Abstract

We propose a scheme for the distillation of partially entangled two-photon Bell and three-photon W states using metamaterials. The distillation of partially entangled Bell states is achieved by using two metamaterials with polarization dependence, one of which is rotated by π/2 around the direction of propagation of the photons. On the other hand, the distillation of three-photon W states is achieved by using one polarization dependent metamaterial and two polarization independent metamaterials. Upon transmission of the photons of the partially entangled states through the metamaterials the entanglement of the states increases and they become distilled. This work opens up new directions in quantum optical state engineering by showing how metamaterials can be used to carry out a quantum information processing task.

© 2015 Optical Society of America

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2014 (4)

A. Vora, J. Gwamuri, N. Pala, A. Kulkarni, J. M. Pearce, and D. O. Güney, “Exchanging Ohmic losses in metamaterial absorbers with useful optical absorption for photovoltaics,” Sci Rep 4, 4901 (2014).
[Crossref] [PubMed]

F. Dominec, C. Kadlec, H. Němec, P. Kužel, and F. Kadlec, “Transition between metamaterial and photonic-crystal behavior in arrays of dielectric rods,” Opt. Express 22(25), 30492–30503 (2014).
[Crossref] [PubMed]

F. Ozaydin, S. Bugu, C. Yesilyurt, A. A. Altintas, M. Tame, and Ş. K. Özdemir, “Fusing multiple W states simultaneously with a Fredkin gate,” Phys. Rev. A 89(4), 042311 (2014).
[Crossref]

K. R. McEnery, M. S. Tame, S. A. Maier, and M. S. Kim, “Tunable negative permeability in a quantum plasmonic metamaterial,” Phys. Rev. A 89(1), 013822 (2014).
[Crossref]

2013 (8)

L. Zhou, Y.-B. Sheng, W.-W. Cheng, L.-Y. Gong, and S.-M. Zhao, “Efficient entanglement concentration for arbitrary single-photon multimode W state,” J. Opt. Soc. Am. B 30(1), 71–78 (2013).
[Crossref]

Y. B. Sheng and L. Zhou, “Efficient W-state entanglement concentration using quantum-dot and optical microcavities,” J. Opt. Soc. Am. B 30(3), 678–686 (2013).
[Crossref]

T. J. Wang and G. L. Long, “Entanglement concentration for arbitrary unknown less-entangled three-photon W states with linear optics,” J. Opt. Soc. Am. B 30(4), 1069–1076 (2013).
[Crossref]

S. Arslanagic, T. V. Hansen, N. A. Mortensen, A. H. Gregersen, O. Sigmund, R. W. Ziolkowski, and O. Breinbjerg, “A review of the scattering-parameter extraction method with clarification of ambiguity issues in relation to metamaterial homogenization,” IEEE Antenn. Propag. M. 55(2), 91–106 (2013).
[Crossref]

M. S. Tame, K. R. McEnery, S. K. Ozdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]

B. J. Lawrie, P. G. Evans, and R. C. Pooser, “Extraordinary optical transmission of multimode quantum correlations via localized surface plasmons,” Phys. Rev. Lett. 110(15), 156802 (2013).
[Crossref] [PubMed]

M. I. Aslam and D. O. Güney, “On negative index metamaterial spacers and their unusual optical properties,” Prog. Electromagn. Res. B 47, 203–217 (2013).
[Crossref]

H. Odabasi, F. Teixeira, and D. O. Güney, “Electrically small, complementary electric-field-coupled resonator antennas,” J. Appl. Phys. 113(8), 084903 (2013).
[Crossref]

2012 (4)

2011 (5)

Ş. K. Özdemir, E. Matsunaga, T. Tashima, T. Yamamoto, M. Koashi, and N. Imoto, “An optical fusion gate for W-states,” New J. Phys. 13(10), 103003 (2011).
[Crossref]

C. García-Meca, J. Hurtado, J. Martí, A. Martínez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phys. Rev. Lett. 106(6), 067402 (2011).
[Crossref] [PubMed]

D. O. Güney, Th. Koschny, and C. M. Soukoulis, “Surface plasmon driven electric and magnetic resonators for metamaterials,” Phys. Rev. B 83(4), 045107 (2011).
[Crossref]

M. Ligare, “Propagation of quantized fields through negative-index media,” J. Mod. Opt. 58(17), 1551–1559 (2011).
[Crossref]

M. I. Aslam and D. O. Güney, “Surface plasmon driven scalable low-loss negative-index metamaterial in the visible spectrum,” Phys. Rev. B 84(19), 195465 (2011).
[Crossref]

2010 (4)

D. O. Güney, T. Koschny, and C. M. Soukoulis, “Intra-connected three-dimensionally isotropic bulk negative index photonic metamaterial,” Opt. Express 18(12), 12348–12353 (2010).
[Crossref] [PubMed]

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quantum Electron. 16(2), 367–375 (2010).
[Crossref]

