Abstract

The interaction between quantum emitters and graphene wrapped nanowire has been investigated using a Green's function technique. The eigenmodes for the graphene wrapped nanowire at various Fermi levels in graphene have been solved exactly. The Dicke subradiance and superradiance resulting from the graphene-mediated interaction have been observed. Based on these phenomena, we have proposed a scheme for a deterministic tunable two-qubit quantum phase gate. The “switching” effect for the quantum phase gate has been realized theoretically by changing an external voltage, which is very beneficial for the quantum-information processing.

© 2015 Optical Society of America

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References

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2015 (1)

K. J. Tielrooij, L. Orona, A. Ferrier, M. Badioli, G. Navickaite, S. Coop, S. Nanot, B. Kalinic, T. Cesca, L. Gaudreau, Q. Ma, A. Centeno, A. Pesquera, A. Zurutuza, H. de Riedmatten, P. Goldner, F. J. García de Abajo, P. Jarillo-Herrero, and F. H. L. Koppens, “Electrical control of optical emitter relaxation pathways enabled by graphene,” Nat. Phys. 11(3), 281–287 (2015).
[Crossref]

2014 (3)

P. Alonso-González, A. Y. Nikitin, F. Golmar, A. Centeno, A. Pesquera, S. Vélez, J. Chen, G. Navickaite, F. Koppens, A. Zurutuza, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Controlling graphene plasmons with resonant metal antennas and spatial conductivity patterns,” Science 344(6190), 1369–1373 (2014).
[Crossref] [PubMed]

J. Lee, W. Bao, L. Ju, P. J. Schuck, F. Wang, and A. Weber-Bargioni, “Switching individual quantum dot emission through electrically controlling resonant energy transfer to graphene,” Nano Lett. 14(12), 7115–7119 (2014).
[Crossref] [PubMed]

J. Ren, J. Yuan, and X. Zhang, “Multi-qubit quantum phase gates based on surface plasmons of a nanosphere,” J. Opt. Soc. Am. B 31(2), 229–236 (2014).
[Crossref]

2013 (6)

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(13), 15618–15626 (2013).
[Crossref] [PubMed]

A. González-Tudela, P. A. Huidobro, L. Martín-Moreno, C. Tejedor, and F. J. García-Vidal, “Theory of strong coupling between quantum emitters and propagating surface plasmons,” Phys. Rev. Lett. 110(12), 126801 (2013).
[Crossref] [PubMed]

T. Hümmer, F. J. García-Vidal, L. Martín-Moreno, and D. Zueco, “Weak and strong coupling regimes in plasmonic QED,” Phys. Rev. B 87(11), 115419 (2013).
[Crossref]

H. Zheng and H. U. Baranger, “Persistent quantum beats and long-distance entanglement from waveguide-mediated interactions,” Phys. Rev. Lett. 110(11), 113601 (2013).
[Crossref] [PubMed]

R. Chen, S. R. Das, C. Jeong, M. R. Khan, D. B. Janes, and M. A. Alam, “Co-percolating graphene-wrapped silver nanowire network for high performance, highly stable, transparent conducting electrodes,” Adv. Funct. Mater. 23(41), 5150–5158 (2013).
[Crossref]

R. D. Artuso and G. W. Bryant, “Quantum dot-quantum dot interactions mediated by a metal nanoparticle: Towards a fully quantum model,” Phys. Rev. B 87(12), 125423 (2013).
[Crossref]

2012 (7)

L. Vicarelli, M. S. Vitiello, D. Coquillat, A. Lombardo, A. C. Ferrari, W. Knap, M. Polini, V. Pellegrini, and A. Tredicucci, “Graphene field-effect transistors as room-temperature terahertz detectors,” Nat. Mater. 11(10), 865–871 (2012).
[Crossref] [PubMed]

S. A. Guebrou, C. Symonds, E. Homeyer, J. C. Plenet, Y. N. Gartstein, V. M. Agranovich, and J. Bellessa, “Coherent emission from a disordered organic semiconductor induced by strong coupling with surface plasmons,” Phys. Rev. Lett. 108(6), 066401 (2012).
[Crossref] [PubMed]

P. A. Huidobro, A. Y. Nikitin, C. González-Ballestero, L. Martín-Moreno, and F. J. García-Vidal, “Superradiance mediated by graphene surface plasmons,” Phys. Rev. B 85(15), 155438 (2012).
[Crossref]

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, “Microcavity-integrated graphene photodetector,” Nano Lett. 12(6), 2773–2777 (2012).
[Crossref] [PubMed]

A. Ferreira, N. M. R. Peres, R. M. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (2012).
[Crossref]

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett. 12(7), 3711–3715 (2012).
[Crossref] [PubMed]

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

2011 (12)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

A. Vakil and N. Engheta, “Transformation Optics Using Graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

K. A. Velizhanin and A. Efimov, “Probing plasmons in graphene by resonance energy transfer,” Phys. Rev. B 84(8), 085401 (2011).
[Crossref]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

