Abstract

Single silicon vacancy (SiV) color centers in diamond have recently shown the ability for high brightness, narrow bandwidth, room temperature single photon emission. This work develops a model describing the three level population dynamics of single SiV centers in diamond nanocrystals on iridium surfaces including an intensity dependent de-shelving process. Furthermore, we investigate the brightness and photostability of single centers and find maximum single photon rates of 6.2 Mcps under continuous excitation. We investigate the collection efficiency of the fluorescence and estimate quantum efficiencies of the SiV centers.

© 2012 OSA

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2012 (3)

X.-W. Chen, M. Agio, and V. Sandoghdar, “Metallo-dielectric hybrid antennas for ultrastrong enhancement of spontaneous emission,” Phys. Rev. Lett.108, 233001 (2012).
[CrossRef]

E. Neu, R. Albrecht, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “Electronic transitions of single silicon vacancy centers in the near-infrared spectral region,” Phys. Rev. B85, 245207 (2012).
[CrossRef]

S. Grudinkin, N. Feoktistov, A. Medvedev, K. Bogdanov, A. Baranov, A. Vul, and V. Golubev, “Luminescent isolated diamond particles with controllably embedded silicon-vacancy colour centres,” J. Phys. D: Appl. Phys.45, 062001 (2012).
[CrossRef]

2011 (9)

R. Chapman and T. Plakhotnik, “Quantitative luminescence microscopy on nitrogen-vacancy centres in diamond: Saturation effects under pulsed excitation,” Chem. Phys. Lett.507, 190–194 (2011).
[CrossRef]

S. Castelletto and A. Boretti, “Radiative and nonradiative decay rates in chromium-related centers in nanodiamonds,” Opt. Lett.36, 4224–4226 (2011).
[CrossRef] [PubMed]

I. Aharonovich, S. Castelletto, D. Simpson, C. Su, A. Greentree, and S. Prawer, “Diamond-based single-photon emitters,” Rep. Prog. Phys.74, 076501 (2011).
[CrossRef]

E. Neu, D. Steinmetz, J. Riedrich-Möller, S. Gsell, M. Fischer, M. Schreck, and C. Becher, “Single photon emission from silicon-vacancy colour centres in chemical vapour deposition nano-diamonds on iridium,” New J. Phys.13, 025012 (2011).
[CrossRef]

E. Neu, C. Arend, E. Gross, F. Guldner, C. Hepp, D. Steinmetz, E. Zscherpel, S. Ghodbane, H. Sternschulte, D. Steinmüller-Nethl, Y. Liang, A. Krueger, and C. Becher, “Narrowband fluorescent nanodiamonds produced from chemical vapor deposition films,” Appl. Phys. Lett.98, 243107 (2011).
[CrossRef]

E. Neu, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “Fluorescence and polarization spectroscopy of single silicon vacancy centers in heteroepitaxial nanodiamonds on iridium,” Phys. Rev. B84, 205211 (2011).
[CrossRef]

J. Greffet, J. Hugonin, M. Besbes, N. Lai, F. Treussart, and J. Roch, “Diamond particles as nanoantennas for nitrogen-vacancy color centers,” Arxiv preprint arXiv:1107.0502 (2011).

U. F. S. D’Haenens-Johansson, A. M. Edmonds, B. L. Green, M. E. Newton, G. Davies, P. M. Martineau, R. U. A. Khan, and D. J. Twitchen, “Optical properties of the neutral silicon split-vacancy center in diamond,” Phys. Rev. B84, 245208 (2011).
[CrossRef]

R. Ulbricht, S. T. van der Post, J. P. Goss, P. R. Briddon, R. Jones, R. U. A. Khan, and M. Bonn, “Single substitutional nitrogen defects revealed as electron acceptor states in diamond using ultrafast spectroscopy,” Phys. Rev. B84, 165202 (2011).
[CrossRef]

2010 (4)

L. Rogers, “How far into the infrared can a colour centre in diamond emit?” Physics Procedia3, 1557–1561 (2010). 10th International Meeting On Hole Burning, Single Molecule, And Related Spectroscopies, 2009, Palm Cove, Australia.
[CrossRef]

B. Smith, D. Gruber, and T. Plakhotnik, “The effects of surface oxidation on luminescence of nano diamonds,” Diam. Relat. Mater.19, 314–318 (2010).
[CrossRef]

C. Bradac, T. Gaebel, N. Naidoo, M. J. Sellars, J. Twamley, L. J. Brown, A. S. Barnard, T. Plakhotnik, A. V. Zvyagin, and J. R. Rabeau, “Observation and control of blinking nitrogen-vacancy centres in discrete nanodiamonds,” Nature Nanotech.5, 345–349 (2010).
[CrossRef]

I. Aharonovich, S. Castelletto, D. A. Simpson, A. D. Greentree, and S. Prawer, “Photophysics of chromium-related diamond single-photon emitters,” Phys. Rev. A81, 043813 (2010).
[CrossRef]

2009 (2)

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

P. Siyushev, V. Jacques, I. Aharonovich, F. Kaiser, T. Müller, L. Lombez, M. Atatüre, S. Castelletto, S. Prawer, F. Jelezko, and J. Wrachtrup, “Low-temperature optical characterization of a near-infrared single-photon emitter in nanodiamonds,” New J. Phys.11, 113029 (2009).
[CrossRef]

2007 (1)

T.-L. Wee, Y.-K. Tzeng, C.-C. Han, H.-C. Chang, W. Fann, J.-H. Hsu, K.-M. Chen, and Y.-C. Yull, “Two-photon excited fluorescence of nitrogen-vacancy centers in proton-irradiated type Ib diamond,” J. Phys. Chem. A111, 9379–9386 (2007).
[CrossRef] [PubMed]

2006 (2)

C. Wang, C. Kurtsiefer, H. Weinfurter, and B. Burchard, “Single photon emission from SiV centres in diamond produced by ion implantation.” J. Phys. B: At. Mol. Opt. Phys.39, 37–41 (2006).
[CrossRef]

E. Wu, V. Jacques, H. Zeng, P. Grangier, F. Treussart, and J.-F. Roch, “Narrow-band single-photon emission in the near infrared for quantum key distribution,” Opt. Express14, 1296–1303 (2006).
[CrossRef] [PubMed]

2005 (1)

B. Lounis and M. Orrit, “Single photon sources,” Rep. Prog. Phys.68, 1129–1179 (2005).
[CrossRef]

2003 (2)

L. Rogobete, H. Schniepp, V. Sandoghdar, and C. Henkel, “Spontaneous emission in nanoscopic dielectric particles,” Opt. Lett.28, 1736–1738 (2003).
[CrossRef] [PubMed]

A. Mora, J. Steeds, and J. Butler, “Relationship between grain boundaries and broad luminescence peaks in CVD diamond films,” Diam. Relat. Mater.12, 310–317 (2003).
[CrossRef]

2000 (3)

K. Iakoubovskii and G. J. Adriaenssens, “Luminescence excitation spectra in diamond,” Phys. Rev. B61, 10174– 10182 (2000).
[CrossRef]

R. Brouri, A. Beveratos, J. Poizat, and P. Grangier, “Photon antibunching in the fluorescence of individual color centers in diamond,” Opt. Lett.25, 1294–1296 (2000).
[CrossRef]

L. Fleury, J. Segura, G. Zumofen, B. Hecht, and U. Wild, “Nonclassical photon statistics in single-molecule fluorescence at room temperature,” Phys. Rev. Lett.84, 1148–1151 (2000).
[CrossRef] [PubMed]

1998 (1)

S. Kitson, P. Jonsson, J. Rarity, and P. Tapster, “Intensity fluctuation spectroscopy of small numbers of dye molecules in a microcavity,” Phys. Rev. A58, 620–627 (1998).
[CrossRef]

1996 (1)

A. V. Turukhin, C.-H. Liu, A. A. Gorokhovsky, R. R. Alfano, and W. Phillips, “Picosecond photoluminescence decay of Si-doped chemical-vapor-deposited diamond films,” Phys. Rev. B54, 16448–16451 (1996).
[CrossRef]

1994 (1)

L. Bergman, M. McClure, J. Glass, and R. Nemanich, “The origin of the broadband luminescence and the effect of nitrogen doping on the optical properties of diamond films,” J. Appl. Phys.76, 3020–3027 (1994).
[CrossRef]

1987 (1)

1979 (1)

I. Osad’ko, “Determination of electron-phonon coupling from structured optical spectra of impurity centers,” Sov. Phys. Usp.22, 311–329 (1979).
[CrossRef]

1978 (1)

R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys.37, 1–65 (1978).
[CrossRef]

1955 (1)

D. Dexter, C. Klick, and G. Russell, “Criterion for the occurrence of luminescence,” Phys. Rev.100, 603–605 (1955).
[CrossRef]

Adriaenssens, G. J.

