## Strong coupling between a dipole emitter and localized plasmons: enhancement by sharp silver tips |

Optics Express, Vol. 21, Issue 23, pp. 27602-27610 (2013)

http://dx.doi.org/10.1364/OE.21.027602

Acrobat PDF (1179 KB)

### Abstract

In this work sharp silver nanotips are analyzed and proposed as useful plasmonic tools to reduce the threshold for the onset of strong coupling in the electromagnetic interaction of a point-like emitter with localized surface plasmons. If compared to similarly-sized spherical nanoparticles, conically-shaped nanoparticles turn out to be extremely useful to reduce the oscillator strength requirements for the emitting dipole, a reduction of the threshold by one sixth being obtained in a double cone configuration. Moreover the transition to the strong coupling regime is analyzed for several cone apertures, revealing a nonmonotonic behavior with the appearance of an optimal cone geometry. The emitted-light spectrum is obtained from the computation of the perturbative decay rate and photonic Lamb shift in the classical framework of the Discrete Dipole Approximation. This combined classical-quantum electrodynamics treatment is useful for the theoretical investigation on nonperturbative light-matter interactions involving complex shaped nanoparticles or aggregates.

© 2013 OSA

## 1. Introduction

1. S. Haroche and J.-M. Raimond, *Exploring the Quantum : Atoms, Cavities and Photons* (Oxford University, 2006). [CrossRef]

*weak-coupling*regime, deexcitation of the dipole is described by means of a decay rate calculated with Fermi golden rule. On the other hand, when the strength of interaction overcomes radiative and nonradiative losses, the system could enter the non-perturbative or

*strong coupling*regime, where the excitation is reversibly exchanged between the emitter and the electromagnetic field. A third recently investigated scenario is the

*ultrastrong coupling*regime [2

2. C. Ciuti and I. Carusotto, “Input-output theory of cavities in the ultra-strong coupling regime: the case of time-independent cavity parameters,” Phys. Rev. A **74**, 033811 (2006). [CrossRef]

4. R. Stassi, A. Ridolfo, O. Di Stefano, M. J. Hartmann, and S. Savasta, “Spontaneous conversion from virtual to real photons in the ultrastrong-coupling regime,” Phys. Rev. Lett. **110**, 243601 (2013). [CrossRef]

*h̄*Ω. This phenomenon is reflected by the recognizable formation of a doublet of peaks in the emitted-light spectrum around the dipole frequency, known with the name of

*vacuum Rabi splitting*. The strong coupling regime has been originally observed for single atoms in high-finesse optical resonators [1

1. S. Haroche and J.-M. Raimond, *Exploring the Quantum : Atoms, Cavities and Photons* (Oxford University, 2006). [CrossRef]

5. J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature **432**, 197–200 (2004). [CrossRef] [PubMed]

8. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot–cavity system,” Nature **445**, 896–899 (2007). [CrossRef] [PubMed]

9. A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature **431**, 162–167 (2004). [CrossRef] [PubMed]

*Q*optical cavities. The reversible exchange of energy between the emitter and electromagnetic modes has interesting potentialities for several applications which span from quantum information to bio-sensors; for this reason, nonperturbative light-matter interaction continues to attract much interest in the nanophotonics community. Strong coupling effects in proximity to metal nanostructures have been the subject of several theoretical [10

10. A. Trügler and U. Hohenester, “Strong coupling between a metallic nanoparticle and a single molecule,” Phys. Rev. B **77**, 115403 (2008). [CrossRef]

17. M. M. Dvoynenko and J. K. Wang, “Revisiting strong coupling between a single molecule and surface plasmons,” Opt Lett. **38**, 760–762 (2013). [CrossRef] [PubMed]

18. Y. Sugawara, T. A. Kelf, J. J. Baumberg, M. E Abdelsalam, and P. N. Bartlett, “Strong coupling between localized plasmons and organic excitons in metal nanovoids,” Phys. Rev. Lett. **97**, 266808 (2006). [CrossRef]

23. A. E. Schlather, N. Large, A. S. Urban, P. Nordlander, and N. J. Halas, “Near-field–mediated plexcitonic coupling and giant Rabi splitting in individual metallic dimers,” Nano Lett. **13**(7), 3281–3286 (2013). [CrossRef]