J. E. Jin, J. H. Lee, D. H. Hwang, D. W. Kim, M. J. Kim, K. S. Son, D. Whang, and S. W. Hwang, “Graphene arch gate SiO2 shell silicon nanowire core field effect transistors,” Appl. Phys. Lett. 99(21), 212102 (2011).
[Crossref]

T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Reversible switching of ultrastrong light-molecule coupling,” Phys. Rev. Lett. 106(19), 196405 (2011).
[Crossref] [PubMed]

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

G. Gómez-Santos and T. Stauber, “Fluorescence quenching in graphene: A fundamental ruler and evidence for transverse plasmons,” Phys. Rev. B 84(16), 165438 (2011).
[Crossref]

M. L. Andersen, S. Stobbe, A. S. Sorensen, and P. Lodahl, “Strongly modified plasmon-matter interaction with mesoscopic quantum emitters,” Nat. Phys. 7(3), 215–218 (2011).
[Crossref]

D. Dzsotjan, J. Kästel, and M. Fleischhauer, “Dipole-dipole shift of quantum emitters coupled to surface plasmons of a nanowire,” Phys. Rev. B 84(7), 075419 (2011).
[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(2), 020501 (2011).
[Crossref] [PubMed]

D. Martín-Cano, A. González-Tudela, L. Martín-Moreno, F. J. García-Vidal, C. Tejedor, and E. Moreno, “Dissipation-driven generation of two-qubit entanglement mediated by plasmonic waveguides,” Phys. Rev. B 84(23), 235306 (2011).
[Crossref]

2010 (8)

D. Martín-Cano, L. Martín-Moreno, F. J. García-Vidal, and E. Moreno, “Resonance energy transfer and superradiance mediated by plasmonic nanowaveguides,” Nano Lett. 10(8), 3129–3134 (2010).
[Crossref] [PubMed]

Z.-J. Yang, N.-C. Kim, J.-B. Li, M.-T. Cheng, S.-D. Liu, Z.-H. Hao, and Q.-Q. Wang, “Surface plasmons amplifications in single Ag nanoring,” Opt. Express 18(5), 4006–4011 (2010).
[Crossref] [PubMed]

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 82(7), 075427 (2010).
[Crossref]

R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical Patch Antennas for Single Photon Emission Using Surface Plasmon Resonances,” Phys. Rev. Lett. 104(2), 026802 (2010).
[Crossref] [PubMed]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

N. M. R. Peres, “The transport properties of graphene: An introduction,” Rev. Mod. Phys. 82(3), 2673–2700 (2010).
[Crossref]

D. E. Gómez, K. C. Vernon, P. Mulvaney, and T. J. Davis, “Surface plasmon mediated strong exciton-photon coupling in semiconductor nanocrystals,” Nano Lett. 10(1), 274–278 (2010).
[Crossref] [PubMed]

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Ozyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
[Crossref] [PubMed]

2009 (5)

A. K. Geim, “Graphene: Status and prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

A. Salomon, C. Genet, and T. W. Ebbesen, “Molecule-light complex: dynamics of hybrid molecule-surface plasmon states,” Angew. Chem. Int. Ed. Engl. 48(46), 8748–8751 (2009).
[Crossref] [PubMed]

T. K. Hakala, J. J. Toppari, A. Kuzyk, M. Pettersson, H. Tikkanen, H. Kunttu, and P. Törmä, “Vacuum Rabi splitting and strong-coupling dynamics for surface-plasmon polaritons and rhodamine 6g molecules,” Phys. Rev. Lett. 103(5), 053602 (2009).
[Crossref] [PubMed]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

2008 (6)

A. Trügler and U. Hohenester, “Strong coupling between a metallic nanoparticle and a single molecule,” Phys. Rev. B 77(11), 115403 (2008).
[Crossref]

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(19), 2212–2214 (2008).
[Crossref] [PubMed]

P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, “Coherent exciton-surface-plasmon-polariton interaction in hybrid metal-semiconductor nanostructures,” Phys. Rev. Lett. 101(11), 116801 (2008).
[Crossref] [PubMed]

J. Bellessa, C. Symonds, C. Meynaud, J. C. Plenet, E. Cambril, A. Miard, L. Ferlazzo, and A. Lemaître, “Exciton/plasmon polaritons in GaAs/Al0.93Ga0.07As heterostructures near a metallic layer,” Phys. Rev. B 78(20), 205326 (2008).
[Crossref]

X. Wang, L. Zhi, and K. Müllen, “Transparent, conductive graphene electrodes for dye-sensitized solar cells,” Nano Lett. 8(1), 323–327 (2008).
[Crossref] [PubMed]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008).
[Crossref]

2007 (3)

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

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(3), 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,” Nature 450(7168), 402–406 (2007).
[Crossref] [PubMed]

2006 (3)

N. M. R. Peres, F. Guinea, and A. H. Castro Neto, “Electronic properties of disordered two-dimensional carbon,” Phys. Rev. B 73(12), 125411 (2006).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref] [PubMed]

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[Crossref] [PubMed]

2005 (1)

J. Dintinger, S. Klein, F. Bustos, W. L. Barnes, and T. W. Ebbesen, “Strong coupling between surface plasmon-polaritons and organic molecules in subwavelength hole arrays,” Phys. Rev. B 71(3), 035424 (2005).
[Crossref]

2004 (1)

J. Bellessa, C. Bonnand, J. C. Plenet, and J. Mugnier, “Strong coupling between surface plasmons and excitons in an organic semiconductor,” Phys. Rev. Lett. 93(3), 036404 (2004).
[Crossref] [PubMed]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Agranovich, V. M.

