## Quantum entangling gates using the strong coupling between two optical emitters and nanowire surface plasmons |

Optics Express, Vol. 21, Issue 13, pp. 15618-15626 (2013)

http://dx.doi.org/10.1364/OE.21.015618

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### Abstract

We propose a scheme to generate quantum entangling gate using one-dimensional surface plasmon waveguide. The protocol is based on the detection of the transmission spectrum of the single optical plasmons passing through two separate three-level emitters on metallic nanowire waveguide. It is shown that the low efficiency in direct detection of the single photon can be avoided by repeating the measurement of the transmission spectrum.

© 2013 OSA

## 1. Introduction

2. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics **4**, 83–91 (2010) [CrossRef] .

3. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature **440**(7083), 508–511 (2006) [CrossRef] [PubMed] .

4. J. Grandidier, S. Massenot, G. C. Francs, A. Bouhelier, J. C. Weeber, L. Markey, A. Dereux, J. Renger, M. U. Gonzáez, and R. Quidant, “Dielectric-loaded surface plasmon polariton waveguides: figures of merit and mode characterization by image and Fourier plane leakage microscopy,” Phys. Rev. B **78**(24), 245419 (2008) [CrossRef] .

5. R. F. Oulton, V. J. Sorger, D. A. Genov, D. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. photonics **2**(8), 496–500 (2008) [CrossRef] .

6. J. Yang, Q. Cao, and C. Zhou, “An explicit formula for metal wire plasmon of terahertz wave,” Opt. Express **17**, 20806–20815 (2009) [CrossRef] [PubMed] .

9. H. Liang, S. Ruan, and M. Zhang, “Terahertz surface wave propagation and focusing on conical metal wires,” Opt. Express **16**, 18241–18248 (2008) [CrossRef] [PubMed] .

10. M. Wächter, M. Nagel, and H. Kurz, “Metallic slit waveguide for dispersion-free low-loss terahertz signal transmission,” Appl. Phys. Lett. **90**, 061111 (2007) [CrossRef] .

11. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. **97**, 053002 (2006) [CrossRef] [PubMed] .

13. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B **76**, 035420 (2007) [CrossRef] .

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**, 402–406 (2007) [CrossRef] [PubMed] .

15. D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Physics **3**, 807–812 (2007) [CrossRef] .

16. C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienaa, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett. **7**, 2784–2788 (2007) [CrossRef] [PubMed] .

25. Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. **109**, 160504 (2012) [CrossRef] [PubMed] .

## 2. Model setup and exact solutions

*g*〉

*, |*

_{n}*s*〉

*and |*

_{n}*e*〉

*(*

_{n}*n*= 1, 2), respectively. The tiny light emitters addressed here can be quantum dots, nitrogen-vacancy center or atoms.

*a*. The energies of the states |

_{k}*g*〉

*and |*

_{n}*e*〉

*are Ω*

_{n}*= 0(the energy origin)and Ω*

_{g,n}*= Ω*

_{e,n}*respectively. Here, the metastable state |*

_{n}*s*〉

*is used for the storage of qubits. The metastable state is not affected during the emitter-surface plasmon interaction, so it can be omitted in the Hamiltonians. The total Hamiltonian can be written as*

_{n}*σ̂*= |

_{een}*e*〉 〈

*e*|

*are the electronic population operators on the excited states. The third term stands for the energies of the propagating surface plasmon modes with frequency*

_{n}*ω*, which is the frequency of the mode of the radiation field corresponding to wave vector

_{k}*k*. In the fourth terms,

*S*

_{n+}= |

*e*〉 〈

*g*|

*is the transition from the ground state to the exited state of the n-th emitters. The transitions between the ground state and the excited state of the two emitters are coupled to the propagating surface plasmon modes with the coupling constant*

_{n}*V*. Here the coupling strength between the surface-plasmon modes and the tiny light emitters can be quite large because

_{k}*V*refers to the effective mode volume for the surface plasmon on the metallic nanowire.

_{eff}15. D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Physics **3**, 807–812 (2007) [CrossRef] .

24. D. Witthaut and A. S. Sørensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New Journal of Physics **12**, 043052 (2012) [CrossRef] .

32. J. T. Shen and S. Fan, “Coherent photon transport from spontaneous emission in one-dimensional waveguide coupled to a two-level system,” Opt. Lett. **30**, 2001–2003 (2005) [CrossRef] [PubMed] .

33. J. T. Shen and S. Fan, “Theory of single-photon transport in a single mode waveguide. I. Coupling to a cavity containing a two-level atom,” Phys. Rev. A **79**, 023837 (2009) [CrossRef] .