K. Iakoubovskii and G. J. Adriaenssens, “Luminescence excitation spectra in diamond,” Phys. Rev. B61, 10174– 10182 (2000).
[CrossRef]

Agio, M.

X.-W. Chen, M. Agio, and V. Sandoghdar, “Metallo-dielectric hybrid antennas for ultrastrong enhancement of spontaneous emission,” Phys. Rev. Lett.108, 233001 (2012).
[CrossRef]

Aharonovich, I.

I. Aharonovich, S. Castelletto, D. Simpson, C. Su, A. Greentree, and S. Prawer, “Diamond-based single-photon emitters,” Rep. Prog. Phys.74, 076501 (2011).
[CrossRef]

I. Aharonovich, S. Castelletto, D. A. Simpson, A. D. Greentree, and S. Prawer, “Photophysics of chromium-related diamond single-photon emitters,” Phys. Rev. A81, 043813 (2010).
[CrossRef]

P. Siyushev, V. Jacques, I. Aharonovich, F. Kaiser, T. Müller, L. Lombez, M. Atatüre, S. Castelletto, S. Prawer, F. Jelezko, and J. Wrachtrup, “Low-temperature optical characterization of a near-infrared single-photon emitter in nanodiamonds,” New J. Phys.11, 113029 (2009).
[CrossRef]

Albrecht, R.

E. Neu, R. Albrecht, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “Electronic transitions of single silicon vacancy centers in the near-infrared spectral region,” Phys. Rev. B85, 245207 (2012).
[CrossRef]

Alfano, R. R.

A. V. Turukhin, C.-H. Liu, A. A. Gorokhovsky, R. R. Alfano, and W. Phillips, “Picosecond photoluminescence decay of Si-doped chemical-vapor-deposited diamond films,” Phys. Rev. B54, 16448–16451 (1996).
[CrossRef]

Arend, C.

E. Neu, C. Arend, E. Gross, F. Guldner, C. Hepp, D. Steinmetz, E. Zscherpel, S. Ghodbane, H. Sternschulte, D. Steinmüller-Nethl, Y. Liang, A. Krueger, and C. Becher, “Narrowband fluorescent nanodiamonds produced from chemical vapor deposition films,” Appl. Phys. Lett.98, 243107 (2011).
[CrossRef]

Atatüre, M.

P. Siyushev, V. Jacques, I. Aharonovich, F. Kaiser, T. Müller, L. Lombez, M. Atatüre, S. Castelletto, S. Prawer, F. Jelezko, and J. Wrachtrup, “Low-temperature optical characterization of a near-infrared single-photon emitter in nanodiamonds,” New J. Phys.11, 113029 (2009).
[CrossRef]

Aulenbacher, K.

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

Axelrod, D.

Balasubramanian, G.

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

Baranov, A.

S. Grudinkin, N. Feoktistov, A. Medvedev, K. Bogdanov, A. Baranov, A. Vul, and V. Golubev, “Luminescent isolated diamond particles with controllably embedded silicon-vacancy colour centres,” J. Phys. D: Appl. Phys.45, 062001 (2012).
[CrossRef]

Barnard, A. S.

C. Bradac, T. Gaebel, N. Naidoo, M. J. Sellars, J. Twamley, L. J. Brown, A. S. Barnard, T. Plakhotnik, A. V. Zvyagin, and J. R. Rabeau, “Observation and control of blinking nitrogen-vacancy centres in discrete nanodiamonds,” Nature Nanotech.5, 345–349 (2010).
[CrossRef]

Becher, C.

E. Neu, R. Albrecht, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “Electronic transitions of single silicon vacancy centers in the near-infrared spectral region,” Phys. Rev. B85, 245207 (2012).
[CrossRef]

E. Neu, C. Arend, E. Gross, F. Guldner, C. Hepp, D. Steinmetz, E. Zscherpel, S. Ghodbane, H. Sternschulte, D. Steinmüller-Nethl, Y. Liang, A. Krueger, and C. Becher, “Narrowband fluorescent nanodiamonds produced from chemical vapor deposition films,” Appl. Phys. Lett.98, 243107 (2011).
[CrossRef]

E. Neu, D. Steinmetz, J. Riedrich-Möller, S. Gsell, M. Fischer, M. Schreck, and C. Becher, “Single photon emission from silicon-vacancy colour centres in chemical vapour deposition nano-diamonds on iridium,” New J. Phys.13, 025012 (2011).
[CrossRef]

E. Neu, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “Fluorescence and polarization spectroscopy of single silicon vacancy centers in heteroepitaxial nanodiamonds on iridium,” Phys. Rev. B84, 205211 (2011).
[CrossRef]

Bergman, L.

L. Bergman, M. McClure, J. Glass, and R. Nemanich, “The origin of the broadband luminescence and the effect of nitrogen doping on the optical properties of diamond films,” J. Appl. Phys.76, 3020–3027 (1994).
[CrossRef]

Besbes, M.

J. Greffet, J. Hugonin, M. Besbes, N. Lai, F. Treussart, and J. Roch, “Diamond particles as nanoantennas for nitrogen-vacancy color centers,” Arxiv preprint arXiv:1107.0502 (2011).

Beveratos, A.

Boersch, M.

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

Bogdanov, K.

S. Grudinkin, N. Feoktistov, A. Medvedev, K. Bogdanov, A. Baranov, A. Vul, and V. Golubev, “Luminescent isolated diamond particles with controllably embedded silicon-vacancy colour centres,” J. Phys. D: Appl. Phys.45, 062001 (2012).
[CrossRef]

Bonn, M.

R. Ulbricht, S. T. van der Post, J. P. Goss, P. R. Briddon, R. Jones, R. U. A. Khan, and M. Bonn, “Single substitutional nitrogen defects revealed as electron acceptor states in diamond using ultrafast spectroscopy,” Phys. Rev. B84, 165202 (2011).
[CrossRef]

Boretti, A.

Boudou, J.

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

Bradac, C.

C. Bradac, T. Gaebel, N. Naidoo, M. J. Sellars, J. Twamley, L. J. Brown, A. S. Barnard, T. Plakhotnik, A. V. Zvyagin, and J. R. Rabeau, “Observation and control of blinking nitrogen-vacancy centres in discrete nanodiamonds,” Nature Nanotech.5, 345–349 (2010).
[CrossRef]

Briddon, P. R.

R. Ulbricht, S. T. van der Post, J. P. Goss, P. R. Briddon, R. Jones, R. U. A. Khan, and M. Bonn, “Single substitutional nitrogen defects revealed as electron acceptor states in diamond using ultrafast spectroscopy,” Phys. Rev. B84, 165202 (2011).
[CrossRef]

Brouri, R.

Brown, L. J.

C. Bradac, T. Gaebel, N. Naidoo, M. J. Sellars, J. Twamley, L. J. Brown, A. S. Barnard, T. Plakhotnik, A. V. Zvyagin, and J. R. Rabeau, “Observation and control of blinking nitrogen-vacancy centres in discrete nanodiamonds,” Nature Nanotech.5, 345–349 (2010).
[CrossRef]

Burchard, B.

C. Wang, C. Kurtsiefer, H. Weinfurter, and B. Burchard, “Single photon emission from SiV centres in diamond produced by ion implantation.” J. Phys. B: At. Mol. Opt. Phys.39, 37–41 (2006).
[CrossRef]

Butler, J.

A. Mora, J. Steeds, and J. Butler, “Relationship between grain boundaries and broad luminescence peaks in CVD diamond films,” Diam. Relat. Mater.12, 310–317 (2003).
[CrossRef]

Castelletto, S.