S. A. Guebrou, C. Symonds, E. Homeyer, J. C. Plenet, Y. N. Gartstein, V. M. Agranovich, and J. Bellessa, “Coherent emission from a disordered organic semiconductor induced by strong coupling with surface plasmons,” Phys. Rev. Lett. 108(6), 066401 (2012).
[Crossref] [PubMed]

Ahn, J.-H.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Ozyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
[Crossref] [PubMed]

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

Akimov, A. V.

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]

Alam, M. A.

R. Chen, S. R. Das, C. Jeong, M. R. Khan, D. B. Janes, and M. A. Alam, “Co-percolating graphene-wrapped silver nanowire network for high performance, highly stable, transparent conducting electrodes,” Adv. Funct. Mater. 23(41), 5150–5158 (2013).
[Crossref]

Alonso-González, P.

P. Alonso-González, A. Y. Nikitin, F. Golmar, A. Centeno, A. Pesquera, S. Vélez, J. Chen, G. Navickaite, F. Koppens, A. Zurutuza, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Controlling graphene plasmons with resonant metal antennas and spatial conductivity patterns,” Science 344(6190), 1369–1373 (2014).
[Crossref] [PubMed]

Andersen, M. L.

M. L. Andersen, S. Stobbe, A. S. Sorensen, and P. Lodahl, “Strongly modified plasmon-matter interaction with mesoscopic quantum emitters,” Nat. Phys. 7(3), 215–218 (2011).
[Crossref]

Andrews, A. M.

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, “Microcavity-integrated graphene photodetector,” Nano Lett. 12(6), 2773–2777 (2012).
[Crossref] [PubMed]

Anger, P.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[Crossref] [PubMed]

Artuso, R. D.

R. D. Artuso and G. W. Bryant, “Quantum dot-quantum dot interactions mediated by a metal nanoparticle: Towards a fully quantum model,” Phys. Rev. B 87(12), 125423 (2013).
[Crossref]

Badioli, M.

K. J. Tielrooij, L. Orona, A. Ferrier, M. Badioli, G. Navickaite, S. Coop, S. Nanot, B. Kalinic, T. Cesca, L. Gaudreau, Q. Ma, A. Centeno, A. Pesquera, A. Zurutuza, H. de Riedmatten, P. Goldner, F. J. García de Abajo, P. Jarillo-Herrero, and F. H. L. Koppens, “Electrical control of optical emitter relaxation pathways enabled by graphene,” Nat. Phys. 11(3), 281–287 (2015).
[Crossref]

Bae, S.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Ozyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
[Crossref] [PubMed]

Balakrishnan, J.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Ozyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
[Crossref] [PubMed]

Bao, W.

J. Lee, W. Bao, L. Ju, P. J. Schuck, F. Wang, and A. Weber-Bargioni, “Switching individual quantum dot emission through electrically controlling resonant energy transfer to graphene,” Nano Lett. 14(12), 7115–7119 (2014).
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Baranger, H. U.

H. Zheng and H. U. Baranger, “Persistent quantum beats and long-distance entanglement from waveguide-mediated interactions,” Phys. Rev. Lett. 110(11), 113601 (2013).
[Crossref] [PubMed]

Barnes, W. L.

J. Dintinger, S. Klein, F. Bustos, W. L. Barnes, and T. W. Ebbesen, “Strong coupling between surface plasmon-polaritons and organic molecules in subwavelength hole arrays,” Phys. Rev. B 71(3), 035424 (2005).
[Crossref]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Bechtel, H. A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Bellessa, J.

S. A. Guebrou, C. Symonds, E. Homeyer, J. C. Plenet, Y. N. Gartstein, V. M. Agranovich, and J. Bellessa, “Coherent emission from a disordered organic semiconductor induced by strong coupling with surface plasmons,” Phys. Rev. Lett. 108(6), 066401 (2012).
[Crossref] [PubMed]

J. Bellessa, C. Symonds, C. Meynaud, J. C. Plenet, E. Cambril, A. Miard, L. Ferlazzo, and A. Lemaître, “Exciton/plasmon polaritons in GaAs/Al0.93Ga0.07As heterostructures near a metallic layer,” Phys. Rev. B 78(20), 205326 (2008).
[Crossref]

J. Bellessa, C. Bonnand, J. C. Plenet, and J. Mugnier, “Strong coupling between surface plasmons and excitons in an organic semiconductor,” Phys. Rev. Lett. 93(3), 036404 (2004).
[Crossref] [PubMed]

Bharadwaj, P.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[Crossref] [PubMed]

Bonaccorso, F.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Bonnand, C.