*v*is the group velocity of the plasmons and can be simplified as the velocity of the light [15

_{g}15. D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Physics **3**, 807–812 (2007) [CrossRef] .

*x*coordinate. Here we assume that a linear and nonde-generate dispersion relation holds over the relevant frequency range, and that a single plasmons comes from the left with energy

*E*=

_{k}*kv*.

_{g}*e*

_{1},

*g*

_{2}〉, |0,

*g*

_{1},

*e*

_{2}〉 and |1,

*g*

_{1},

*g*

_{2}〉, where |0〉 is the vacuum state of the incident pulse with zero photons. Thus the energy eigenvectors can be expanded in the base of an invariant subspace in the form. The coefficients

*e*(

_{kn}*n*= 1, 2) are the probability amplitudes of the two emitters in the excited states respectively. For a plasmon incident from the left,

*r*and

*t*

_{1}are the transmission and reflection amplitudes at the −

*d*site, and

*r*

_{1}and

*t*are those at the

*d*-th site. Since we only care about the overall performance of the system, we need to obtain the coefficients

*r*and

*t*.

*H*|

*E*〉 =

_{k}*E*|

_{k}*E*〉 results in the following equation:

_{k}*k*given by where the phase shifts of the two emitters are

*R*= 1 −

*T*.

*T*(

*k*) for the different states of the two identical emitters. For the two emitters located in the ground stat |

*g*

_{1},

*g*

_{2}〉, the total transmission turns out:

*g*

_{1},

*s*

_{2}〉 or |

*s*

_{1},

*g*

_{2}〉, which is equal to the case when the single plasmon couples only with one emitter, the total transmission can be simplified as

*s*

_{1},

*s*

_{2}〉, the incident plasmons totally arrive at the terminal end of the metal wire because the surface plasmons do not interact with the two emitters at all. Then the total transmission can be written as

_{1}= Ω

_{2}and that the plasmon energy

*E*=

_{k}*c*|

*k*|. The incident plasmon wave number

*k*(−3 ≤

*k*≤ 5) and the distance

*d*= 10

*a*are properly chosen, where a is the lattice constant, and all other parameters are in units of

*k*.

*T*(

_{ss}*k*), which means that the emitters do not influence the transmission of surface plasmon because of the decoupling between them. For cases of

*T*(

_{gs}*k*) and

*T*(

_{gg}*k*), the transmission spectrum vary with the wave number of the incident photon

*k*, which are shown by the black cashed line and blue solid line respectively in Fig. 2. In the following, we shall make a brief analysis of the commons and differences of the transmission spectra for the two cases. Firstly, both of the transmission amplitudes increase with the detuning between the frequency of the emitters transitions and that of the incident plasmon, because the propagating single plasmons cannot excite the emitters with transition energy far away from the energy band. Thus the single plasmons pass through the two emitters with high probability. Secondly, when the energy of the incident plasmon matches the transition energies of two emitters, the incident plasmon is totally reflected, and the frequency band appears, which acts as a photon filter. Although the trends of the two cases are similar at first sight, one of the most obvious differences between the two curves is the fast oscillation in the case of

*T*(

_{gg}*k*), which is caused by the multiple interference of the waves in the region sandwiched by the two emitters. In the case of

*T*(

_{gs}*k*), the scattering process of a single plasmon off the two emitters is equivalent to that of the single emitter; therefore, the fast oscillations disappear. This is also the most important property to distinguish the two different scattering processes. In all, the above describes the different transmission spectrum caused by the strong coupling between the single plasmon and the different states of the two emitters. In realistic situation, the direct detection of the single photon is quite difficult. The generation of a high-fidelity entangling gate requires the perfect scattering process, the infinite Purcell factor and the high-efficient detector. Here we propose the scheme to repeat the detection and accordingly avoid the difficulties in single-photon detection. The transmission spectrum become much easier to measure when the single plasmons are controlled to pass through the detector one after another. This is helpful to us in distinguishing the above different cases. Specifically, when both the emitters are in the ground states, we can detect the transmission amplitude as the fast oscillation spectrum. When the two emitters are in the metastable states, the plasmon shall transmit on the metal wire waveguide as if the two emitters did not exist. As long as the transmission spectrum is detected as a parabolic curve, we can know one of the emitters is in the ground state and the other is in the metastable states, but we cannot distinguish them. This provides the basis for the generation of the entangling state.