I. Aharonovich, S. Castelletto, D. Simpson, C. Su, A. Greentree, and S. Prawer, “Diamond-based single-photon emitters,” Rep. Prog. Phys.74, 076501 (2011).
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I. Aharonovich, S. Castelletto, D. A. Simpson, A. D. Greentree, and S. Prawer, “Photophysics of chromium-related diamond single-photon emitters,” Phys. Rev. A81, 043813 (2010).
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P. Siyushev, V. Jacques, I. Aharonovich, F. Kaiser, T. Müller, L. Lombez, M. Atatüre, S. Castelletto, S. Prawer, F. Jelezko, and J. Wrachtrup, “Low-temperature optical characterization of a near-infrared single-photon emitter in nanodiamonds,” New J. Phys.11, 113029 (2009).
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R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys.37, 1–65 (1978).
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T.-L. Wee, Y.-K. Tzeng, C.-C. Han, H.-C. Chang, W. Fann, J.-H. Hsu, K.-M. Chen, and Y.-C. Yull, “Two-photon excited fluorescence of nitrogen-vacancy centers in proton-irradiated type Ib diamond,” J. Phys. Chem. A111, 9379–9386 (2007).
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R. Chapman and T. Plakhotnik, “Quantitative luminescence microscopy on nitrogen-vacancy centres in diamond: Saturation effects under pulsed excitation,” Chem. Phys. Lett.507, 190–194 (2011).
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T.-L. Wee, Y.-K. Tzeng, C.-C. Han, H.-C. Chang, W. Fann, J.-H. Hsu, K.-M. Chen, and Y.-C. Yull, “Two-photon excited fluorescence of nitrogen-vacancy centers in proton-irradiated type Ib diamond,” J. Phys. Chem. A111, 9379–9386 (2007).
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X.-W. Chen, M. Agio, and V. Sandoghdar, “Metallo-dielectric hybrid antennas for ultrastrong enhancement of spontaneous emission,” Phys. Rev. Lett.108, 233001 (2012).
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J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

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U. F. S. D’Haenens-Johansson, A. M. Edmonds, B. L. Green, M. E. Newton, G. Davies, P. M. Martineau, R. U. A. Khan, and D. J. Twitchen, “Optical properties of the neutral silicon split-vacancy center in diamond,” Phys. Rev. B84, 245208 (2011).
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Davies, G.

U. F. S. D’Haenens-Johansson, A. M. Edmonds, B. L. Green, M. E. Newton, G. Davies, P. M. Martineau, R. U. A. Khan, and D. J. Twitchen, “Optical properties of the neutral silicon split-vacancy center in diamond,” Phys. Rev. B84, 245208 (2011).
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D. Dexter, C. Klick, and G. Russell, “Criterion for the occurrence of luminescence,” Phys. Rev.100, 603–605 (1955).
[CrossRef]

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U. F. S. D’Haenens-Johansson, A. M. Edmonds, B. L. Green, M. E. Newton, G. Davies, P. M. Martineau, R. U. A. Khan, and D. J. Twitchen, “Optical properties of the neutral silicon split-vacancy center in diamond,” Phys. Rev. B84, 245208 (2011).
[CrossRef]

Erdmann, R.

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

Fann, W.

T.-L. Wee, Y.-K. Tzeng, C.-C. Han, H.-C. Chang, W. Fann, J.-H. Hsu, K.-M. Chen, and Y.-C. Yull, “Two-photon excited fluorescence of nitrogen-vacancy centers in proton-irradiated type Ib diamond,” J. Phys. Chem. A111, 9379–9386 (2007).
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Feoktistov, N.

S. Grudinkin, N. Feoktistov, A. Medvedev, K. Bogdanov, A. Baranov, A. Vul, and V. Golubev, “Luminescent isolated diamond particles with controllably embedded silicon-vacancy colour centres,” J. Phys. D: Appl. Phys.45, 062001 (2012).
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E. Neu, R. Albrecht, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “Electronic transitions of single silicon vacancy centers in the near-infrared spectral region,” Phys. Rev. B85, 245207 (2012).
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E. Neu, D. Steinmetz, J. Riedrich-Möller, S. Gsell, M. Fischer, M. Schreck, and C. Becher, “Single photon emission from silicon-vacancy colour centres in chemical vapour deposition nano-diamonds on iridium,” New J. Phys.13, 025012 (2011).
[CrossRef]

E. Neu, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “Fluorescence and polarization spectroscopy of single silicon vacancy centers in heteroepitaxial nanodiamonds on iridium,” Phys. Rev. B84, 205211 (2011).
[CrossRef]

Fleury, L.

L. Fleury, J. Segura, G. Zumofen, B. Hecht, and U. Wild, “Nonclassical photon statistics in single-molecule fluorescence at room temperature,” Phys. Rev. Lett.84, 1148–1151 (2000).
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Gaebel, T.

C. Bradac, T. Gaebel, N. Naidoo, M. J. Sellars, J. Twamley, L. J. Brown, A. S. Barnard, T. Plakhotnik, A. V. Zvyagin, and J. R. Rabeau, “Observation and control of blinking nitrogen-vacancy centres in discrete nanodiamonds,” Nature Nanotech.5, 345–349 (2010).
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Ghodbane, S.

E. Neu, C. Arend, E. Gross, F. Guldner, C. Hepp, D. Steinmetz, E. Zscherpel, S. Ghodbane, H. Sternschulte, D. Steinmüller-Nethl, Y. Liang, A. Krueger, and C. Becher, “Narrowband fluorescent nanodiamonds produced from chemical vapor deposition films,” Appl. Phys. Lett.98, 243107 (2011).
[CrossRef]

Glass, J.

L. Bergman, M. McClure, J. Glass, and R. Nemanich, “The origin of the broadband luminescence and the effect of nitrogen doping on the optical properties of diamond films,” J. Appl. Phys.76, 3020–3027 (1994).
[CrossRef]

Golubev, V.

S. Grudinkin, N. Feoktistov, A. Medvedev, K. Bogdanov, A. Baranov, A. Vul, and V. Golubev, “Luminescent isolated diamond particles with controllably embedded silicon-vacancy colour centres,” J. Phys. D: Appl. Phys.45, 062001 (2012).
[CrossRef]

Gorokhovsky, A. A.

A. V. Turukhin, C.-H. Liu, A. A. Gorokhovsky, R. R. Alfano, and W. Phillips, “Picosecond photoluminescence decay of Si-doped chemical-vapor-deposited diamond films,” Phys. Rev. B54, 16448–16451 (1996).
[CrossRef]

Goss, J. P.

R. Ulbricht, S. T. van der Post, J. P. Goss, P. R. Briddon, R. Jones, R. U. A. Khan, and M. Bonn, “Single substitutional nitrogen defects revealed as electron acceptor states in diamond using ultrafast spectroscopy,” Phys. Rev. B84, 165202 (2011).
[CrossRef]

Grangier, P.

Green, B. L.

U. F. S. D’Haenens-Johansson, A. M. Edmonds, B. L. Green, M. E. Newton, G. Davies, P. M. Martineau, R. U. A. Khan, and D. J. Twitchen, “Optical properties of the neutral silicon split-vacancy center in diamond,” Phys. Rev. B84, 245208 (2011).
[CrossRef]

Greentree, A.

I. Aharonovich, S. Castelletto, D. Simpson, C. Su, A. Greentree, and S. Prawer, “Diamond-based single-photon emitters,” Rep. Prog. Phys.74, 076501 (2011).
[CrossRef]

Greentree, A. D.

I. Aharonovich, S. Castelletto, D. A. Simpson, A. D. Greentree, and S. Prawer, “Photophysics of chromium-related diamond single-photon emitters,” Phys. Rev. A81, 043813 (2010).
[CrossRef]

Greffet, J.

J. Greffet, J. Hugonin, M. Besbes, N. Lai, F. Treussart, and J. Roch, “Diamond particles as nanoantennas for nitrogen-vacancy color centers,” Arxiv preprint arXiv:1107.0502 (2011).

Gross, E.

E. Neu, C. Arend, E. Gross, F. Guldner, C. Hepp, D. Steinmetz, E. Zscherpel, S. Ghodbane, H. Sternschulte, D. Steinmüller-Nethl, Y. Liang, A. Krueger, and C. Becher, “Narrowband fluorescent nanodiamonds produced from chemical vapor deposition films,” Appl. Phys. Lett.98, 243107 (2011).
[CrossRef]

Grotz, B.

