temperature annealing,” Phys. Rev. B 88(7), 075206 (2013).
[Crossref]

Yu, Y.-C.

T.-L. Wee, Y.-K. Tzeng, C.-C. Han, H.-C. Chang, W. Fann, J.-H. Hsu, K.-M. Chen, and Y.-C. Yu, “Two-photon Excited Fluorescence of Nitrogen-Vacancy Centers in Proton-Irradiated Type Ib Diamond,” J. Phys. Chem. A 111(38), 9379–9386 (2007).
[Crossref] [PubMed]

Zaitsev, A.

S. Pezzagna, D. Rogalla, D. Wildanger, J. Meijer, and A. Zaitsev, “Creation and nature of optical centres in diamond for single-photon emission—overview and critical remarks,” New J. Phys. 13(3), 035024 (2011).
[Crossref]

Zibrov, A. S.

Y. Chu, N. P. de Leon, B. J. Shields, B. Hausmann, R. Evans, E. Togan, M. J. Burek, M. Markham, A. Stacey, A. S. Zibrov, A. Yacoby, D. J. Twitchen, M. Loncar, H. Park, P. Maletinsky, and M. D. Lukin, “Coherent Optical Transitions in Implanted Nitrogen Vacancy Centers,” Nano Lett. 14(4), 1982–1986 (2014).
[Crossref] [PubMed]

Zierl, C.

A. Batalov, C. Zierl, T. Gaebel, P. Neumann, I. Y. Chan, G. Balasubramanian, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Temporal Coherence Of Photons Emitted by Single Nitrogen-Vacancy Defect Centers in Diamond Using Optical Rabi-Oscillations,” Phys. Rev. Lett. 100(7), 077401 (2008).
[Crossref] [PubMed]

Appl. Phys. B (1)

T. Gaebel, M. Domhan, C. Wittmann, I. Popa, F. Jelezko, J. Rabeau, A. Greentree, S. Prawer, E. Trajkov, P. R. Hemmer, and J. Wrachtrup, “Photochromism in single nitrogen-vacancy defect in diamond,” Appl. Phys. B 82(2), 243–246 (2006).
[Crossref]

Diamond Related Materials (5)

F. C. Waldermann, P. Olivero, J. Nunn, K. Surmacz, Z. Y. Wang, D. Jaksch, R. A. Taylor, I. A. Walmsley, M. Draganski, P. Reichart, A. D. Greentree, D. N. Jamieson, and S. Prawer, “Creating diamond color centers for quantum optical applications,” Diamond Related Materials 16(11), 1887–1895 (2007).
[Crossref]

I. Friel, S. L. Clewes, H. K. Dhillon, N. Perkins, D. J. Twitchen, and G. A. Scarsbrook, “Control of surface and bulk crystalline quality in single crystal diamond grown by chemical vapour deposition,” Diamond Related Materials 18(5-8), 808–815 (2009).
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M. M. Biener, J. Biener, S. O. Kucheyev, Y. M. Wang, B. El-Dasher, N. E. Teslich, A. V. Hamza, H. Obloh, W. Mueller-Sebert, M. Wolfer, T. Fuchs, M. Grimm, A. Kriele, and C. Wild, “Controlled incorporation of mid-to-high Z transition metals in CVD diamond,” Diamond Related Materials 19(5-6), 643–647 (2010).
[Crossref]