*g*. This quantity increases with the oscillator strength

*f*of the emitter and decreases with the effective volume

*V*

_{eff}of the mode (which quantifies the degree of localization of the field). The threshold for entering the strong coupling regime can be expressed as

*g*> |

*γ*−

*γ*

_{0}|/4, where

*γ*and

*γ*

_{0}are the linewidths of the electromagnetic mode and the emitter, respectively [24

24. L.C. Andreani, G. Panzarini, and J.-M. Gérard, “Strong-coupling regime for quantum boxes in pillar microcavities: Theory,” Phys. Rev. B **60**, 13276–13279 (1999). [CrossRef]

*Q*optical microcavities, since modal effective volumes are constrained by the diffraction limit, nonperturbative effects are generally reached by reducing the cavity

*γ*and the emitter

*γ*

_{0}decay rates, for instance with low temperatures in order to get very long nonradiative exciton decay times. In plasmonic systems, on the contrary, the linewidth of plasmon modes is usually very large, due to Ohmic losses inside the metal, but the criterion could be equally satisfied as an effect of the subwavelength effective volumes which characterize surface plasmons. As a side advantage, higher temperatures are sufficient with respect to traditional dielectric systems.

25. B. T. Draine and P. J. Flatau, “Discrete dipole approximation for scattering calculations,” J. Opt. Soc. Am. A **11**, 1491–1499 (1994). [CrossRef]

26. M. A. Yurkin and A. G. Hoekstra, ADDA, available at http://code.google.com/p/a-dda/.

27. S. D’Agostino, F. Della Sala, and L. C. Andreani, “Dipole-excited surface plasmons in metallic nanoparticles: Engineering decay dynamics within the discrete-dipole approximation,” Phys. Rev. B **87**, 205413 (2013). [CrossRef]

28. S. D’Agostino, F. Della Sala, and L. C. Andreani, “Dipole Decay Rates Engineering via Silver Nanocones”, Plasmonics **8**, 1079–1086 (2013). [CrossRef]

27. S. D’Agostino, F. Della Sala, and L. C. Andreani, “Dipole-excited surface plasmons in metallic nanoparticles: Engineering decay dynamics within the discrete-dipole approximation,” Phys. Rev. B **87**, 205413 (2013). [CrossRef]

29. F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A Hybrid Plasmonic-Photonic Nanodevice for Label-Free Detection of a Few Molecules,” Nano Lett. **8**, 2321–2327 (2008). [CrossRef] [PubMed]

31. F. De Angelis, R. Proietti Zaccaria, M. Francardi, C. Liberale, and E. Di Fabrizio, “Multi-scheme approach for efficient surface plasmon polariton generation in metallic conical tips on AFM-based cantilevers,” Opt. Express **19**, 22268 (2011). [CrossRef] [PubMed]

10. A. Trügler and U. Hohenester, “Strong coupling between a metallic nanoparticle and a single molecule,” Phys. Rev. B **77**, 115403 (2008). [CrossRef]

11. E. Waks and D. Sridharan, “Cavity QED treatment of interactions between a metal nanoparticle and a dipole emitter,” Phys. Rev. A **82**, 043845 (2010). [CrossRef]

13. C. Van Vlack, P. T. Kristensen, and S. Hughes, “Spontaneous emission spectra and quantum light-matter interactions from a strongly coupled quantum dot metal-nanoparticle system,” Phys. Rev. B **85**, 075303 (2012). [CrossRef]

15. A. Salomon, R. J. Gordon, Y. Prior, T. Seideman, and M. Sukharev, “Strong coupling between molecular excited states and surface plasmon modes of a slit array in a thin metal film,” Phys. Rev. Lett. **109**, 073002 (2012). [CrossRef] [PubMed]

17. M. M. Dvoynenko and J. K. Wang, “Revisiting strong coupling between a single molecule and surface plasmons,” Opt Lett. **38**, 760–762 (2013). [CrossRef] [PubMed]

## 2. Method

**r**

_{0}in proximity to a metal nanostructure is given by the expression [16

16. F. Alpeggiani, S. D’Agostino, and L. C. Andreani, “Surface plasmons and strong light-matter coupling in metallic nanoshells,” Phys. Rev. B **86**, 035421 (2012). [CrossRef]