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

Gruber, D.

B. Smith, D. Gruber, and T. Plakhotnik, “The effects of surface oxidation on luminescence of nano diamonds,” Diam. Relat. Mater.19, 314–318 (2010).
[CrossRef]

Grudinkin, S.

S. Grudinkin, N. Feoktistov, A. Medvedev, K. Bogdanov, A. Baranov, A. Vul, and V. Golubev, “Luminescent isolated diamond particles with controllably embedded silicon-vacancy colour centres,” J. Phys. D: Appl. Phys.45, 062001 (2012).
[CrossRef]

Gsell, S.

E. Neu, R. Albrecht, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “Electronic transitions of single silicon vacancy centers in the near-infrared spectral region,” Phys. Rev. B85, 245207 (2012).
[CrossRef]

E. Neu, D. Steinmetz, J. Riedrich-Möller, S. Gsell, M. Fischer, M. Schreck, and C. Becher, “Single photon emission from silicon-vacancy colour centres in chemical vapour deposition nano-diamonds on iridium,” New J. Phys.13, 025012 (2011).
[CrossRef]

E. Neu, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “Fluorescence and polarization spectroscopy of single silicon vacancy centers in heteroepitaxial nanodiamonds on iridium,” Phys. Rev. B84, 205211 (2011).
[CrossRef]

Guldner, F.

E. Neu, C. Arend, E. Gross, F. Guldner, C. Hepp, D. Steinmetz, E. Zscherpel, S. Ghodbane, H. Sternschulte, D. Steinmüller-Nethl, Y. Liang, A. Krueger, and C. Becher, “Narrowband fluorescent nanodiamonds produced from chemical vapor deposition films,” Appl. Phys. Lett.98, 243107 (2011).
[CrossRef]

Han, C.-C.

T.-L. Wee, Y.-K. Tzeng, C.-C. Han, H.-C. Chang, W. Fann, J.-H. Hsu, K.-M. Chen, and Y.-C. Yull, “Two-photon excited fluorescence of nitrogen-vacancy centers in proton-irradiated type Ib diamond,” J. Phys. Chem. A111, 9379–9386 (2007).
[CrossRef] [PubMed]

Hecht, B.

L. Fleury, J. Segura, G. Zumofen, B. Hecht, and U. Wild, “Nonclassical photon statistics in single-molecule fluorescence at room temperature,” Phys. Rev. Lett.84, 1148–1151 (2000).
[CrossRef] [PubMed]

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, Cambridge, UK, 2006).
[CrossRef]

Hellen, E. H.

Hemmer, P.

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

Henkel, C.

Hepp, C.

E. Neu, C. Arend, E. Gross, F. Guldner, C. Hepp, D. Steinmetz, E. Zscherpel, S. Ghodbane, H. Sternschulte, D. Steinmüller-Nethl, Y. Liang, A. Krueger, and C. Becher, “Narrowband fluorescent nanodiamonds produced from chemical vapor deposition films,” Appl. Phys. Lett.98, 243107 (2011).
[CrossRef]

Hsu, J.-H.

T.-L. Wee, Y.-K. Tzeng, C.-C. Han, H.-C. Chang, W. Fann, J.-H. Hsu, K.-M. Chen, and Y.-C. Yull, “Two-photon excited fluorescence of nitrogen-vacancy centers in proton-irradiated type Ib diamond,” J. Phys. Chem. A111, 9379–9386 (2007).
[CrossRef] [PubMed]

Hugonin, J.

J. Greffet, J. Hugonin, M. Besbes, N. Lai, F. Treussart, and J. Roch, “Diamond particles as nanoantennas for nitrogen-vacancy color centers,” Arxiv preprint arXiv:1107.0502 (2011).

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K. Iakoubovskii and G. J. Adriaenssens, “Luminescence excitation spectra in diamond,” Phys. Rev. B61, 10174– 10182 (2000).
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P. Siyushev, V. Jacques, I. Aharonovich, F. Kaiser, T. Müller, L. Lombez, M. Atatüre, S. Castelletto, S. Prawer, F. Jelezko, and J. Wrachtrup, “Low-temperature optical characterization of a near-infrared single-photon emitter in nanodiamonds,” New J. Phys.11, 113029 (2009).
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E. Wu, V. Jacques, H. Zeng, P. Grangier, F. Treussart, and J.-F. Roch, “Narrow-band single-photon emission in the near infrared for quantum key distribution,” Opt. Express14, 1296–1303 (2006).
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P. Siyushev, V. Jacques, I. Aharonovich, F. Kaiser, T. Müller, L. Lombez, M. Atatüre, S. Castelletto, S. Prawer, F. Jelezko, and J. Wrachtrup, “Low-temperature optical characterization of a near-infrared single-photon emitter in nanodiamonds,” New J. Phys.11, 113029 (2009).
[CrossRef]

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

Jones, R.

R. Ulbricht, S. T. van der Post, J. P. Goss, P. R. Briddon, R. Jones, R. U. A. Khan, and M. Bonn, “Single substitutional nitrogen defects revealed as electron acceptor states in diamond using ultrafast spectroscopy,” Phys. Rev. B84, 165202 (2011).
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S. Kitson, P. Jonsson, J. Rarity, and P. Tapster, “Intensity fluctuation spectroscopy of small numbers of dye molecules in a microcavity,” Phys. Rev. A58, 620–627 (1998).
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Kaiser, F.

P. Siyushev, V. Jacques, I. Aharonovich, F. Kaiser, T. Müller, L. Lombez, M. Atatüre, S. Castelletto, S. Prawer, F. Jelezko, and J. Wrachtrup, “Low-temperature optical characterization of a near-infrared single-photon emitter in nanodiamonds,” New J. Phys.11, 113029 (2009).
[CrossRef]

Khan, R. U. A.

R. Ulbricht, S. T. van der Post, J. P. Goss, P. R. Briddon, R. Jones, R. U. A. Khan, and M. Bonn, “Single substitutional nitrogen defects revealed as electron acceptor states in diamond using ultrafast spectroscopy,” Phys. Rev. B84, 165202 (2011).
[CrossRef]

U. F. S. D’Haenens-Johansson, A. M. Edmonds, B. L. Green, M. E. Newton, G. Davies, P. M. Martineau, R. U. A. Khan, and D. J. Twitchen, “Optical properties of the neutral silicon split-vacancy center in diamond,” Phys. Rev. B84, 245208 (2011).
[CrossRef]

Kitson, S.

S. Kitson, P. Jonsson, J. Rarity, and P. Tapster, “Intensity fluctuation spectroscopy of small numbers of dye molecules in a microcavity,” Phys. Rev. A58, 620–627 (1998).
[CrossRef]

Klick, C.

D. Dexter, C. Klick, and G. Russell, “Criterion for the occurrence of luminescence,” Phys. Rev.100, 603–605 (1955).
[CrossRef]

Kolesov, R.

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

Krueger, A.

E. Neu, C. Arend, E. Gross, F. Guldner, C. Hepp, D. Steinmetz, E. Zscherpel, S. Ghodbane, H. Sternschulte, D. Steinmüller-Nethl, Y. Liang, A. Krueger, and C. Becher, “Narrowband fluorescent nanodiamonds produced from chemical vapor deposition films,” Appl. Phys. Lett.98, 243107 (2011).
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Kurtsiefer, C.

C. Wang, C. Kurtsiefer, H. Weinfurter, and B. Burchard, “Single photon emission from SiV centres in diamond produced by ion implantation.” J. Phys. B: At. Mol. Opt. Phys.39, 37–41 (2006).
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Lai, N.

J. Greffet, J. Hugonin, M. Besbes, N. Lai, F. Treussart, and J. Roch, “Diamond particles as nanoantennas for nitrogen-vacancy color centers,” Arxiv preprint arXiv:1107.0502 (2011).

Liang, Y.

E. Neu, C. Arend, E. Gross, F. Guldner, C. Hepp, D. Steinmetz, E. Zscherpel, S. Ghodbane, H. Sternschulte, D. Steinmüller-Nethl, Y. Liang, A. Krueger, and C. Becher, “Narrowband fluorescent nanodiamonds produced from chemical vapor deposition films,” Appl. Phys. Lett.98, 243107 (2011).
[CrossRef]

Liu, C.-H.