V. G. Vins and E. V. Pestryakov, “Color centers in diamond crystals: Their potential use in tunable and femtosecond lasers,” Diamond Related Materials 15(4-8), 569–571 (2006).
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H. Hanzawa, Y. Nisida, and T. Kato, “Measurement of decay time for the NV centre in Ib diamond with a picosecond laser pulse,” Diamond Related Materials 6(11), 1595–1598 (1997).
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C. M. Breeding and J. E. Shigley, “The ‘type’ classification system of diamonds and its importance in gemology,” Gems & Gemology 45(2), 96–111 (2009).
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A. J. Kemp, J. M. Hopkins, A. J. Maclean, N. Schulz, M. Rattunde, J. Wagner, and D. Burns, “Thermal Management in 2.3- μm Semiconductor Disk Lasers: A Finite Element Analysis,” IEEE J. Quantum Electron. 44(2), 125–135 (2008).
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V. G. Savitski, I. Friel, J. E. Hastie, M. D. Dawson, D. Burns, and A. J. Kemp, “Characterization of Single-Crystal Synthetic Diamond for Multi-Watt Continuous-Wave Raman Lasers,” IEEE J. Quantum Electron. 48(3), 328–337 (2012).
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N. B. Manson and R. L. McMurtrie, “Issues concerning the nitrogen-vacancy center in diamond,” J. Lumin. 127(1), 98–103 (2007).
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J. Phys. Chem. A (1)

T.-L. Wee, Y.-K. Tzeng, C.-C. Han, H.-C. Chang, W. Fann, J.-H. Hsu, K.-M. Chen, and Y.-C. Yu, “Two-photon Excited Fluorescence of Nitrogen-Vacancy Centers in Proton-Irradiated Type Ib Diamond,” J. Phys. Chem. A 111(38), 9379–9386 (2007).
[Crossref] [PubMed]

J. Phys. Condens. Matter (4)

R. S. Balmer, J. R. Brandon, S. L. Clewes, H. K. Dhillon, J. M. Dodson, I. Friel, P. N. Inglis, T. D. Madgwick, M. L. Markham, T. P. Mollart, N. Perkins, G. A. Scarsbrook, D. J. Twitchen, A. J. Whitehead, J. J. Wilman, and S. M. Woollard, “Chemical vapour deposition synthetic diamond: materials, technology and applications,” J. Phys. Condens. Matter 21(36), 364221 (2009).
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A. T. Collins and I. Kiflawi, “The annealing of radiation damage in type Ia diamond,” J. Phys. Condens. Matter 21(36), 364209 (2009).
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Laser Photonics Rev. (1)

R. J. Williams, J. Nold, M. Strecker, O. Kitzler, A. McKay, T. Schreiber, and R. P. Mildren, “Efficient Raman frequency conversion of high-power fiber lasers in diamond,” Laser Photonics Rev. 9(4), 405–411 (2015).
[Crossref]

Nano Lett. (1)

Y. Chu, N. P. de Leon, B. J. Shields, B. Hausmann, R. Evans, E. Togan, M. J. Burek, M. Markham, A. Stacey, A. S. Zibrov, A. Yacoby, D. J. Twitchen, M. Loncar, H. Park, P. Maletinsky, and M. D. Lukin, “Coherent Optical Transitions in Implanted Nitrogen Vacancy Centers,” Nano Lett. 14(4), 1982–1986 (2014).
[Crossref] [PubMed]

Nat. Commun. (1)

J. Jeske, 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. Ohshima, 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).
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Nat. Photonics (1)

I. Aharonovich, A. D. Greentree, and S. Prawer, “Diamond photonics,” Nat. Photonics 5(7), 397–405 (2011).
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New J. Phys. (3)

J. Jeske, J. H. Cole, and A. D. Greentree, “Laser threshold magnetometry,” New J. Phys. 18(1), 013015 (2016).
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S. Pezzagna, D. Rogalla, D. Wildanger, J. Meijer, and A. Zaitsev, “Creation and nature of optical centres in diamond for single-photon emission—overview and critical remarks,” New J. Phys. 13(3), 035024 (2011).
[Crossref]

N. Aslam, G. Waldherr, P. Neumann, F. Jelezko, and J. Wrachtrup, “Photo-induced ionization dynamics of the nitrogen vacancy defect in diamond investigated by single-shot charge state detection,” New J. Phys. 15(1), 013064 (2013).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rep. (1)

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), 1–45 (2013).
[Crossref]

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Phys. Rev. B (3)