*ω*is the emitted frequency,

*ω*

_{0}the dipole transition frequency,

*q*(

*ω*) the quantum yield of the system, Γ(

*ω*) the perturbative dipole decay rate (calculated from the Fermi golden rule), and

*δω*(

*ω*) the photonic (anomalous) Lamb shift. The quantum yield is defined as the ratio between the radiative decay rate Γ

*(*

_{R}*ω*) and the total decay rate Γ(

*ω*). Nonperturbative dynamical effects are entirely contained in the term

*S′*(

*ω*), here named

*dipole spectrum*, which depends on both radiative and non-radiative plasmonic decay channels. In principle, the dipole spectrum can be directly measured with near field experiments. On the other hand, the prefactor containing the quantum yield depends only on the radiative decay channel and accounts for the propagation of light from the emitter to the far-field detector.

**∞**and used Kramers–Kronig relations.

**G⃡**

_{tot}=

**G⃡**

_{free}+

**G⃡**

_{sc}is the dyadic Green function containing the free–space term and the scattering term originating from the electromagnetic response of the metal. As it can be inferred from Eqs. (3) and (4), our expression for the far-field spectrum in Eq. (1) is the RWA equivalent of that reported in [33

33. Peijun Yao, C. Van Vlack, A. Reza, M. Patterson, M. M. Dignam, and S. Hughes, “Ultrahigh Purcell factors and Lamb shifts in slow-light metamaterial waveguides,” Phys. Rev. B **80**, 195106 (2009). [CrossRef]

*δω*depends on the dipole moment of the emitter

*p̃*

_{0}; in this work, however, we equivalently employ the dipole oscillator strength

*δω*, being quadratic with

*p̃*

_{0}, become linear with the oscillator strength

*f*.

*d*= 1/16 nm for the metallic scatterers, this discretization being enough to ensure a good convergence level [27

27. S. D’Agostino, F. Della Sala, and L. C. Andreani, “Dipole-excited surface plasmons in metallic nanoparticles: Engineering decay dynamics within the discrete-dipole approximation,” Phys. Rev. B **87**, 205413 (2013). [CrossRef]

## 3. Results

*f*= 1 dipole) are plotted for Ag cones with five different tip apertures as a function of the dipole frequency and compared to the one obtained for an Ag sphere of the same size. For these sharp cones excited in an extremely near region, total decay rates are strongly peaked around a single surface plasmon resonance and result about 10 times larger than those which can be achieved with rounded tips with a curvature radius of 3 nm [27

**87**, 205413 (2013). [CrossRef]

16. F. Alpeggiani, S. D’Agostino, and L. C. Andreani, “Surface plasmons and strong light-matter coupling in metallic nanoshells,” Phys. Rev. B **86**, 035421 (2012). [CrossRef]

*γ*< 4

*f*Γ

_{max}, where

*γ*and Γ

_{max}are the full width at half maximum and the maximum height of the peak, respectively, this being due to the linear dependence of the total decay rate on

*f*. Thus, for each plasmonic system characterized by

*γ*and Γ

_{max}, we can define the

*threshold oscillator strength f*

_{th}=

*γ*/(4Γ

_{max}), which provides a good starting estimate of the minimal coupling required to enter the nonperturbative regime.

*θ*=

*π*/13 tip shows an important decrease of the oscillator strength with respect to the spherical geometry. However, a non-monotonic behavior of

*f*

_{th}as a function of the aperture can be noticed: the oscillator strength decreases with decreasing aperture until an optimal value of

*π*/13 is reached, but further reducing the aperture reverses the trend and increases again the threshold oscillator strength. The trend of Fig. 1(b) is mostly determined by the behavior of the linewidth

*γ*, which has a minimum for the

*π*/13 aperture, as shown in Fig. 1(a). This is in relation with the fact that small-aperture cones, in spite of presenting a stronger localization of the electric field (the well-known

*superfocusing effect*), are characterized also by a wider frequency distribution of the plasmonic modes, which results in a broader lineshape. For large-aperture cones, on the other hand, the linewidth increases towards the limiting value for a flat surface.