A. V. Turukhin, C.-H. Liu, A. A. Gorokhovsky, R. R. Alfano, and W. Phillips, “Picosecond photoluminescence decay of Si-doped chemical-vapor-deposited diamond films,” Phys. Rev. B54, 16448–16451 (1996).
[CrossRef]

Lombez, L.

P. Siyushev, V. Jacques, I. Aharonovich, F. Kaiser, T. Müller, L. Lombez, M. Atatüre, S. Castelletto, S. Prawer, F. Jelezko, and J. Wrachtrup, “Low-temperature optical characterization of a near-infrared single-photon emitter in nanodiamonds,” New J. Phys.11, 113029 (2009).
[CrossRef]

Lounis, B.

B. Lounis and M. Orrit, “Single photon sources,” Rep. Prog. Phys.68, 1129–1179 (2005).
[CrossRef]

Martineau, P. M.

U. F. S. D’Haenens-Johansson, A. M. Edmonds, B. L. Green, M. E. Newton, G. Davies, P. M. Martineau, R. U. A. Khan, and D. J. Twitchen, “Optical properties of the neutral silicon split-vacancy center in diamond,” Phys. Rev. B84, 245208 (2011).
[CrossRef]

McClure, M.

L. Bergman, M. McClure, J. Glass, and R. Nemanich, “The origin of the broadband luminescence and the effect of nitrogen doping on the optical properties of diamond films,” J. Appl. Phys.76, 3020–3027 (1994).
[CrossRef]

Medvedev, A.

S. Grudinkin, N. Feoktistov, A. Medvedev, K. Bogdanov, A. Baranov, A. Vul, and V. Golubev, “Luminescent isolated diamond particles with controllably embedded silicon-vacancy colour centres,” J. Phys. D: Appl. Phys.45, 062001 (2012).
[CrossRef]

Mora, A.

A. Mora, J. Steeds, and J. Butler, “Relationship between grain boundaries and broad luminescence peaks in CVD diamond films,” Diam. Relat. Mater.12, 310–317 (2003).
[CrossRef]

Müller, T.

P. Siyushev, V. Jacques, I. Aharonovich, F. Kaiser, T. Müller, L. Lombez, M. Atatüre, S. Castelletto, S. Prawer, F. Jelezko, and J. Wrachtrup, “Low-temperature optical characterization of a near-infrared single-photon emitter in nanodiamonds,” New J. Phys.11, 113029 (2009).
[CrossRef]

Naidoo, N.

C. Bradac, T. Gaebel, N. Naidoo, M. J. Sellars, J. Twamley, L. J. Brown, A. S. Barnard, T. Plakhotnik, A. V. Zvyagin, and J. R. Rabeau, “Observation and control of blinking nitrogen-vacancy centres in discrete nanodiamonds,” Nature Nanotech.5, 345–349 (2010).
[CrossRef]

Naydenov, B.

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

Nemanich, R.

L. Bergman, M. McClure, J. Glass, and R. Nemanich, “The origin of the broadband luminescence and the effect of nitrogen doping on the optical properties of diamond films,” J. Appl. Phys.76, 3020–3027 (1994).
[CrossRef]

Neu, E.

E. Neu, R. Albrecht, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “Electronic transitions of single silicon vacancy centers in the near-infrared spectral region,” Phys. Rev. B85, 245207 (2012).
[CrossRef]

E. Neu, D. Steinmetz, J. Riedrich-Möller, S. Gsell, M. Fischer, M. Schreck, and C. Becher, “Single photon emission from silicon-vacancy colour centres in chemical vapour deposition nano-diamonds on iridium,” New J. Phys.13, 025012 (2011).
[CrossRef]

E. Neu, C. Arend, E. Gross, F. Guldner, C. Hepp, D. Steinmetz, E. Zscherpel, S. Ghodbane, H. Sternschulte, D. Steinmüller-Nethl, Y. Liang, A. Krueger, and C. Becher, “Narrowband fluorescent nanodiamonds produced from chemical vapor deposition films,” Appl. Phys. Lett.98, 243107 (2011).
[CrossRef]

E. Neu, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “Fluorescence and polarization spectroscopy of single silicon vacancy centers in heteroepitaxial nanodiamonds on iridium,” Phys. Rev. B84, 205211 (2011).
[CrossRef]

Newton, M. E.

U. F. S. D’Haenens-Johansson, A. M. Edmonds, B. L. Green, M. E. Newton, G. Davies, P. M. Martineau, R. U. A. Khan, and D. J. Twitchen, “Optical properties of the neutral silicon split-vacancy center in diamond,” Phys. Rev. B84, 245208 (2011).
[CrossRef]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, Cambridge, UK, 2006).
[CrossRef]

Orrit, M.

B. Lounis and M. Orrit, “Single photon sources,” Rep. Prog. Phys.68, 1129–1179 (2005).
[CrossRef]

Osad’ko, I.

I. Osad’ko, “Determination of electron-phonon coupling from structured optical spectra of impurity centers,” Sov. Phys. Usp.22, 311–329 (1979).
[CrossRef]

Phillips, W.

A. V. Turukhin, C.-H. Liu, A. A. Gorokhovsky, R. R. Alfano, and W. Phillips, “Picosecond photoluminescence decay of Si-doped chemical-vapor-deposited diamond films,” Phys. Rev. B54, 16448–16451 (1996).
[CrossRef]

Plakhotnik, T.

R. Chapman and T. Plakhotnik, “Quantitative luminescence microscopy on nitrogen-vacancy centres in diamond: Saturation effects under pulsed excitation,” Chem. Phys. Lett.507, 190–194 (2011).
[CrossRef]

C. Bradac, T. Gaebel, N. Naidoo, M. J. Sellars, J. Twamley, L. J. Brown, A. S. Barnard, T. Plakhotnik, A. V. Zvyagin, and J. R. Rabeau, “Observation and control of blinking nitrogen-vacancy centres in discrete nanodiamonds,” Nature Nanotech.5, 345–349 (2010).
[CrossRef]

B. Smith, D. Gruber, and T. Plakhotnik, “The effects of surface oxidation on luminescence of nano diamonds,” Diam. Relat. Mater.19, 314–318 (2010).
[CrossRef]

Poizat, J.

Prawer, S.

I. Aharonovich, S. Castelletto, D. Simpson, C. Su, A. Greentree, and S. Prawer, “Diamond-based single-photon emitters,” Rep. Prog. Phys.74, 076501 (2011).
[CrossRef]

I. Aharonovich, S. Castelletto, D. A. Simpson, A. D. Greentree, and S. Prawer, “Photophysics of chromium-related diamond single-photon emitters,” Phys. Rev. A81, 043813 (2010).
[CrossRef]

P. Siyushev, V. Jacques, I. Aharonovich, F. Kaiser, T. Müller, L. Lombez, M. Atatüre, S. Castelletto, S. Prawer, F. Jelezko, and J. Wrachtrup, “Low-temperature optical characterization of a near-infrared single-photon emitter in nanodiamonds,” New J. Phys.11, 113029 (2009).
[CrossRef]

Prock, A.

R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys.37, 1–65 (1978).
[CrossRef]

Rabeau, J. R.

C. Bradac, T. Gaebel, N. Naidoo, M. J. Sellars, J. Twamley, L. J. Brown, A. S. Barnard, T. Plakhotnik, A. V. Zvyagin, and J. R. Rabeau, “Observation and control of blinking nitrogen-vacancy centres in discrete nanodiamonds,” Nature Nanotech.5, 345–349 (2010).
[CrossRef]

Rarity, J.

S. Kitson, P. Jonsson, J. Rarity, and P. Tapster, “Intensity fluctuation spectroscopy of small numbers of dye molecules in a microcavity,” Phys. Rev. A58, 620–627 (1998).
[CrossRef]

Reuter, R.

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

Riedrich-Möller, J.

E. Neu, D. Steinmetz, J. Riedrich-Möller, S. Gsell, M. Fischer, M. Schreck, and C. Becher, “Single photon emission from silicon-vacancy colour centres in chemical vapour deposition nano-diamonds on iridium,” New J. Phys.13, 025012 (2011).
[CrossRef]

Roch, J.

J. Greffet, J. Hugonin, M. Besbes, N. Lai, F. Treussart, and J. Roch, “Diamond particles as nanoantennas for nitrogen-vacancy color centers,” Arxiv preprint arXiv:1107.0502 (2011).