J. Bellessa, C. Bonnand, J. C. Plenet, and J. Mugnier, “Strong coupling between surface plasmons and excitons in an organic semiconductor,” Phys. Rev. Lett. 93(3), 036404 (2004).
[Crossref] [PubMed]

Bryant, G. W.

R. D. Artuso and G. W. Bryant, “Quantum dot-quantum dot interactions mediated by a metal nanoparticle: Towards a fully quantum model,” Phys. Rev. B 87(12), 125423 (2013).
[Crossref]

Bustos, F.

J. Dintinger, S. Klein, F. Bustos, W. L. Barnes, and T. W. Ebbesen, “Strong coupling between surface plasmon-polaritons and organic molecules in subwavelength hole arrays,” Phys. Rev. B 71(3), 035424 (2005).
[Crossref]

Cambril, E.

J. Bellessa, C. Symonds, C. Meynaud, J. C. Plenet, E. Cambril, A. Miard, L. Ferlazzo, and A. Lemaître, “Exciton/plasmon polaritons in GaAs/Al0.93Ga0.07As heterostructures near a metallic layer,” Phys. Rev. B 78(20), 205326 (2008).
[Crossref]

Casanova, F.

P. Alonso-González, A. Y. Nikitin, F. Golmar, A. Centeno, A. Pesquera, S. Vélez, J. Chen, G. Navickaite, F. Koppens, A. Zurutuza, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Controlling graphene plasmons with resonant metal antennas and spatial conductivity patterns,” Science 344(6190), 1369–1373 (2014).
[Crossref] [PubMed]

Castro Neto, A. H.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[Crossref]

N. M. R. Peres, F. Guinea, and A. H. Castro Neto, “Electronic properties of disordered two-dimensional carbon,” Phys. Rev. B 73(12), 125411 (2006).
[Crossref]

Centeno, A.

K. J. Tielrooij, L. Orona, A. Ferrier, M. Badioli, G. Navickaite, S. Coop, S. Nanot, B. Kalinic, T. Cesca, L. Gaudreau, Q. Ma, A. Centeno, A. Pesquera, A. Zurutuza, H. de Riedmatten, P. Goldner, F. J. García de Abajo, P. Jarillo-Herrero, and F. H. L. Koppens, “Electrical control of optical emitter relaxation pathways enabled by graphene,” Nat. Phys. 11(3), 281–287 (2015).
[Crossref]

P. Alonso-González, A. Y. Nikitin, F. Golmar, A. Centeno, A. Pesquera, S. Vélez, J. Chen, G. Navickaite, F. Koppens, A. Zurutuza, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Controlling graphene plasmons with resonant metal antennas and spatial conductivity patterns,” Science 344(6190), 1369–1373 (2014).
[Crossref] [PubMed]

Cesca, T.

K. J. Tielrooij, L. Orona, A. Ferrier, M. Badioli, G. Navickaite, S. Coop, S. Nanot, B. Kalinic, T. Cesca, L. Gaudreau, Q. Ma, A. Centeno, A. Pesquera, A. Zurutuza, H. de Riedmatten, P. Goldner, F. J. García de Abajo, P. Jarillo-Herrero, and F. H. L. Koppens, “Electrical control of optical emitter relaxation pathways enabled by graphene,” Nat. Phys. 11(3), 281–287 (2015).
[Crossref]

Chang, D. E.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[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]

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(3), 035420 (2007).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref] [PubMed]

Chen, G.-Y.

Chen, J.

P. Alonso-González, A. Y. Nikitin, F. Golmar, A. Centeno, A. Pesquera, S. Vélez, J. Chen, G. Navickaite, F. Koppens, A. Zurutuza, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Controlling graphene plasmons with resonant metal antennas and spatial conductivity patterns,” Science 344(6190), 1369–1373 (2014).
[Crossref] [PubMed]

Chen, R.

R. Chen, S. R. Das, C. Jeong, M. R. Khan, D. B. Janes, and M. A. Alam, “Co-percolating graphene-wrapped silver nanowire network for high performance, highly stable, transparent conducting electrodes,” Adv. Funct. Mater. 23(41), 5150–5158 (2013).
[Crossref]

Chen, Y.-N.

Cheng, M.-T.

Choi, C.-G.

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

Choi, H. K.

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

Choi, J.-Y.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

Choi, M.

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

Choi, S.-Y.

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

Chuu, D.-S.

Coop, S.

K. J. Tielrooij, L. Orona, A. Ferrier, M. Badioli, G. Navickaite, S. Coop, S. Nanot, B. Kalinic, T. Cesca, L. Gaudreau, Q. Ma, A. Centeno, A. Pesquera, A. Zurutuza, H. de Riedmatten, P. Goldner, F. J. García de Abajo, P. Jarillo-Herrero, and F. H. L. Koppens, “Electrical control of optical emitter relaxation pathways enabled by graphene,” Nat. Phys. 11(3), 281–287 (2015).
[Crossref]

Coquillat, D.

L. Vicarelli, M. S. Vitiello, D. Coquillat, A. Lombardo, A. C. Ferrari, W. Knap, M. Polini, V. Pellegrini, and A. Tredicucci, “Graphene field-effect transistors as room-temperature terahertz detectors,” Nat. Mater. 11(10), 865–871 (2012).
[Crossref] [PubMed]

Das, S. R.

