## Plasmonic resonators for enhanced diamond NV- center single photon sources |

Optics Express, Vol. 19, Issue 6, pp. 5268-5276 (2011)

http://dx.doi.org/10.1364/OE.19.005268

Acrobat PDF (1181 KB)

### Abstract

We propose a novel source of non-classical light consisting of plasmonic aperture with single-crystal diamond containing a single Nitrogen-Vacancy (NV) color center. Theoretical calculations of optimal structures show that these devices can simultaneously enhance optical pumping by a factor of 7, spontaneous emission rates by Fp ~50 (Purcell factor), and offer collection efficiencies up to 40%. These excitation and collection enhancements occur over a broad range of wavelengths (~30nm), and are independently tunable with device geometry, across the excitation (~530nm) and emission (~600-800nm) spectrum of the NV center. Implementing this system with top-down techniques in bulk diamond crystals will provide a scalable architecture for a myriad of diamond NV center applications.

© 2011 OSA

## Introduction

1. F. Jelezko and J. Wrachtrup, “Single defect centres in diamond: A review,” Phys. Status Solidi **203**(13), 3207–3225 (2006) (a). [CrossRef]

7. J. R. Maze, P. L. Stanwix, J. S. Hodges, S. Hong, J. M. Taylor, P. Cappellaro, L. Jiang, M. V. Dutt, E. Togan, A. S. Zibrov, A. Yacoby, R. L. Walsworth, and M. D. Lukin, “Nanoscale magnetic sensing with an individual electronic spin in diamond,” Nature **455**(7213), 644–648 (2008). [CrossRef] [PubMed]

1. F. Jelezko and J. Wrachtrup, “Single defect centres in diamond: A review,” Phys. Status Solidi **203**(13), 3207–3225 (2006) (a). [CrossRef]

3. G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. **8**(5), 383–387 (2009). [CrossRef] [PubMed]

8. F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. **92**(7), 076401 (2004). [CrossRef] [PubMed]

10. R. Hanson, V. V. Dobrovitski, A. E. Feiguin, O. Gywat, and D. D. Awschalom, “Coherent dynamics of a single spin interacting with an adjustable spin bath,” Science **320**(5874), 352–355 (2008). [CrossRef] [PubMed]

4. J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, “High-sensitivity diamond magnetometer with nanoscale resolution,” Nat. Phys. **4**(10), 810–816 (2008). [CrossRef]

11. T. M. Babinec, B. J. M. Hausmann, M. Khan, Y. Zhang, J. R. Maze, P. R. Hemmer, and M. Loncar, “A diamond nanowire single-photon source,” Nat. Nanotechnol. **5**(3), 195–199 (2010). [CrossRef] [PubMed]

13. S. Schietinger, M. Barth, T. Aichele, and O. Benson, “Plasmon-enhanced single photon emission from a nanoassembled metal-diamond hybrid structure at room temperature,” Nano Lett. **9**(4), 1694–1698 (2009). [CrossRef] [PubMed]

14. A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature **450**(7168), 402–406 (2007). [CrossRef] [PubMed]

17. B. Hausmann, M. Khan, Y. Zhang, T. Babinec, K. Martinick, M. McCutcheon, P. Hemmer, and M. Loncar, “Fabrication of diamond nanowires for quantum information processing applications,” Diamond Related Materials **19**(5-6), 621–629 (2010). [CrossRef]

## Results and discussion

18. L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics **50**(5), 4094–4106 (1994). [CrossRef] [PubMed]

19. H. Shin, P. Catrysse, and S. Fan, “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B **72**(8), 085436 (2005). [CrossRef]

*decreases*as the dimensions of the waveguide are decreased beyond a certain value, while the confinement of a plasmonic aperture

*increases*as the dimensions are decreased. The confinement properties of a circular dielectric waveguide and a circular plasmonic aperture can be compared with the effective mode area, which is defined in a similar way to the more familiar term effective mode volume [20

20. H. Iwase, D. Englund, and J. Vucković, “Analysis of the Purcell effect in photonic and plasmonic crystals with losses,” Opt. Express **18**(16), 16546–16560 (2010). [CrossRef] [PubMed]

21. Y. Gong and J. Vučković, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett. **90**(3), 033113 (2007). [CrossRef]

^{2}when the radius is 45 nm. We also show the mode area as a function of radius for a diamond nanowire for comparison. The mode for the diamond nanowire is significantly delocalized for radii smaller than 60 nm. Electric energy density for the plasmonic aperture is plotted in the inset of Fig. 2(a). Energy density is maximum in the center of the dielectric core and it is fairly uniform within the dielectric core. As a result, a radially polarized dipole is expected to have significant overlap with the aperture mode regardless of its radial position within the aperture. In addition, the effective mode index and propagation lengths are plotted as a function of aperture radius in Fig. 2(b) at a wavelength of 637 nm. The mode index is closer to 0 for smaller apertures and 2.4, index of the core material, for larger apertures. Propagation lengths are significantly short for very small apertures.