T. Yamamoto, T. Umeda, K. Watanabe, S. Onoda, M. L. Markham, D. J. Twitchen, B. Naydenov, L. P. McGuinness, T. Teraji, S. Koizumi, F. Dolde, H. Fedder, J. Honert, J. Wrachtrup, T. Ohshima, F. Jelezko, and J. Isoya, “Extending spin coherence times of diamond qubits by high-temperature annealing,” Phys. Rev. B 88(7), 075206 (2013).
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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).
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D. Gatto Monticone, F. Quercioli, R. Mercatelli, S. Soria, S. Borini, T. Poli, M. Vannoni, E. Vittone, and P. Olivero, “Systematic study of defect-related quenching of NV luminescence in diamond with time-correlated single-photon counting spectroscopy,” Phys. Rev. B 88(15), 155201 (2013).
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K. Beha, A. Batalov, N. B. Manson, R. Bratschitsch, and A. Leitenstorfer, “Optimum Photoluminescence Excitation and Recharging Cycle of Single Nitrogen-Vacancy Centers in Ultrapure Diamond,” Phys. Rev. Lett. 109(9), 097404 (2012).
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A. Batalov, C. Zierl, T. Gaebel, P. Neumann, I. Y. Chan, G. Balasubramanian, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Temporal Coherence Of Photons Emitted by Single Nitrogen-Vacancy Defect Centers in Diamond Using Optical Rabi-Oscillations,” Phys. Rev. Lett. 100(7), 077401 (2008).
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Figures (8)

Fig. 1
Fig. 1 Sample E6NV under white light a) and UV illumination b). Sample E6H3D under white light c) and UV illumination d).
Fig. 2
Fig. 2 Room temperature unpolarised absorption spectra for sample E6NV and E6H3D.
Fig. 3
Fig. 3 Absorption spectra of samples E6NV and E6H3D, taken at 77 K.
Fig. 4
Fig. 4 Luminescence spectra of the diamond samples and Ti:sapphire crystal pumped at 532 nm (a) and at 447 nm (b) measured using an integrating sphere. Examples of the matching the long-wavelength tail of the emission spectra (rescaled) from the low-concentrated sample (ADCVD, green lines) to that of the samples E6H3D (a) and E6NV (b) are also shown.
Fig. 5
Fig. 5 Luminescence decay of the samples E6NV (a) and E6H3D (b) at emission wavelengths >640 nm at the pump wavelengths of 448 and 562 nm: dots - experimental results, solid lines - best fits using single- (pump wavelength 448 nm) and double- (pump wavelength 562 nm) exponential decay models.
Fig. 6
Fig. 6 Results of correction of the luminescence spectra of diamond samples pumped at 532 (a) and 447 nm (b) for contribution of emission from NV0 (a) and H3 CC (b).
Fig. 7
Fig. 7 The emission cross sections of NV- and NV0 CC (σem,) for samples E6NV and E6H3D calculated using Eq. (4). The difference in the shape of the cross section spectra is attributed to the difference in CC concentration and its contribution to the luminescence spectra.
Fig. 8
Fig. 8 Calculated gain spectra of NV- (a) and NV0 (b) at the pump wavelength of 532 nm (a) and 447 nm (b) for different inversion factors β and for the two samples under study.

Tables (3)

Tables Icon

Table 1 Defect concentrations in samples estimated by the integrated ZPLs in absorption measurements taken at 77K

Tables Icon

Table 2 Results of quantum yield measurements

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Table 3 Results of luminescence lifetime measurements in diamond samples

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

Φ = Φ x 1 a + a Φ x
Φ x = Q s A x A s 1 T s 1 T x ( n x n s ) 2
a = 1 0 I x ( λ ) d λ 0 I l o w ( λ ) d λ
σ e m ( λ ) = λ 5 τ r ( λ I ( λ ) d λ ) 8 π n 2 c I ( λ )
g = σ e m N N V β α a b s

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