**87**, 205413 (2013). [CrossRef]

*d*with an approximate

*d*

^{−4}dependence, i.e., a simple doubling of the dipole–tip distance increases the threshold oscillator strength by a factor ∼ 16. As a consequence, very close proximity of the emitter to the metallic nanostructure is crucial for the investigation of nonperturbative effects. From this point of view, the conical geometry has a clear advantage, as it is naturally suitable to a raster scanning configuration [30

30. F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nature Nanotech. **5**, 67–72 (2010). [CrossRef]

*S′*(

*ω*) is plotted as a function of the emitted frequency and of the oscillator strength for a dipole in resonance with the surface plasmon frequency. The upper panel (a) refers to a silver nanosphere, whereas the lower panel (b) refers to a

*θ*=

*π*/13 nanocone. In both cases the onset of vacuum Rabi splitting is clearly visible, but the minimal oscillator strength required for the sphere is far higher than for the cone, in agreement with our previous considerations. The threshold oscillator strength

*f*

_{th}is a mathematical quantity that essentially characterizes the transition between the over-damping and the under-damping regimes in the decay probability of the dipole. However, notice that, due to the finite width of the peaks, the oscillator strength should be somewhat larger than the threshold value to obtain an appreciable splitting in the spectrum. Nevertheless,

*f*

_{th}is taken as a well-defined lower bound for the dipole coupling strength needed to achieve strong-coupling interaction.

*θ*=

*π*/13, which corresponds to the optimal one (sketch in Fig. 3). The dipole is 2 nm distant from each cone and oriented along the symmetry axis. Numerical simulations, reported elsewhere [27

**87**, 205413 (2013). [CrossRef]

*bonding*combination of the resonances reported in Fig. 1. The higher decay rate registered in this case is responsible for a much lower threshold in the oscillator strength (

*f*

_{th}≃ 6) with respect to the single cone configuration (

*f*

_{th}≃ 13) with an anti-crossing behavior of the peak maxima in the emitted spectrum well visible at

*f*= 20 [Fig. 3(b)]. The double-cone effect depends on the distance between the two cones, as discussed in [27

**87**, 205413 (2013). [CrossRef]

*S*(

*ω*) and compare them with the dipole spectra

*S′*(

*ω*) for the three different structures here analyzed (sphere, cone and double cone) and for several oscillator strengths, in the range 10 – 50. This comparison is presented in order to shed light on the effect of the plasmonic quantum yield, in view of real far-field spectroscopy measurements. As in most plasmonic systems, the quantum yield for the systems under consideration is low, due to the prevalence of non-radiative modes at short distance. This effect competes with the strong enhancement of light–matter coupling induced by the localization of the plasmonic field. The resulting radiative decay rate, however, remains significantly higher than the free-space decay rate — up to a few orders of magnitude for the double cone configuration [27

**87**, 205413 (2013). [CrossRef]

*l*= 1 dipolar surface plasmon at

*ω*≃ 3.5eV. However, the optimal resonance frequency for the transition to the strong coupling regime is around

*ω*≃ 3.66eV, as an effect of the excitation of higher-order strongly non-radiative plasmon modes. As a consequence, the vacuum Rabi splitting results strongly quenched in the far-field for the spherical geometry. This is not the case of the cone (b) and double cone (c) systems, for which the maximum of the radiative decay rate coincides with the maximum of the field enhancement, as a result of the excitation of the strongly radiative mode. In these cases, the fingerprint of vacuum Rabi splitting, even if partially modulated by the quantum yield, survives even in the far field spectrum.