Roch, J.-F.

Rogers, L.

L. Rogers, “How far into the infrared can a colour centre in diamond emit?” Physics Procedia3, 1557–1561 (2010). 10th International Meeting On Hole Burning, Single Molecule, And Related Spectroscopies, 2009, Palm Cove, Australia.
[CrossRef]

Rogobete, L.

Russell, G.

D. Dexter, C. Klick, and G. Russell, “Criterion for the occurrence of luminescence,” Phys. Rev.100, 603–605 (1955).
[CrossRef]

Sandoghdar, V.

X.-W. Chen, M. Agio, and V. Sandoghdar, “Metallo-dielectric hybrid antennas for ultrastrong enhancement of spontaneous emission,” Phys. Rev. Lett.108, 233001 (2012).
[CrossRef]

L. Rogobete, H. Schniepp, V. Sandoghdar, and C. Henkel, “Spontaneous emission in nanoscopic dielectric particles,” Opt. Lett.28, 1736–1738 (2003).
[CrossRef] [PubMed]

Schniepp, H.

Schreck, M.

E. Neu, R. Albrecht, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “Electronic transitions of single silicon vacancy centers in the near-infrared spectral region,” Phys. Rev. B85, 245207 (2012).
[CrossRef]

E. Neu, D. Steinmetz, J. Riedrich-Möller, S. Gsell, M. Fischer, M. Schreck, and C. Becher, “Single photon emission from silicon-vacancy colour centres in chemical vapour deposition nano-diamonds on iridium,” New J. Phys.13, 025012 (2011).
[CrossRef]

E. Neu, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “Fluorescence and polarization spectroscopy of single silicon vacancy centers in heteroepitaxial nanodiamonds on iridium,” Phys. Rev. B84, 205211 (2011).
[CrossRef]

Segura, J.

L. Fleury, J. Segura, G. Zumofen, B. Hecht, and U. Wild, “Nonclassical photon statistics in single-molecule fluorescence at room temperature,” Phys. Rev. Lett.84, 1148–1151 (2000).
[CrossRef] [PubMed]

Sellars, M. J.

C. Bradac, T. Gaebel, N. Naidoo, M. J. Sellars, J. Twamley, L. J. Brown, A. S. Barnard, T. Plakhotnik, A. V. Zvyagin, and J. R. Rabeau, “Observation and control of blinking nitrogen-vacancy centres in discrete nanodiamonds,” Nature Nanotech.5, 345–349 (2010).
[CrossRef]

Sennour, M.

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

Silbey, R.

R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys.37, 1–65 (1978).
[CrossRef]

Simpson, D.

I. Aharonovich, S. Castelletto, D. Simpson, C. Su, A. Greentree, and S. Prawer, “Diamond-based single-photon emitters,” Rep. Prog. Phys.74, 076501 (2011).
[CrossRef]

Simpson, D. A.

I. Aharonovich, S. Castelletto, D. A. Simpson, A. D. Greentree, and S. Prawer, “Photophysics of chromium-related diamond single-photon emitters,” Phys. Rev. A81, 043813 (2010).
[CrossRef]

Siyushev, P.

P. Siyushev, V. Jacques, I. Aharonovich, F. Kaiser, T. Müller, L. Lombez, M. Atatüre, S. Castelletto, S. Prawer, F. Jelezko, and J. Wrachtrup, “Low-temperature optical characterization of a near-infrared single-photon emitter in nanodiamonds,” New J. Phys.11, 113029 (2009).
[CrossRef]

Smith, B.

B. Smith, D. Gruber, and T. Plakhotnik, “The effects of surface oxidation on luminescence of nano diamonds,” Diam. Relat. Mater.19, 314–318 (2010).
[CrossRef]

Steeds, J.

A. Mora, J. Steeds, and J. Butler, “Relationship between grain boundaries and broad luminescence peaks in CVD diamond films,” Diam. Relat. Mater.12, 310–317 (2003).
[CrossRef]

Steinmetz, D.

E. Neu, D. Steinmetz, J. Riedrich-Möller, S. Gsell, M. Fischer, M. Schreck, and C. Becher, “Single photon emission from silicon-vacancy colour centres in chemical vapour deposition nano-diamonds on iridium,” New J. Phys.13, 025012 (2011).
[CrossRef]

E. Neu, C. Arend, E. Gross, F. Guldner, C. Hepp, D. Steinmetz, E. Zscherpel, S. Ghodbane, H. Sternschulte, D. Steinmüller-Nethl, Y. Liang, A. Krueger, and C. Becher, “Narrowband fluorescent nanodiamonds produced from chemical vapor deposition films,” Appl. Phys. Lett.98, 243107 (2011).
[CrossRef]

Steinmüller-Nethl, D.

E. Neu, C. Arend, E. Gross, F. Guldner, C. Hepp, D. Steinmetz, E. Zscherpel, S. Ghodbane, H. Sternschulte, D. Steinmüller-Nethl, Y. Liang, A. Krueger, and C. Becher, “Narrowband fluorescent nanodiamonds produced from chemical vapor deposition films,” Appl. Phys. Lett.98, 243107 (2011).
[CrossRef]

Sternschulte, H.

E. Neu, C. Arend, E. Gross, F. Guldner, C. Hepp, D. Steinmetz, E. Zscherpel, S. Ghodbane, H. Sternschulte, D. Steinmüller-Nethl, Y. Liang, A. Krueger, and C. Becher, “Narrowband fluorescent nanodiamonds produced from chemical vapor deposition films,” Appl. Phys. Lett.98, 243107 (2011).
[CrossRef]

Su, C.

I. Aharonovich, S. Castelletto, D. Simpson, C. Su, A. Greentree, and S. Prawer, “Diamond-based single-photon emitters,” Rep. Prog. Phys.74, 076501 (2011).
[CrossRef]

Tapster, P.

S. Kitson, P. Jonsson, J. Rarity, and P. Tapster, “Intensity fluctuation spectroscopy of small numbers of dye molecules in a microcavity,” Phys. Rev. A58, 620–627 (1998).
[CrossRef]

Thorel, A.

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

Tisler, J.

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

Treussart, F.

J. Greffet, J. Hugonin, M. Besbes, N. Lai, F. Treussart, and J. Roch, “Diamond particles as nanoantennas for nitrogen-vacancy color centers,” Arxiv preprint arXiv:1107.0502 (2011).

E. Wu, V. Jacques, H. Zeng, P. Grangier, F. Treussart, and J.-F. Roch, “Narrow-band single-photon emission in the near infrared for quantum key distribution,” Opt. Express14, 1296–1303 (2006).
[CrossRef] [PubMed]

Turukhin, A. V.

A. V. Turukhin, C.-H. Liu, A. A. Gorokhovsky, R. R. Alfano, and W. Phillips, “Picosecond photoluminescence decay of Si-doped chemical-vapor-deposited diamond films,” Phys. Rev. B54, 16448–16451 (1996).
[CrossRef]

Twamley, J.

C. Bradac, T. Gaebel, N. Naidoo, M. J. Sellars, J. Twamley, L. J. Brown, A. S. Barnard, T. Plakhotnik, A. V. Zvyagin, and J. R. Rabeau, “Observation and control of blinking nitrogen-vacancy centres in discrete nanodiamonds,” Nature Nanotech.5, 345–349 (2010).
[CrossRef]

Twitchen, D. J.

U. F. S. D’Haenens-Johansson, A. M. Edmonds, B. L. Green, M. E. Newton, G. Davies, P. M. Martineau, R. U. A. Khan, and D. J. Twitchen, “Optical properties of the neutral silicon split-vacancy center in diamond,” Phys. Rev. B84, 245208 (2011).
[CrossRef]

Tzeng, Y.-K.

T.-L. Wee, Y.-K. Tzeng, C.-C. Han, H.-C. Chang, W. Fann, J.-H. Hsu, K.-M. Chen, and Y.-C. Yull, “Two-photon excited fluorescence of nitrogen-vacancy centers in proton-irradiated type Ib diamond,” J. Phys. Chem. A111, 9379–9386 (2007).
[CrossRef] [PubMed]

Ulbricht, R.