**ρ**, polarized dipoles throughout this paper. This polarization is appropriate for NV centers that can be found in [111] terminated diamond crystals. Permittivity values from Johnson&Christy [22] were used for silver and permittivity values from Palik [23] were used for diamond. SE rate enhancement factors were calculated by comparing the total power emitted from the dipole when it was placed in the plasmonic cavity to the total power emission when it is in infinitely thick bulk diamond. The equivalence of the classical calculation and quantum mechanical calculation has been investigated in refs [24

24. Y. Xu, R. K. Lee, and A. Yariv, “Quantum analysis and the classical analysis of spontaneous emission in a microcavity,” Phys. Rev. A **61**(3), 033807 (2000). [CrossRef]

25. Y. Xu, R. K. Lee, and A. Yariv, “Finite-difference time-domain analysis of spontaneous emission in a microdisk cavity,” Phys. Rev. A **61**(3), 33808 (2000). [CrossRef]

_{cavity}/Γ

_{free}, is equal to P

_{cavity}/P

_{free,}where P

_{cavity}and P

_{free}are the total power emitted from a classical dipole when it is in the cavity and in free space, respectively. In addition, the coupling rates into various decay channels can be calculated by using the ratio of the power coupled into the corresponding channels to the total emitted power. The total emitted power is calculated by integrating the Poynting's vector over a closed surface enclosing only the source. The power coupled into the various channels is calculated by using a similar procedure. For instance, the coupling rate into surface plasmons is calculated by integrating the surface parallel component of the Poynting's vector. We observe two resonances in the SE rate enhancement spectrum for this particular dipole position. The resonances are red shifted when the radius or the height of the aperture is increased. The response of the two resonances to a change in height is quite different. While the resonance at the shorter wavelengths red shifts almost linearly with an increase in height, the shift in the location of the second resonance is negligible for apertures taller than 250 nm. To explain this feature, we consider a simple Fabry-Perot model. The resonance condition is such that the total phase due to propagation and reflection is an integer multiple of π,

^{st}, 2

^{nd}, 3

^{rd}and 4

^{th}resonance of the structure with height 350 nm and radius 50 nm. It can be seen that the shape of the SE-rate curves follow expected FP resonance profile. However, we note that the SE Rate enhancement factors do not vanish at the nodes of Fabry-Perot resonances (Fig. 3(d)), and it is as large as 2 for the 2

^{nd}order mode. This is attributed to the direct coupling of the dipole to the radiation modes and surface plasmons that exist at the metal-air interface.

26. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A **20**(3), 569–572 (2003). [CrossRef]

27. M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O’Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett. **94**(7), 071101 (2009). [CrossRef]

*Fc*is the SE rate enhancement due to the plasmonic cavity mode, W

_{E}and W

_{M}are the stored electric and magnetic energies, respectively. Mode volume, V, has the same form as the effective mode area except the integration is over a large volume. This expression is similar to the Purcell factor formula used for dielectric cavities [28

28. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. **95**(1), 013904 (2005). [CrossRef] [PubMed]

20. H. Iwase, D. Englund, and J. Vucković, “Analysis of the Purcell effect in photonic and plasmonic crystals with losses,” Opt. Express **18**(16), 16546–16560 (2010). [CrossRef] [PubMed]

## Conclusion

## Acknowledgments

## References and links

1. | F. Jelezko and J. Wrachtrup, “Single defect centres in diamond: A review,” Phys. Status Solidi |

2. | G. Balasubramanian, I. Y. Chan, R. Kolesov, M. Al-Hmoud, J. Tisler, C. Shin, C. Kim, A. Wojcik, P. R. Hemmer, A. Krueger, T. Hanke, A. Leitenstorfer, R. Bratschitsch, F. Jelezko, and J. Wrachtrup, “Nanoscale imaging magnetometry with diamond spins under ambient conditions,” Nature |

3. | G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. |

4. | J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, “High-sensitivity diamond magnetometer with nanoscale resolution,” Nat. Phys. |