## 3. Entangling gate for the two emitters

*g*

_{1}〉 + |

*s*

_{1}〉) ⊗ (|

*g*

_{2}〉 + |

*s*

_{2}〉). This step can be realized by the following procedure. Because the two emitters are separated, we can manipulate either of the emitters independently. Therefore, we simply describe the preparation of superposition state of the single emitters. Firstly, we initialize the emitter in |

*g*〉 and apply two classical fields on the two transitions between |

*g*〉 → |

*e*〉 and |

*g*〉 → |

*s*〉 with Rabi frequencies Ω

_{1}(

*t*) and Ω

_{2}(

*t*) respectively to form two-photon Raman resonant. Now the effective Hamiltonian can be written as

*H*= Ω

_{eff}*(|*

_{eff}*g*〉 〈

*s*|+|

*s*〉 〈

*g*|), where Ω

*= Ω*

_{eff}_{1}Ω

_{2}/Δ, and Δ is the single photon detuning of the two classical fields from their corresponding transitions. Performing the effective Hamiltonian on the ground state and choosing appropriate time to satisfy Ω

*=*

_{eff}t*π*/4, we can finally get the superposition state we need. The qubit can be prepared in arbitrary superposition state and was already experimentally demonstrated [34

34. M. P. A. Jones, J. Beugnon, A. Gaëtan, J. Zhang, G. Messin, A. Browaeys, and P. Grangier, “Fast quantum state control of a single trapped neutral atom,” Phys. Rev. A **75**, 040301(R) (2007) [CrossRef] .

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**, 402–406 (2007) [CrossRef] [PubMed] .

35. H. S. Nguyen, G. Sallen, C. Voisin, Ph. Roussignol, C. Diederichs, and G. Cassabois, “Ultra-coherent single photon source,” Appl. Phys. Lett. **99**, 26 (2011) [CrossRef] .

**3**, 807–812 (2007) [CrossRef] .

*g*

_{1}〉 + |

*s*

_{1}〉) ⊗ (|

*g*

_{2}〉 + |

*s*

_{2}〉), and send trains of single plasmons to interact with the two emitters successively. Then the quantum state of the whole system can be written as where n denotes the number of the incident single plasmons. Here three quantum state |

*A*〉, |

*B*〉 and |

*C*〉 denote three different photon states after the scattering process. If the transmitted photons are detected to be in state |

*C*〉, the detection projects the two-emitters state onto the entangled state. While if the transmitted photons are detected to be in state |

*A*〉 or |

*B*〉, the operation should be discarded. Obviously, we can see that the transmission spectrum can be easily measured as long as the number of the incident single plasmons is large enough. Therefore, this scheme can avoid the low efficiency in the detection of the single photon and high fidelity is accordingly guaranteed. It has already been experimentally demonstrated that high resolution can be obtained by measurements of the transmission spectrum [36

36. H. Zhang, R. McConnell, S. Ćuk, Q. Lin, M. H. S. Smith, I. D. Leroux, and V. Vuletić, “Collective state measurement of mesoscopic ensembles with single-atom resolution,” Phys. Rev. Lett. **109**, 133603 (2012) [CrossRef] [PubMed] .

## 4. Conclusions

## Acknowledgments

## References and links

1. | H. Raether, |

2. | D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics |

3. | S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature |

4. | J. Grandidier, S. Massenot, G. C. Francs, A. Bouhelier, J. C. Weeber, L. Markey, A. Dereux, J. Renger, M. U. Gonzáez, and R. Quidant, “Dielectric-loaded surface plasmon polariton waveguides: figures of merit and mode characterization by image and Fourier plane leakage microscopy,” Phys. Rev. B |

5. | R. F. Oulton, V. J. Sorger, D. A. Genov, D. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. photonics |

6. | J. Yang, Q. Cao, and C. Zhou, “An explicit formula for metal wire plasmon of terahertz wave,” Opt. Express |

7. | J. Yang, Q. Cao, and C. Zhou, “An analytical recurrence formula for the zero-order metal wire plasmon of terahertz wave,” J. Opt. Soc. Am. A |

8. | J. Yang, Q. Cao, and C. Zhou, “Theory for terahertz plasmons of metallic nanowires with sub-skin-depth diameters,” Opt. Express |

9. | H. Liang, S. Ruan, and M. Zhang, “Terahertz surface wave propagation and focusing on conical metal wires,” Opt. Express |

10. | M. Wächter, M. Nagel, and H. Kurz, “Metallic slit waveguide for dispersion-free low-loss terahertz signal transmission,” Appl. Phys. Lett. |

11. | D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. |

12. | Z. Jacob and V. M. Shalaev, “plasmonics goes quantum,” Science |

13. | D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B |

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. | D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Physics |