R. Chen, S. R. Das, C. Jeong, M. R. Khan, D. B. Janes, and M. A. Alam, “Co-percolating graphene-wrapped silver nanowire network for high performance, highly stable, transparent conducting electrodes,” Adv. Funct. Mater. 23(41), 5150–5158 (2013).
[Crossref]

Davis, T. J.

D. E. Gómez, K. C. Vernon, P. Mulvaney, and T. J. Davis, “Surface plasmon mediated strong exciton-photon coupling in semiconductor nanocrystals,” Nano Lett. 10(1), 274–278 (2010).
[Crossref] [PubMed]

de Riedmatten, H.

K. J. Tielrooij, L. Orona, A. Ferrier, M. Badioli, G. Navickaite, S. Coop, S. Nanot, B. Kalinic, T. Cesca, L. Gaudreau, Q. Ma, A. Centeno, A. Pesquera, A. Zurutuza, H. de Riedmatten, P. Goldner, F. J. García de Abajo, P. Jarillo-Herrero, and F. H. L. Koppens, “Electrical control of optical emitter relaxation pathways enabled by graphene,” Nat. Phys. 11(3), 281–287 (2015).
[Crossref]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Detz, H.

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, “Microcavity-integrated graphene photodetector,” Nano Lett. 12(6), 2773–2777 (2012).
[Crossref] [PubMed]

Dintinger, J.

J. Dintinger, S. Klein, F. Bustos, W. L. Barnes, and T. W. Ebbesen, “Strong coupling between surface plasmon-polaritons and organic molecules in subwavelength hole arrays,” Phys. Rev. B 71(3), 035424 (2005).
[Crossref]

Dzsotjan, D.

D. Dzsotjan, J. Kästel, and M. Fleischhauer, “Dipole-dipole shift of quantum emitters coupled to surface plasmons of a nanowire,” Phys. Rev. B 84(7), 075419 (2011).
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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 82(7), 075427 (2010).
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Ebbesen, T. W.

T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Reversible switching of ultrastrong light-molecule coupling,” Phys. Rev. Lett. 106(19), 196405 (2011).
[Crossref] [PubMed]

A. Salomon, C. Genet, and T. W. Ebbesen, “Molecule-light complex: dynamics of hybrid molecule-surface plasmon states,” Angew. Chem. Int. Ed. Engl. 48(46), 8748–8751 (2009).
[Crossref] [PubMed]

J. Dintinger, S. Klein, F. Bustos, W. L. Barnes, and T. W. Ebbesen, “Strong coupling between surface plasmon-polaritons and organic molecules in subwavelength hole arrays,” Phys. Rev. B 71(3), 035424 (2005).
[Crossref]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Efimov, A.

K. A. Velizhanin and A. Efimov, “Probing plasmons in graphene by resonance energy transfer,” Phys. Rev. B 84(8), 085401 (2011).
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Engheta, N.

A. Vakil and N. Engheta, “Transformation Optics Using Graphene,” Science 332(6035), 1291–1294 (2011).
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Esteban, R.

R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical Patch Antennas for Single Photon Emission Using Surface Plasmon Resonances,” Phys. Rev. Lett. 104(2), 026802 (2010).
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Falkovsky, L. A.

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

Ferlazzo, L.

J. Bellessa, C. Symonds, C. Meynaud, J. C. Plenet, E. Cambril, A. Miard, L. Ferlazzo, and A. Lemaître, “Exciton/plasmon polaritons in GaAs/Al0.93Ga0.07As heterostructures near a metallic layer,” Phys. Rev. B 78(20), 205326 (2008).
[Crossref]

Ferrari, A. C.

L. Vicarelli, M. S. Vitiello, D. Coquillat, A. Lombardo, A. C. Ferrari, W. Knap, M. Polini, V. Pellegrini, and A. Tredicucci, “Graphene field-effect transistors as room-temperature terahertz detectors,” Nat. Mater. 11(10), 865–871 (2012).
[Crossref] [PubMed]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Ferreira, A.

A. Ferreira, N. M. R. Peres, R. M. Ribeiro, and T. Stauber, “Graphene-based photodetector with two cavities,” Phys. Rev. B 85(11), 115438 (2012).
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K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
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S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
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S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Ozyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
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L. Vicarelli, M. S. Vitiello, D. Coquillat, A. Lombardo, A. C. Ferrari, W. Knap, M. Polini, V. Pellegrini, and A. Tredicucci, “Graphene field-effect transistors as room-temperature terahertz detectors,” Nat. Mater. 11(10), 865–871 (2012).
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L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett. 12(7), 3711–3715 (2012).
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Koppens, F.

P. Alonso-González, A. Y. Nikitin, F. Golmar, A. Centeno, A. Pesquera, S. Vélez, J. Chen, G. Navickaite, F. Koppens, A. Zurutuza, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Controlling graphene plasmons with resonant metal antennas and spatial conductivity patterns,” Science 344(6190), 1369–1373 (2014).
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Koppens, F. H. L.