5. | S. Prawer and A. D. Greentree, “Applied physics. Diamond for quantum computing,” Science |

6. | A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J. P. Poizat, and P. Grangier, “Single photon quantum cryptography,” Phys. Rev. Lett. |

7. | J. R. Maze, P. L. Stanwix, J. S. Hodges, S. Hong, J. M. Taylor, P. Cappellaro, L. Jiang, M. V. Dutt, E. Togan, A. S. Zibrov, A. Yacoby, R. L. Walsworth, and M. D. Lukin, “Nanoscale magnetic sensing with an individual electronic spin in diamond,” Nature |

8. | F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. |

9. | F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. |

10. | R. Hanson, V. V. Dobrovitski, A. E. Feiguin, O. Gywat, and D. D. Awschalom, “Coherent dynamics of a single spin interacting with an adjustable spin bath,” Science |

11. | T. M. Babinec, B. J. M. Hausmann, M. Khan, Y. Zhang, J. R. Maze, P. R. Hemmer, and M. Loncar, “A diamond nanowire single-photon source,” Nat. Nanotechnol. |

12. | J. P. Hadden, J. P. Harrison, A. C. Stanley-Clarke, L. Marseglia, Y. D. Ho, B. R. Patton, J. L. O'Brien, and J. G. Rarity, “Strongly enhanced photon collection from diamond defect centres under micro-fabricated integrated solid immersion lenses,” arXiv:1006.2093v2 (2010). |

13. | S. Schietinger, M. Barth, T. Aichele, and O. Benson, “Plasmon-enhanced single photon emission from a nanoassembled metal-diamond hybrid structure at room temperature,” Nano Lett. |

14. | A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature |

15. | B. M. Hausmann, “Top-Down Fabricated Hybrid Diamond-Plasmon Nanoparticles,” in |

16. | B. J. Hausmann, T. M. Babinec, J. T. Choy, J. S. Hodges, S. Hong, I. Bulu, A. Yacoby, M. D. Lukin, and M. Lončar, “Single Color Centers Implanted in Diamond Nanostructures,” Arxiv preprint arXiv:1009.4224 (2010). |

17. | B. Hausmann, M. Khan, Y. Zhang, T. Babinec, K. Martinick, M. McCutcheon, P. Hemmer, and M. Loncar, “Fabrication of diamond nanowires for quantum information processing applications,” Diamond Related Materials |

18. | L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics |

19. | H. Shin, P. Catrysse, and S. Fan, “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B |

20. | H. Iwase, D. Englund, and J. Vucković, “Analysis of the Purcell effect in photonic and plasmonic crystals with losses,” Opt. Express |

21. | Y. Gong and J. Vučković, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett. |

22. | P. B. Johnson, and R. W. Christy, |

23. | E. D. Palik, |

24. | Y. Xu, R. K. Lee, and A. Yariv, “Quantum analysis and the classical analysis of spontaneous emission in a microcavity,” Phys. Rev. A |

25. | Y. Xu, R. K. Lee, and A. Yariv, “Finite-difference time-domain analysis of spontaneous emission in a microdisk cavity,” Phys. Rev. A |

26. | S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A |

27. | M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O’Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett. |

28. | D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. |

**OCIS Codes**

(240.6680) Optics at surfaces : Surface plasmons

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: January 24, 2011

Revised Manuscript: February 25, 2011

Manuscript Accepted: February 26, 2011

Published: March 7, 2011

**Citation**

Irfan Bulu, Thomas Babinec, Birgit Hausmann, Jennifer T. Choy, and Marko Loncar, "Plasmonic resonators for enhanced diamond NV- center single photon sources," Opt. Express **19**, 5268-5276 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-6-5268