16. | C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienaa, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett. |

17. | G. Y. Chen, Y. N. Chen, and D. S. Chuu, “Spontaneous emission of quantum dot excitons into surface plasmons in a nanowire,” Opt. Lett. |

18. | Z. J. Yang, N. C. Kim, J. B. Li, M. T. Chen, S. D. Liu, Z. H. Hao, and Q. Q. Wang, “Surface plasmons amplifications in single Ag nanoring,” Opt. Express |

19. | A. G. Tudela, F. J. Rodriguez, L. Quiroga, and C. Tejedor, “Dissipative dynamics of a solid-state qubit coupled to surface plasmons: From non-Markov to Markov regimes,” Phys. Rev. B |

20. | D. Dzsotjan, A. S. Sørensen, and M. Fleischhauer, “Quantum emitters coupled to surface plasmons of a nanowire: A Green’s function approach,” Phys. Rev. B |

21. | W. Chen, G. Y. Chen, and Y. N. Chen, “Coherent transport of nanowire surface plasmons coupled to quantum dots,” Opt. Express |

22. | A. Huck, S. Kumar, A. Shakoor, and U. L. Andersen, “Controlled coupling of a single nitrogen-vacancy center to a silver nanowire,” Phys. Rev. Lett. |

23. | J. Li and R. Yu, “Single-plasmon scattering grating using nanowire surface plasmon coupled to nanodiamond nitrogen-vacancy center,” Opt. Express |

24. | D. Witthaut and A. S. Sørensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New Journal of Physics |

25. | Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett. |

26. | M. A. Nielsen and I. A. Chuang, |

27. | S. Haroche and J. M. Raimond, |

28. | A. Gonzalez-Tudela, D. Martin-Cano, E. Moreno, L. Martin-Moreno, C. Tejedor, and F. J. Garcia-Vidal, “Entanglement of two qubits mediated by one-dimensional plasmonic waveguides,” Phys. Rev. Lett. |

29. | L. Slodickačka, G. Hétet, N. Röck, P. Schindler, M. Hennrich, and R. Blatt, “Atom-atom entanglement by single-photon detection,” Phys. Rev. Lett. |

30. | C. Cabrillo, J. I. Cirac, P. García-Fernández, and P. Zoller, “Creation of entangled states of distant atoms by interference,” Phys. Rev. A |

31. | Y. L. Lim, A. Beige, and L. C. Kwek, “Repeat-until-success linear optics distributed quantum computing” Phys. Rev. Lett. |

32. | J. T. Shen and S. Fan, “Coherent photon transport from spontaneous emission in one-dimensional waveguide coupled to a two-level system,” Opt. Lett. |

33. | J. T. Shen and S. Fan, “Theory of single-photon transport in a single mode waveguide. I. Coupling to a cavity containing a two-level atom,” Phys. Rev. A |

34. | M. P. A. Jones, J. Beugnon, A. Gaëtan, J. Zhang, G. Messin, A. Browaeys, and P. Grangier, “Fast quantum state control of a single trapped neutral atom,” Phys. Rev. A |

35. | H. S. Nguyen, G. Sallen, C. Voisin, Ph. Roussignol, C. Diederichs, and G. Cassabois, “Ultra-coherent single photon source,” Appl. Phys. Lett. |

36. | H. Zhang, R. McConnell, S. Ćuk, Q. Lin, M. H. S. Smith, I. D. Leroux, and V. Vuletić, “Collective state measurement of mesoscopic ensembles with single-atom resolution,” Phys. Rev. Lett. |

**OCIS Codes**

(240.6680) Optics at surfaces : Surface plasmons

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: April 29, 2013

Revised Manuscript: May 25, 2013

Manuscript Accepted: June 6, 2013

Published: June 21, 2013

**Citation**

J. Yang, G. W. Lin, Y. P. Niu, and S. Q. Gong, "Quantum entangling gates using the strong coupling between two optical emitters and nanowire surface plasmons," Opt. Express **21**, 15618-15626 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-13-15618