16. F. Alpeggiani, S. D’Agostino, and L. C. Andreani, “Surface plasmons and strong light-matter coupling in metallic nanoshells,” Phys. Rev. B **86**, 035421 (2012). [CrossRef]

**86**, 035421 (2012). [CrossRef]

29. F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A Hybrid Plasmonic-Photonic Nanodevice for Label-Free Detection of a Few Molecules,” Nano Lett. **8**, 2321–2327 (2008). [CrossRef] [PubMed]

*outside*the nanoparticle is also favourable for experimental probing by raster scanning of a nanotip [30

30. F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nature Nanotech. **5**, 67–72 (2010). [CrossRef]

## 4. Conclusion

## Acknowledgment

## References and links

1. | S. Haroche and J.-M. Raimond, |

2. | C. Ciuti and I. Carusotto, “Input-output theory of cavities in the ultra-strong coupling regime: the case of time-independent cavity parameters,” Phys. Rev. A |

3. | A. Ridolfo, O. Di Stefano, N. Fina, R. Saija, and S. Savasta, “Quantum plasmonics with quantum dot-metal nanoparticle molecules: Influence of the Fano effect on photon statistics,” Phys. Rev. Lett. |

4. | R. Stassi, A. Ridolfo, O. Di Stefano, M. J. Hartmann, and S. Savasta, “Spontaneous conversion from virtual to real photons in the ultrastrong-coupling regime,” Phys. Rev. Lett. |

5. | J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature |

6. | T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature |

7. | E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. |

8. | K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot–cavity system,” Nature |

9. | A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature |

10. | A. Trügler and U. Hohenester, “Strong coupling between a metallic nanoparticle and a single molecule,” Phys. Rev. B |

11. | E. Waks and D. Sridharan, “Cavity QED treatment of interactions between a metal nanoparticle and a dipole emitter,” Phys. Rev. A |

12. | S. Savasta, R. Saija, A. Ridolfo, O. Di Stefano, P. Denti, and F. Borghese, “Nanopolaritons: vacuum Rabi splitting with a single quantum dot in the center of a dimer nanoantenna,” ACS Nano |

13. | C. Van Vlack, P. T. Kristensen, and S. Hughes, “Spontaneous emission spectra and quantum light-matter interactions from a strongly coupled quantum dot metal-nanoparticle system,” Phys. Rev. B |

14. | Y. He, C. Jiang, B. Chen, J.-J. Li, and K.-D. Zhu, “Optical determination of vacuum Rabi splitting in a semiconductor quantum dot induced by a metal nanoparticle,” Opt. Lett. |

15. | A. Salomon, R. J. Gordon, Y. Prior, T. Seideman, and M. Sukharev, “Strong coupling between molecular excited states and surface plasmon modes of a slit array in a thin metal film,” Phys. Rev. Lett. |

16. | F. Alpeggiani, S. D’Agostino, and L. C. Andreani, “Surface plasmons and strong light-matter coupling in metallic nanoshells,” Phys. Rev. B |

17. | M. M. Dvoynenko and J. K. Wang, “Revisiting strong coupling between a single molecule and surface plasmons,” Opt Lett. |

18. | Y. Sugawara, T. A. Kelf, J. J. Baumberg, M. E Abdelsalam, and P. N. Bartlett, “Strong coupling between localized plasmons and organic excitons in metal nanovoids,” Phys. Rev. Lett. |

19. | G. A. Wurtz, P. R. Evans, W. Hendren, R. Atkinson, W. Dickson, R. J. Pollard, and A. V. Zayats, “Molecular plasmonics with tunable exciton–plasmon coupling strength in J-aggregate hybridized Au nanorod assemblies,” Nano Lett. |

20. | Nche T. Fofang, Tae-Ho Park, Oara Neumann, Nikolay A. Mirin, Peter Nordlander, and Naomi J. Halas, “Plex-citonic nanoparticles: plasmon-exciton coupling in nanoshell-J-aggregate complexes,” Nano Lett. |

21. | J. Bellessa, C. Symonds, K. Vynck, A. Lemaitre, A. Brioude, L. Beaur, J. C. Plenet, P. Viste, D. Felbacq, E. Cambril, and P. Valvin, “Giant Rabi splitting between localized mixed plasmon-exciton states in a two-dimensional array of nanosize metallic disks in an organic semiconductor,” Phys. Rev. B |

22. | N. I. Cade, T. Ritman-Meer, and D. Richards, “Strong coupling of localized plasmons and molecular excitons in nanostructured silver films,” Phys. Rev. B |

23. | A. E. Schlather, N. Large, A. S. Urban, P. Nordlander, and N. J. Halas, “Near-field–mediated plexcitonic coupling and giant Rabi splitting in individual metallic dimers,” Nano Lett. |