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### References

- F. Jelezko and J. Wrachtrup, “Single defect centres in diamond: A review,” Phys. Status Solidi 203(13), 3207–3225 (2006) (a). [CrossRef]
- G. Balasubramanian, I. Y. Chan, R. Kolesov, M. Al-Hmoud, J. Tisler, C. Shin, C. Kim, A. Wojcik, P. R. Hemmer, A. Krueger, T. Hanke, A. Leitenstorfer, R. Bratschitsch, F. Jelezko, and J. Wrachtrup, “Nanoscale imaging magnetometry with diamond spins under ambient conditions,” Nature 455(7213), 648–651 (2008). [CrossRef] [PubMed]
- G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8(5), 383–387 (2009). [CrossRef] [PubMed]
- J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, and M. D. Lukin, “High-sensitivity diamond magnetometer with nanoscale resolution,” Nat. Phys. 4(10), 810–816 (2008). [CrossRef]
- S. Prawer and A. D. Greentree, “Applied physics. Diamond for quantum computing,” Science 320(5883), 1601–1602 (2008). [CrossRef] [PubMed]
- A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J. P. Poizat, and P. Grangier, “Single photon quantum cryptography,” Phys. Rev. Lett. 89(18), 187901 (2002). [CrossRef] [PubMed]
- J. R. Maze, P. L. Stanwix, J. S. Hodges, S. Hong, J. M. Taylor, P. Cappellaro, L. Jiang, M. V. Dutt, E. Togan, A. S. Zibrov, A. Yacoby, R. L. Walsworth, and M. D. Lukin, “Nanoscale magnetic sensing with an individual electronic spin in diamond,” Nature 455(7213), 644–648 (2008). [CrossRef] [PubMed]
- F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92(7), 076401 (2004). [CrossRef] [PubMed]
- F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004). [CrossRef] [PubMed]
- R. Hanson, V. V. Dobrovitski, A. E. Feiguin, O. Gywat, and D. D. Awschalom, “Coherent dynamics of a single spin interacting with an adjustable spin bath,” Science 320(5874), 352–355 (2008). [CrossRef] [PubMed]
- T. M. Babinec, B. J. M. Hausmann, M. Khan, Y. Zhang, J. R. Maze, P. R. Hemmer, and M. Loncar, “A diamond nanowire single-photon source,” Nat. Nanotechnol. 5(3), 195–199 (2010). [CrossRef] [PubMed]
- J. P. Hadden, J. P. Harrison, A. C. Stanley-Clarke, L. Marseglia, Y. D. Ho, B. R. Patton, J. L. O'Brien, and J. G. Rarity, “Strongly enhanced photon collection from diamond defect centres under micro-fabricated integrated solid immersion lenses,” arXiv:1006.2093v2 (2010).
- S. Schietinger, M. Barth, T. Aichele, and O. Benson, “Plasmon-enhanced single photon emission from a nanoassembled metal-diamond hybrid structure at room temperature,” Nano Lett. 9(4), 1694–1698 (2009). [CrossRef] [PubMed]
- A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450(7168), 402–406 (2007). [CrossRef] [PubMed]
- B. M. Hausmann, “Top-Down Fabricated Hybrid Diamond-Plasmon Nanoparticles,” in CLEO/QELS (2010).
- B. J. Hausmann, T. M. Babinec, J. T. Choy, J. S. Hodges, S. Hong, I. Bulu, A. Yacoby, M. D. Lukin, and M. Lončar, “Single Color Centers Implanted in Diamond Nanostructures,” Arxiv preprint arXiv:1009.4224 (2010).
- B. Hausmann, M. Khan, Y. Zhang, T. Babinec, K. Martinick, M. McCutcheon, P. Hemmer, and M. Loncar, “Fabrication of diamond nanowires for quantum information processing applications,” Diamond Related Materials 19(5-6), 621–629 (2010). [CrossRef]
- L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 50(5), 4094–4106 (1994). [CrossRef] [PubMed]
- H. Shin, P. Catrysse, and S. Fan, “Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes,” Phys. Rev. B 72(8), 085436 (2005). [CrossRef]
- H. Iwase, D. Englund, and J. Vucković, “Analysis of the Purcell effect in photonic and plasmonic crystals with losses,” Opt. Express 18(16), 16546–16560 (2010). [CrossRef] [PubMed]
- Y. Gong and J. Vučković, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett. 90(3), 033113 (2007). [CrossRef]
- P. B. Johnson, and R. W. Christy, Optical Constants of the Noble Metals, No. 12 (1972), Vol. 6.
- E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, n.d.).
- Y. Xu, R. K. Lee, and A. Yariv, “Quantum analysis and the classical analysis of spontaneous emission in a microcavity,” Phys. Rev. A 61(3), 033807 (2000). [CrossRef]
- Y. Xu, R. K. Lee, and A. Yariv, “Finite-difference time-domain analysis of spontaneous emission in a microdisk cavity,” Phys. Rev. A 61(3), 33808 (2000). [CrossRef]
- S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003). [CrossRef]
- M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O’Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett. 94(7), 071101 (2009). [CrossRef]
- D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95(1), 013904 (2005). [CrossRef] [PubMed]

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