K. J. Tielrooij, L. Orona, A. Ferrier, M. Badioli, G. Navickaite, S. Coop, S. Nanot, B. Kalinic, T. Cesca, L. Gaudreau, Q. Ma, A. Centeno, A. Pesquera, A. Zurutuza, H. de Riedmatten, P. Goldner, F. J. García de Abajo, P. Jarillo-Herrero, and F. H. L. Koppens, “Electrical control of optical emitter relaxation pathways enabled by graphene,” Nat. Phys. 11(3), 281–287 (2015).
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P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, “Coherent exciton-surface-plasmon-polariton interaction in hybrid metal-semiconductor nanostructures,” Phys. Rev. Lett. 101(11), 116801 (2008).
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T. K. Hakala, J. J. Toppari, A. Kuzyk, M. Pettersson, H. Tikkanen, H. Kunttu, and P. Törmä, “Vacuum Rabi splitting and strong-coupling dynamics for surface-plasmon polaritons and rhodamine 6g molecules,” Phys. Rev. Lett. 103(5), 053602 (2009).
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J. Lee, W. Bao, L. Ju, P. J. Schuck, F. Wang, and A. Weber-Bargioni, “Switching individual quantum dot emission through electrically controlling resonant energy transfer to graphene,” Nano Lett. 14(12), 7115–7119 (2014).
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J. E. Jin, J. H. Lee, D. H. Hwang, D. W. Kim, M. J. Kim, K. S. Son, D. Whang, and S. W. Hwang, “Graphene arch gate SiO2 shell silicon nanowire core field effect transistors,” Appl. Phys. Lett. 99(21), 212102 (2011).
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S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
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S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
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S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
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K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
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S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Ozyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
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S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Ozyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
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P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, “Coherent exciton-surface-plasmon-polariton interaction in hybrid metal-semiconductor nanostructures,” Phys. Rev. Lett. 101(11), 116801 (2008).
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M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, “Microcavity-integrated graphene photodetector,” Nano Lett. 12(6), 2773–2777 (2012).
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Lin, G. W.

Liu, M.

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
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D. Martín-Cano, L. Martín-Moreno, F. J. García-Vidal, and E. Moreno, “Resonance energy transfer and superradiance mediated by plasmonic nanowaveguides,” Nano Lett. 10(8), 3129–3134 (2010).
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P. Vasa, R. Pomraenke, S. Schwieger, Y. I. Mazur, V. Kunets, P. Srinivasan, E. Johnson, J. E. Kihm, D. S. Kim, E. Runge, G. Salamo, and C. Lienau, “Coherent exciton-surface-plasmon-polariton interaction in hybrid metal-semiconductor nanostructures,” Phys. Rev. Lett. 101(11), 116801 (2008).
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J. Bellessa, C. Symonds, C. Meynaud, J. C. Plenet, E. Cambril, A. Miard, L. Ferlazzo, and A. Lemaître, “Exciton/plasmon polaritons in GaAs/Al0.93Ga0.07As heterostructures near a metallic layer,” Phys. Rev. B 78(20), 205326 (2008).
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S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
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D. Martín-Cano, A. González-Tudela, L. Martín-Moreno, F. J. García-Vidal, C. Tejedor, and E. Moreno, “Dissipation-driven generation of two-qubit entanglement mediated by plasmonic waveguides,” Phys. Rev. B 84(23), 235306 (2011).
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D. Martín-Cano, L. Martín-Moreno, F. J. García-Vidal, and E. Moreno, “Resonance energy transfer and superradiance mediated by plasmonic nanowaveguides,” Nano Lett. 10(8), 3129–3134 (2010).
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M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, and T. Mueller, “Microcavity-integrated graphene photodetector,” Nano Lett. 12(6), 2773–2777 (2012).
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X. Wang, L. Zhi, and K. Müllen, “Transparent, conductive graphene electrodes for dye-sensitized solar cells,” Nano Lett. 8(1), 323–327 (2008).
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K. J. Tielrooij, L. Orona, A. Ferrier, M. Badioli, G. Navickaite, S. Coop, S. Nanot, B. Kalinic, T. Cesca, L. Gaudreau, Q. Ma, A. Centeno, A. Pesquera, A. Zurutuza, H. de Riedmatten, P. Goldner, F. J. García de Abajo, P. Jarillo-Herrero, and F. H. L. Koppens, “Electrical control of optical emitter relaxation pathways enabled by graphene,” Nat. Phys. 11(3), 281–287 (2015).
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P. Alonso-González, A. Y. Nikitin, F. Golmar, A. Centeno, A. Pesquera, S. Vélez, J. Chen, G. Navickaite, F. Koppens, A. Zurutuza, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Controlling graphene plasmons with resonant metal antennas and spatial conductivity patterns,” Science 344(6190), 1369–1373 (2014).
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P. A. Huidobro, A. Y. Nikitin, C. González-Ballestero, L. Martín-Moreno, and F. J. García-Vidal, “Superradiance mediated by graphene surface plasmons,” Phys. Rev. B 85(15), 155438 (2012).
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Figures (6)