24. | L.C. Andreani, G. Panzarini, and J.-M. Gérard, “Strong-coupling regime for quantum boxes in pillar microcavities: Theory,” Phys. Rev. B |

25. | B. T. Draine and P. J. Flatau, “Discrete dipole approximation for scattering calculations,” J. Opt. Soc. Am. A |

26. | M. A. Yurkin and A. G. Hoekstra, ADDA, available at http://code.google.com/p/a-dda/. |

27. | S. D’Agostino, F. Della Sala, and L. C. Andreani, “Dipole-excited surface plasmons in metallic nanoparticles: Engineering decay dynamics within the discrete-dipole approximation,” Phys. Rev. B |

28. | S. D’Agostino, F. Della Sala, and L. C. Andreani, “Dipole Decay Rates Engineering via Silver Nanocones”, Plasmonics |

29. | F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A Hybrid Plasmonic-Photonic Nanodevice for Label-Free Detection of a Few Molecules,” Nano Lett. |

30. | F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nature Nanotech. |

31. | F. De Angelis, R. Proietti Zaccaria, M. Francardi, C. Liberale, and E. Di Fabrizio, “Multi-scheme approach for efficient surface plasmon polariton generation in metallic conical tips on AFM-based cantilevers,” Opt. Express |

32. | E. D. Palik, |

33. | Peijun Yao, C. Van Vlack, A. Reza, M. Patterson, M. M. Dignam, and S. Hughes, “Ultrahigh Purcell factors and Lamb shifts in slow-light metamaterial waveguides,” Phys. Rev. B |

**OCIS Codes**

(240.6680) Optics at surfaces : Surface plasmons

(270.5580) Quantum optics : Quantum electrodynamics

**ToC Category:**

Plasmonics

**History**

Original Manuscript: July 29, 2013

Revised Manuscript: October 10, 2013

Manuscript Accepted: October 11, 2013

Published: November 4, 2013

**Citation**

Stefania D’Agostino, Filippo Alpeggiani, and Lucio Claudio Andreani, "Strong coupling between a dipole emitter and localized plasmons: enhancement by sharp silver tips," Opt. Express **21**, 27602-27610 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-23-27602

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### References

- S. Haroche and J.-M. Raimond, Exploring the Quantum : Atoms, Cavities and Photons (Oxford University, 2006). [CrossRef]
- C. Ciuti and I. Carusotto, “Input-output theory of cavities in the ultra-strong coupling regime: the case of time-independent cavity parameters,” Phys. Rev. A74, 033811 (2006). [CrossRef]
- A. Ridolfo, O. Di Stefano, N. Fina, R. Saija, and S. Savasta, “Quantum plasmonics with quantum dot-metal nanoparticle molecules: Influence of the Fano effect on photon statistics,” Phys. Rev. Lett.105, 263601 (2010). [CrossRef]
- R. Stassi, A. Ridolfo, O. Di Stefano, M. J. Hartmann, and S. Savasta, “Spontaneous conversion from virtual to real photons in the ultrastrong-coupling regime,” Phys. Rev. Lett.110, 243601 (2013). [CrossRef]
- J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432, 197–200 (2004). [CrossRef] [PubMed]
- T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature432, 200–203 (2004). [CrossRef] [PubMed]
- E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett.95, 067401 (2005). [CrossRef] [PubMed]
- K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Fält, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot–cavity system,” Nature445, 896–899 (2007). [CrossRef] [PubMed]
- A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature431, 162–167 (2004). [CrossRef] [PubMed]
- A. Trügler and U. Hohenester, “Strong coupling between a metallic nanoparticle and a single molecule,” Phys. Rev. B77, 115403 (2008). [CrossRef]
- E. Waks and D. Sridharan, “Cavity QED treatment of interactions between a metal nanoparticle and a dipole emitter,” Phys. Rev. A82, 043845 (2010). [CrossRef]
- S. Savasta, R. Saija, A. Ridolfo, O. Di Stefano, P. Denti, and F. Borghese, “Nanopolaritons: vacuum Rabi splitting with a single quantum dot in the center of a dimer nanoantenna,” ACS Nano4(11), 6369–6376 (2010). [CrossRef] [PubMed]
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