R. Ulbricht, S. T. van der Post, J. P. Goss, P. R. Briddon, R. Jones, R. U. A. Khan, and M. Bonn, “Single substitutional nitrogen defects revealed as electron acceptor states in diamond using ultrafast spectroscopy,” Phys. Rev. B84, 165202 (2011).
[CrossRef]

van der Post, S. T.

R. Ulbricht, S. T. van der Post, J. P. Goss, P. R. Briddon, R. Jones, R. U. A. Khan, and M. Bonn, “Single substitutional nitrogen defects revealed as electron acceptor states in diamond using ultrafast spectroscopy,” Phys. Rev. B84, 165202 (2011).
[CrossRef]

Vul, A.

S. Grudinkin, N. Feoktistov, A. Medvedev, K. Bogdanov, A. Baranov, A. Vul, and V. Golubev, “Luminescent isolated diamond particles with controllably embedded silicon-vacancy colour centres,” J. Phys. D: Appl. Phys.45, 062001 (2012).
[CrossRef]

Wang, C.

C. Wang, C. Kurtsiefer, H. Weinfurter, and B. Burchard, “Single photon emission from SiV centres in diamond produced by ion implantation.” J. Phys. B: At. Mol. Opt. Phys.39, 37–41 (2006).
[CrossRef]

C. Wang, “A solid-state single photon source based on color centers in diamond,” Ph.D. thesis, Technische Universität München (2007).

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. Yull, “Two-photon excited fluorescence of nitrogen-vacancy centers in proton-irradiated type Ib diamond,” J. Phys. Chem. A111, 9379–9386 (2007).
[CrossRef] [PubMed]

Weinfurter, H.

C. Wang, C. Kurtsiefer, H. Weinfurter, and B. Burchard, “Single photon emission from SiV centres in diamond produced by ion implantation.” J. Phys. B: At. Mol. Opt. Phys.39, 37–41 (2006).
[CrossRef]

Wild, U.

L. Fleury, J. Segura, G. Zumofen, B. Hecht, and U. Wild, “Nonclassical photon statistics in single-molecule fluorescence at room temperature,” Phys. Rev. Lett.84, 1148–1151 (2000).
[CrossRef] [PubMed]

Wrachtrup, J.

P. Siyushev, V. Jacques, I. Aharonovich, F. Kaiser, T. Müller, L. Lombez, M. Atatüre, S. Castelletto, S. Prawer, F. Jelezko, and J. Wrachtrup, “Low-temperature optical characterization of a near-infrared single-photon emitter in nanodiamonds,” New J. Phys.11, 113029 (2009).
[CrossRef]

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

Wu, E.

Yull, 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. Yull, “Two-photon excited fluorescence of nitrogen-vacancy centers in proton-irradiated type Ib diamond,” J. Phys. Chem. A111, 9379–9386 (2007).
[CrossRef] [PubMed]

Zeng, H.

Zscherpel, E.

E. Neu, C. Arend, E. Gross, F. Guldner, C. Hepp, D. Steinmetz, E. Zscherpel, S. Ghodbane, H. Sternschulte, D. Steinmüller-Nethl, Y. Liang, A. Krueger, and C. Becher, “Narrowband fluorescent nanodiamonds produced from chemical vapor deposition films,” Appl. Phys. Lett.98, 243107 (2011).
[CrossRef]

Zumofen, G.

L. Fleury, J. Segura, G. Zumofen, B. Hecht, and U. Wild, “Nonclassical photon statistics in single-molecule fluorescence at room temperature,” Phys. Rev. Lett.84, 1148–1151 (2000).
[CrossRef] [PubMed]

Zvyagin, A. V.

C. Bradac, T. Gaebel, N. Naidoo, M. J. Sellars, J. Twamley, L. J. Brown, A. S. Barnard, T. Plakhotnik, A. V. Zvyagin, and J. R. Rabeau, “Observation and control of blinking nitrogen-vacancy centres in discrete nanodiamonds,” Nature Nanotech.5, 345–349 (2010).
[CrossRef]

ACS Nano (1)

J. Tisler, G. Balasubramanian, B. Naydenov, R. Kolesov, B. Grotz, R. Reuter, J. Boudou, P. Curmi, M. Sennour, A. Thorel, M. Boersch, K. Aulenbacher, R. Erdmann, P. Hemmer, F. Jelezko, and J. Wrachtrup, “Fluorescence and Spin Properties of Defects in Single Digit Nanodiamonds,” ACS Nano3, 1959–1965 (2009).
[CrossRef] [PubMed]

Adv. Chem. Phys. (1)

R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys.37, 1–65 (1978).
[CrossRef]

Appl. Phys. Lett. (1)

E. Neu, C. Arend, E. Gross, F. Guldner, C. Hepp, D. Steinmetz, E. Zscherpel, S. Ghodbane, H. Sternschulte, D. Steinmüller-Nethl, Y. Liang, A. Krueger, and C. Becher, “Narrowband fluorescent nanodiamonds produced from chemical vapor deposition films,” Appl. Phys. Lett.98, 243107 (2011).
[CrossRef]

Chem. Phys. Lett. (1)

R. Chapman and T. Plakhotnik, “Quantitative luminescence microscopy on nitrogen-vacancy centres in diamond: Saturation effects under pulsed excitation,” Chem. Phys. Lett.507, 190–194 (2011).
[CrossRef]

Diam. Relat. Mater. (2)

B. Smith, D. Gruber, and T. Plakhotnik, “The effects of surface oxidation on luminescence of nano diamonds,” Diam. Relat. Mater.19, 314–318 (2010).
[CrossRef]

A. Mora, J. Steeds, and J. Butler, “Relationship between grain boundaries and broad luminescence peaks in CVD diamond films,” Diam. Relat. Mater.12, 310–317 (2003).
[CrossRef]

J. Appl. Phys. (1)

L. Bergman, M. McClure, J. Glass, and R. Nemanich, “The origin of the broadband luminescence and the effect of nitrogen doping on the optical properties of diamond films,” J. Appl. Phys.76, 3020–3027 (1994).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. B: At. Mol. Opt. Phys. (1)

C. Wang, C. Kurtsiefer, H. Weinfurter, and B. Burchard, “Single photon emission from SiV centres in diamond produced by ion implantation.” J. Phys. B: At. Mol. Opt. Phys.39, 37–41 (2006).
[CrossRef]

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. Yull, “Two-photon excited fluorescence of nitrogen-vacancy centers in proton-irradiated type Ib diamond,” J. Phys. Chem. A111, 9379–9386 (2007).
[CrossRef] [PubMed]

J. Phys. D: Appl. Phys. (1)

S. Grudinkin, N. Feoktistov, A. Medvedev, K. Bogdanov, A. Baranov, A. Vul, and V. Golubev, “Luminescent isolated diamond particles with controllably embedded silicon-vacancy colour centres,” J. Phys. D: Appl. Phys.45, 062001 (2012).
[CrossRef]

Nature Nanotech. (1)

C. Bradac, T. Gaebel, N. Naidoo, M. J. Sellars, J. Twamley, L. J. Brown, A. S. Barnard, T. Plakhotnik, A. V. Zvyagin, and J. R. Rabeau, “Observation and control of blinking nitrogen-vacancy centres in discrete nanodiamonds,” Nature Nanotech.5, 345–349 (2010).
[CrossRef]

New J. Phys. (2)

P. Siyushev, V. Jacques, I. Aharonovich, F. Kaiser, T. Müller, L. Lombez, M. Atatüre, S. Castelletto, S. Prawer, F. Jelezko, and J. Wrachtrup, “Low-temperature optical characterization of a near-infrared single-photon emitter in nanodiamonds,” New J. Phys.11, 113029 (2009).
[CrossRef]

E. Neu, D. Steinmetz, J. Riedrich-Möller, S. Gsell, M. Fischer, M. Schreck, and C. Becher, “Single photon emission from silicon-vacancy colour centres in chemical vapour deposition nano-diamonds on iridium,” New J. Phys.13, 025012 (2011).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. (1)

D. Dexter, C. Klick, and G. Russell, “Criterion for the occurrence of luminescence,” Phys. Rev.100, 603–605 (1955).
[CrossRef]

Phys. Rev. A (2)

I. Aharonovich, S. Castelletto, D. A. Simpson, A. D. Greentree, and S. Prawer, “Photophysics of chromium-related diamond single-photon emitters,” Phys. Rev. A81, 043813 (2010).
[CrossRef]