Fig. 1
Fig. 1 Two emitters with electric moments d A and d B (vertical to the axis of the wire) near a graphene wrapped nanowire. The distance between them is marked by d, and the distance between the two QEs and the axis of the wire is r A . The radius of the nanowire is R.
Fig. 2
Fig. 2 (a) Allowed k z components of the guided modes for a graphene wrapped nanowire with the permittivity ε 1 =-50 (the absorption of graphene and nanowire is ignored) as a function of the wire radii R, the lines in different colors represent different cylindrical harmonic order n, and the Fermi level is taken as 0.62eV . (b) The fundamental mode (n = 0) with different Fermi levels in the radius region from R/ λ 0 =0.0100 to R/ λ 0 =0.0104 and (c) in the region from R/ λ 0 =0.0080 to R/ λ 0 =0.0084 .
Fig. 3
Fig. 3 The k z component of the fundamental mode as a function of the Fermi level, when the radius of the nanowire is fixed at R=0.008 λ 0 (a) and R=0.01 λ 0 (b). (c) Optical conductivity of the uniform graphene. Here the wavelength λ=1μm is taken, and 1/γ=0.25ps . The solid and dashed lines represent the real and imaginary parts of the conductivity, respectively. And in order to show a clear corresponding to the above two pictures, the x-axis in Fig. 3(c) has been marked by the Fermi level, not the energy of the incident photons.
Fig. 4
Fig. 4 The imaginary part of the r ^ r ^ component of the Green's tensor for n = 0 mode, Im[ G rr (0) ( r A , r A ,ω; k z )] , as a function of k z λ 0 with different Fermi levels around the resonance frequency k z at R/ λ 0 =0.008 (a) and R/ λ 0 =0.01 (b). The dash line represents the naked metal wire. (c) and (d) show Im[ G rr (0) ( r A , r A ,ω; k z )] and its half-width at half maximum (HWHM) of the resonance peak as a function of the Fermi level, respectively. The other parameters of the system are taken as ε 1 =-50+0.6i , and r A =1.5R .
Fig. 5
Fig. 5 (a) The interference term Γ AB /Γ as a function of the QE distance from the nanowire axis with various Fermi levels E f = 1.5eV, 0.62eV and 0.1eV at d/ λ 0 =0.83 . (b)The interference term Γ AB /Γ as a function of the distance d/ λ 0 between the two QEs with various Fermi levels E f = 1.5eV, 0.62eV and 0.1eV at r A =2.5R . The other parameters of the system are taken as ε 1 =-50+0.6i and R=0.01 λ 0 .
Fig. 6
Fig. 6 (a) Realization of a deterministic two-qubit tunable quantum phase gate by applying external classical 2π pulses using |gg , |sg , |se , |gs , |es , subradiant and superradiant states. (b) The fidelity as a function of the distance between two QEs with various Fermi levels. The other parameters are taken as R/ λ 0 =0.01 and r A =2.5R . (c) The fidelity as a function of the distance between two QEs with wire R/ λ 0 =0.008 (blue), R/ λ 0 =0.01 (red) and R/ λ 0 =0.02 (black). In such a case, E f =1.5eV and r A =2.5R . (d) The fidelity as a function of the Fermi level at R/ λ 0 =0.005 and r A =2.5R when the distances between two QEs are 0.684 λ 0 (black), 0.912 λ 0 (blue) and 1.14 λ 0 (red).

Equations (18)