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### References

- H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).
- D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4, 83–91 (2010). [CrossRef]
- S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440(7083), 508–511 (2006). [CrossRef] [PubMed]
- J. Grandidier, S. Massenot, G. C. Francs, A. Bouhelier, J. C. Weeber, L. Markey, A. Dereux, J. Renger, M. U. Gonzáez, and R. Quidant, “Dielectric-loaded surface plasmon polariton waveguides: figures of merit and mode characterization by image and Fourier plane leakage microscopy,” Phys. Rev. B78(24), 245419 (2008). [CrossRef]
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- J. Yang, Q. Cao, and C. Zhou, “An explicit formula for metal wire plasmon of terahertz wave,” Opt. Express17, 20806–20815 (2009). [CrossRef] [PubMed]
- J. Yang, Q. Cao, and C. Zhou, “An analytical recurrence formula for the zero-order metal wire plasmon of terahertz wave,” J. Opt. Soc. Am. A27, 1608–1612 (2010). [CrossRef]
- J. Yang, Q. Cao, and C. Zhou, “Theory for terahertz plasmons of metallic nanowires with sub-skin-depth diameters,” Opt. Express18, 18550–18557 (2010). [CrossRef] [PubMed]
- H. Liang, S. Ruan, and M. Zhang, “Terahertz surface wave propagation and focusing on conical metal wires,” Opt. Express16, 18241–18248 (2008). [CrossRef] [PubMed]
- M. Wächter, M. Nagel, and H. Kurz, “Metallic slit waveguide for dispersion-free low-loss terahertz signal transmission,” Appl. Phys. Lett.90, 061111 (2007). [CrossRef]
- D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett.97, 053002 (2006). [CrossRef] [PubMed]
- Z. Jacob and V. M. Shalaev, “plasmonics goes quantum,” Science334, 755–756 (2011). [CrossRef]
- D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B76, 035420 (2007). [CrossRef]
- 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,” Nature450, 402–406 (2007). [CrossRef] [PubMed]
- D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Physics3, 807–812 (2007). [CrossRef]
- C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienaa, “Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source,” Nano Lett.7, 2784–2788 (2007). [CrossRef] [PubMed]
- G. Y. Chen, Y. N. Chen, and D. S. Chuu, “Spontaneous emission of quantum dot excitons into surface plasmons in a nanowire,” Opt. Lett.33, 2212–2214 (2008). [CrossRef] [PubMed]
- Z. J. Yang, N. C. Kim, J. B. Li, M. T. Chen, S. D. Liu, Z. H. Hao, and Q. Q. Wang, “Surface plasmons amplifications in single Ag nanoring,” Opt. Express18, 4006–4011 (2010). [CrossRef] [PubMed]
- A. G. Tudela, F. J. Rodriguez, L. Quiroga, and C. Tejedor, “Dissipative dynamics of a solid-state qubit coupled to surface plasmons: From non-Markov to Markov regimes,” Phys. Rev. B82, 115334 (2010). [CrossRef]
- D. Dzsotjan, A. S. Sørensen, and M. Fleischhauer, “Quantum emitters coupled to surface plasmons of a nanowire: A Green’s function approach,” Phys. Rev. B82, 075427 (2010). [CrossRef]
- W. Chen, G. Y. Chen, and Y. N. Chen, “Coherent transport of nanowire surface plasmons coupled to quantum dots,” Opt. Express18, 10360–10368 (2010). [CrossRef] [PubMed]
- A. Huck, S. Kumar, A. Shakoor, and U. L. Andersen, “Controlled coupling of a single nitrogen-vacancy center to a silver nanowire,” Phys. Rev. Lett.106, 096801 (2011). [CrossRef] [PubMed]
- J. Li and R. Yu, “Single-plasmon scattering grating using nanowire surface plasmon coupled to nanodiamond nitrogen-vacancy center,” Opt. Express19, 20991–21002 (2011). [CrossRef] [PubMed]
- D. Witthaut and A. S. Sørensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New Journal of Physics12, 043052 (2012). [CrossRef]
- Y. Li, L. Aolita, D. E. Chang, and L. C. Kwek, “Robust-fidelity atom-photon entangling gates in the weak-coupling regime,” Phys. Rev. Lett.109, 160504 (2012). [CrossRef] [PubMed]
- M. A. Nielsen and I. A. Chuang, Quantum Computing and Quantum Information (Cambridge, 2000).
- S. Haroche and J. M. Raimond, Exploring the Quantum (Oxford, 2006). [CrossRef]
- A. Gonzalez-Tudela, D. Martin-Cano, E. Moreno, L. Martin-Moreno, C. Tejedor, and F. J. Garcia-Vidal, “Entanglement of two qubits mediated by one-dimensional plasmonic waveguides,” Phys. Rev. Lett.106, 020501 (2011). [CrossRef] [PubMed]
- L. Slodickačka, G. Hétet, N. Röck, P. Schindler, M. Hennrich, and R. Blatt, “Atom-atom entanglement by single-photon detection,” Phys. Rev. Lett.110, 083603 (2013). [CrossRef] [PubMed]
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