S. Kitson, P. Jonsson, J. Rarity, and P. Tapster, “Intensity fluctuation spectroscopy of small numbers of dye molecules in a microcavity,” Phys. Rev. A58, 620–627 (1998).
[CrossRef]

Phys. Rev. B (6)

U. F. S. D’Haenens-Johansson, A. M. Edmonds, B. L. Green, M. E. Newton, G. Davies, P. M. Martineau, R. U. A. Khan, and D. J. Twitchen, “Optical properties of the neutral silicon split-vacancy center in diamond,” Phys. Rev. B84, 245208 (2011).
[CrossRef]

R. Ulbricht, S. T. van der Post, J. P. Goss, P. R. Briddon, R. Jones, R. U. A. Khan, and M. Bonn, “Single substitutional nitrogen defects revealed as electron acceptor states in diamond using ultrafast spectroscopy,” Phys. Rev. B84, 165202 (2011).
[CrossRef]

E. Neu, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “Fluorescence and polarization spectroscopy of single silicon vacancy centers in heteroepitaxial nanodiamonds on iridium,” Phys. Rev. B84, 205211 (2011).
[CrossRef]

K. Iakoubovskii and G. J. Adriaenssens, “Luminescence excitation spectra in diamond,” Phys. Rev. B61, 10174– 10182 (2000).
[CrossRef]

A. V. Turukhin, C.-H. Liu, A. A. Gorokhovsky, R. R. Alfano, and W. Phillips, “Picosecond photoluminescence decay of Si-doped chemical-vapor-deposited diamond films,” Phys. Rev. B54, 16448–16451 (1996).
[CrossRef]

E. Neu, R. Albrecht, M. Fischer, S. Gsell, M. Schreck, and C. Becher, “Electronic transitions of single silicon vacancy centers in the near-infrared spectral region,” Phys. Rev. B85, 245207 (2012).
[CrossRef]

Phys. Rev. Lett. (2)

L. Fleury, J. Segura, G. Zumofen, B. Hecht, and U. Wild, “Nonclassical photon statistics in single-molecule fluorescence at room temperature,” Phys. Rev. Lett.84, 1148–1151 (2000).
[CrossRef] [PubMed]

X.-W. Chen, M. Agio, and V. Sandoghdar, “Metallo-dielectric hybrid antennas for ultrastrong enhancement of spontaneous emission,” Phys. Rev. Lett.108, 233001 (2012).
[CrossRef]

Physics Procedia (1)

L. Rogers, “How far into the infrared can a colour centre in diamond emit?” Physics Procedia3, 1557–1561 (2010). 10th International Meeting On Hole Burning, Single Molecule, And Related Spectroscopies, 2009, Palm Cove, Australia.
[CrossRef]

Rep. Prog. Phys. (2)

B. Lounis and M. Orrit, “Single photon sources,” Rep. Prog. Phys.68, 1129–1179 (2005).
[CrossRef]

I. Aharonovich, S. Castelletto, D. Simpson, C. Su, A. Greentree, and S. Prawer, “Diamond-based single-photon emitters,” Rep. Prog. Phys.74, 076501 (2011).
[CrossRef]

Sov. Phys. Usp. (1)

I. Osad’ko, “Determination of electron-phonon coupling from structured optical spectra of impurity centers,” Sov. Phys. Usp.22, 311–329 (1979).
[CrossRef]

Other (4)

J. Greffet, J. Hugonin, M. Besbes, N. Lai, F. Treussart, and J. Roch, “Diamond particles as nanoantennas for nitrogen-vacancy color centers,” Arxiv preprint arXiv:1107.0502 (2011).

C. Wang, “A solid-state single photon source based on color centers in diamond,” Ph.D. thesis, Technische Universität München (2007).

E. D. Palik and G. Ghosh, eds., Handbook of Optical Constants of Solids (Academic Press, New York, 1998).

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, Cambridge, UK, 2006).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Histograms of (a) maximum obtainable photon rates at saturation I (b) saturation powers Psat. Histograms take into account emitters from randomly oriented NDs and (001) NIs. NDs: excitation at 671 nm. NIs: excitation at 695–696 nm.

Fig. 2
Fig. 2

g(2) functions for varying excitation power. Consecutive g(2) functions have been shifted for clarity (lowest excitation power g(2) function in each graph not shifted, higher (lower) excitation power g(2) functions shifted by 1 (0.5) each). (a) emitter ND3 (lower graph 0.03,0.11,0.15,0.49Psat, upper graph 0.6,0.8,1.2,1.7,3.5,5.8Psat). (b) emitter ND1, g(2) includes background correction (lower graph 0.08,0.17,0.28,0.47Psat, upper graph 1.5,3.3,6.3,11.9,23.5,32.7Psat). (c) emitter NI1(lower graph 0.01,0.02,0.03,0.07Psat, upper graph 0.2,0.3,0.6,1.1,1.4Psat).

Fig. 3
Fig. 3

Schematic representation of the extended three level model employed to explain the population dynamics of single SiV centers, explanation see text.

Fig. 4
Fig. 4

Intensity dependence of the parameters a, τ1 and τ2: (a) emitter ND1, (b) ND2, (c) ND3, (d) ND4 (exc. 705 nm), (e) NI1, (f) NI7. Blue solid lines represent fitting curves according to the intensity dependent de-shelving model. Red dashed lines represent the excitation power dependence from the model with constant rates.

Fig. 5
Fig. 5

Histograms of rate coefficients k21, k23, k31 and d obtained from the model of saturating de-shelving. The histograms take into account emitters from NIs as well as randomly oriented NDs.

Fig. 6
Fig. 6

Fluorescence timetraces of single SiV centers (a) SiV center with fully photostable emission (emitter ND4, excited at 695 nm). (b) Emitter with destabilization at higher excitation power and permanent photobleaching (emitter NI1). (c) Emitter with longer time intervals of fluorescence intermittence (emitter NI6). The count rate of each emitter has been calculated in time windows of 100 ms for the lowest excitation power (50 ms for higher excitation powers).

Fig. 7
Fig. 7

Emissions characteristics of a point-like oscillating dipole in vacuum near an Ir surface for orientation parallel (blue solid curves) and perpendicular (red dashed curves) to the interface. The emission wavelength is 740 nm and the intrinsic quantum yield is 5%. (a) Effective quantum yield as a function of distance from the Ir surface. (b) Radiation pattern for a dipole located 80 nm above the Ir surface. The thin curves refer to a dipole in free space. (c) Collection efficiency as a function of distance for a microscope objective with NA=0.8.

Tables (2)

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Table 1 Rate coefficients deduced from the limiting values of a, τ1 and τ2 using the three level model including intensity dependent de-shelving and parameters c and σ obtained from the fits. For comparison also Psat is given.

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Table 2 Rate coefficients ki j, maximum excited state population N 2 (P → ∞), maximum photon rate I and quantum efficiency ηqe for individual SiV centers. To calculate the quantum efficiency, we use a collection efficiency of 78% (28%) for a parallel (perpendicular) dipole, corresponding to an emitter distance of 75 nm.

Equations (15)

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I = I P P + P sat + c backgr P .
g ( 2 ) ( τ ) = 1 ( 1 + a ) e | τ | / τ 1 + a e | τ | / τ 2
τ 1 , 2 = 2 / ( A ± A 2 4 B )
A = k 12 + k 21 + k 23 + k 31
B = k 12 k 23 + k 12 k 31 + k 21 k 31 + k 23 k 31
a = 1 τ 2 k 31 k 31 ( τ 2 τ 1 )
g m ( 2 ) ( τ ) = 1 + ( g ( 2 ) ( τ ) 1 ) p e 2 .
σ = k 23 k 31 + k 21 k 31 ( k 23 + k 31 ) P sat .
k 31 = d P P + c + k 31 0 ,
k 31 0 = 1 τ 2 0
d = 1 τ 2 ( 1 + a ) 1 τ 2 0 a + 1
k 23 = 1 τ 2 k 31 0 d
k 21 = 1 τ 1 0 k 23
I = η det η qe k 21 N 2 ( P ) = η det η qe k 21 1 + k 23 k 31 0 + d
η = η 0 ( 1 η 0 ) γ 0 / γ r + η 0 / η a .

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