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H ^ = d 3 r 0 dω ω f ^ ( r ,ω) f ^ ( r ,ω)+ A 1 2 ω A σ ^ Az A [ σ ^ A E ^ (+) ( r A ) d A +H.c.] ,
E ^ (+) ( r )=i π ε 0 0 dω ω 2 c 2 d 3 r ε I ( r ,ω) G ( r , r ,ω) f ^ ( r ,ω),
G 0 ( r , r ,ω)= r ^ r ^ δ( r r ) k 0 2 + i 8π d k z n=0 2 δ n,0 k r 0 2 × { M e o 1 n ( k z , r ) M e o n ( k z , r )+ N e o 1 n ( k z , r ) N e o n ( k z , r )] [ M e o n ( k z , r ) M e o 1 n ( k z , r )+ N e o n ( k z , r ) N e o 1 n ( k z , r )] r> r r< r ,
G S ( r , r ,ω)= i 8π d k z n=0 2 δ n,0 k r 0 2 ×{[ A o e n R M e o 1 n ( k z , r )+ B e o n R N o e 1 n ( k z , r )] M e o 1 n ( k z , r )+ [ C o e n R N e o 1 n ( k z , r )+ D e o n R M o e 1 n ( k z , r )] N e o 1 n ( k z , r )},
G T ( r , r ,ω)= i 8π d k z n=0 2 δ n,0 k r 0 2 ×{[ A o e n T M e o 1 n ( k z , r )+ B e o n T N o e 1 n ( k z , r )] M e o 1 n ( k z , r )+ [ C o e n T N e o 1 n ( k z , r )+ D e o n T M o e 1 n ( k z , r )] N e o 1 n ( k z , r )},
( M e,n ( k z r) M o,n ( k z r) )=×[ Z n ( k r 0,1 r)( cosnϕ sinnϕ ) e i k z z z ^ ] ( N e,n ( k z r) N o,n ( k z r) )= 1 k 0,1 ×( M e,n ( k z r) M o,n ( k z r) ).
n 2 k z 2 a 2 ( 1 k r0 2 1 k r1 2 ) 2 ( σ s ω k r0 μ 0 k r1 2 k r0 2 H n ( ρ 0 ) H n ( ρ 0 ) +i)( σ s ω k r1 μ 1 k r1 2 k r0 2 J n ( ρ 1 ) J n ( ρ 1 ) +i)= {[ 1 k r0 H n ( ρ 0 ) H n ( ρ 0 ) 1 k r1 J n ( ρ 1 ) J n ( ρ 1 ) ]+ i σ s ω μ 0 k r1 k r0 H n ( ρ 0 ) H n ( ρ 0 ) J n ( ρ 1 ) J n ( ρ 1 ) } ×{[ k 0 2 k r0 H n ( ρ 0 ) H n ( ρ 0 ) k 1 2 k r1 J n ( ρ 1 ) J n ( ρ 1 ) ]+i σ s ω μ 0 (1+ n 2 k z 2 a 2 k r1 2 k r0 2 )}.
σ i = σ 0 (1+ 1 π arctan ω2 E f γ 1 π arctan ω+2 E f γ ),
σ i = σ 0 1 2π ln (2 E f +ω) 2 + (γ) 2 (2 E f ω) 2 + (γ) 2 ,
|ψ(t)= A C A (t) e i( ω A ω ¯ )t |A|{0} + d 3 r 0 dω[ C Li ( r ,ω,t) e i( ω A ω ¯ )t |L|{ 1 i ( r ,ω)}] ,
C 1 (t)= 0 t d t K 1 (t t ) C 1 ( t ) C 2 (t)= 0 t d t K 2 (t t ) C 2 ( t ) ,
K AB (t t )= 1 π ε 0 0 dω ω 2 c 2 e i(ω ω A )(t t ) d A Im G ( r A , r B ,ω) d B ,
C 1 (t)= e ( Γ 1 /2+i δ 1 )t C 1 (0) C 2 (t)= e ( Γ 2 /2+i δ 2 )t C 2 (0),
Γ AB = 2 k A 2 ε 0 d A Im G ( r A , r B , ω A ) d B ,
Γ= 2 k A 2 ε 0 d A Im G ( r A , r A , ω A ) d A .
G ( r A , r A , ω A )= n [ 0 k 0 d k z G (n) ( r A , r A , ω A ; k z )+ k 0 d k z G (n) ( r A , r A , ω A ; k z ) ],
[ k r 0 H n ( ρ 0 ) in k z k 0 a H n ( ρ 0 ) k r 1 J n ( ρ 1 ) ± in k z k 1 a J n ( ρ 1 ) 0 k r 0 2 k 0 H n ( ρ 0 ) 0 k r 1 2 k 1 J n ( ρ 1 ) i[ k r 0 2 ω μ 0 H n ( ρ 0 ) i σ S k r 0 H n ( ρ 0 )] ± i σ S n k z k 0 a H n ( ρ 0 ) i k r 1 2 ω μ 1 J n ( ρ 1 ) 0 n k z ω μ 0 a H n ( ρ 0 ) i k 0 k r 0 ω μ 0 H n ( ρ 0 ) ± n k z ω μ 1 a J n ( ρ 1 ) i k 1 k r 1 ω μ 1 J n ( ρ 1 ) + σ S k r 1 2 k 1 J n ( ρ 1 ) ][ D e o n R C o e n R D e o n T C o e n T ]=[ ± in k z k 0 a J n ( ρ 0 ) k r 0 2 k 0 J n ( ρ 0 ) i σ S n k z k 0 a J n ( ρ 0 ) i k 0 k r 0 ω μ 0 J n ( ρ 0 ) ]
[ k r 0 H n ( ρ 0 ) in k z k 0 a H n ( ρ 0 ) k r 1 J n ( ρ 1 ) ± in k z k 1 a J n ( ρ 1 ) 0 k r 0 2 k 0 H n ( ρ 0 ) 0 k r 1 2 k 1 J n ( ρ 1 ) [ i k r 0 2 ω μ 0 H n ( ρ 0 ) + σ S k r 0 H n ( ρ 0 )] ± i σ S n k z k 0 a H n ( ρ 0 ) i k r 1 2 ω μ 1 J n ( ρ 1 ) 0 n k z ω μ 0 a H n ( ρ 0 ) i k 0 k r 0 ω μ 0 H n ( ρ 0 ) ± n k z ω μ 1 a J n ( ρ 1 ) [ i k 1 k r 1 ω μ 1 J n ( ρ 1 ) + σ S k r 1 2 k 1 J n ( ρ 1 )] ][ A o e n R B e o n R A o e n T B e o n T ]=[ k r 0 J n ( ρ 0 ) 0 [ σ S k r 0 J n ( ρ 0 ) i k r 0 2 J n ( ρ 0 ) ω μ 0 ] ± n k z J n ( ρ 0 ) ω μ 0 a ].

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