D. Ballester, M. S. Tame, and M. S. Kim, “Quantum theory of surface-plasmon polariton scattering,” Phys. Rev. A 82(1), 012325 (2010).
[Crossref]

T. Tashima, T. Kitano, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Demonstration of local expansion toward large-scale entangled webs,” Phys. Rev. Lett. 105(21), 210503 (2010).
[Crossref] [PubMed]

2009 (9)

T. Tashima, S. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local expansion of photonic W state using a polarization-dependent beamsplitter,” New J. Phys. 11(2), 023024 (2009).
[Crossref]

T. Tashima, T. Wakatsuki, S. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon w state,” Phys. Rev. Lett. 102(13), 130502 (2009).
[Crossref] [PubMed]

H. Nemec, P. Kuzel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, “Tunable terahertz metamaterials with negative permeability,” Phys. Rev. B 79(24), 241108 (2009).
[Crossref]

M. Lapine, D. Powell, M. Gorkunov, I. Shadrivov, R. Marques, and Y. Kivshar, “Structural tunability in metamaterials,” Appl. Phys. Lett. 95(8), 084105 (2009).
[Crossref]

J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B 80(3), 035109 (2009).
[Crossref]

D. O. Güney, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Connected bulk negative index photonic metamaterials,” Opt. Lett. 34(4), 506–508 (2009).
[Crossref] [PubMed]

D. O. Güney and D. A. Meyer, “Negative refraction gives rise to the Klein paradox,” Phys. Rev. A 79(6), 063834 (2009).
[Crossref]

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[Crossref]

D. Ballester, M. S. Tame, C. Lee, J. Lee, and M. S. Kim, “Long-range surface plasmon-polariton excitation at the quantum level,” Phys. Rev. A 79(5), 053845 (2009).
[Crossref]

2008 (8)

M. S. Tame, C. Lee, J. Lee, D. Ballester, M. Paternostro, A. V. Zayats, and M. S. Kim, “Single-photon excitation of surface plasmon polaritons,” Phys. Rev. Lett. 101(19), 190504 (2008).
[Crossref] [PubMed]

T. Xu, Y. Zhao, J. Ma, C. Wang, J. Cui, C. Du, and X. Luo, “Sub-diffraction-limited interference photolithography with metamaterials,” Opt. Express 16(18), 13579–13584 (2008).
[Crossref] [PubMed]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

H.-T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008).
[Crossref]

M. V. Gorkunov and M. A. Osipov, “Tunability of wire-grid metamaterial immersed into nematic liquid crystal,” J. Appl. Phys. 103(3), 036101 (2008).
[Crossref]

T. H. Hand and S. A. Cummer, “Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings,” J. Appl. Phys. 103(6), 066105 (2008).
[Crossref]

T. Yamamoto, K. Hayashi, S. K. Özdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat. Photonics 2(8), 488–491 (2008).
[Crossref]

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater. 7(7), 543–546 (2008).
[Crossref] [PubMed]

2007 (7)

2006 (2)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443(7113), 838–841 (2006).
[Crossref] [PubMed]

2005 (3)

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2004 (2)

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1 Pt 2), 016608 (2004).
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2003 (3)

J. L. van Velsen, J. Tworzydlo, and C. W. J. Beenakker, “Scattering theory of plasmon-assisted entanglement transfer and distillation,” Phys. Rev. A 68(4), 043807 (2003).
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2002 (4)

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M. I. Aslam and D. O. Güney, “On negative index metamaterial spacers and their unusual optical properties,” Prog. Electromagn. Res. B 47, 203–217 (2013).
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M. I. Aslam and D. O. Güney, “Dual band double-negative polarization independent metamaterial for the visible spectrum,” J. Opt. Soc. Am. B 29(10), 2839–2847 (2012).
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M. S. Tame, C. Lee, J. Lee, D. Ballester, M. Paternostro, A. V. Zayats, and M. S. Kim, “Single-photon excitation of surface plasmon polaritons,” Phys. Rev. Lett. 101(19), 190504 (2008).
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J. L. van Velsen, J. Tworzydlo, and C. W. J. Beenakker, “Scattering theory of plasmon-assisted entanglement transfer and distillation,” Phys. Rev. A 68(4), 043807 (2003).
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Bell, S. E.

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R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443(7113), 838–841 (2006).
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S. Arslanagic, T. V. Hansen, N. A. Mortensen, A. H. Gregersen, O. Sigmund, R. W. Ziolkowski, and O. Breinbjerg, “A review of the scattering-parameter extraction method with clarification of ambiguity issues in relation to metamaterial homogenization,” IEEE Antenn. Propag. M. 55(2), 91–106 (2013).
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R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443(7113), 838–841 (2006).
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F. Ozaydin, S. Bugu, C. Yesilyurt, A. A. Altintas, M. Tame, and Ş. K. Özdemir, “Fusing multiple W states simultaneously with a Fredkin gate,” Phys. Rev. A 89(4), 042311 (2014).
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I. Bulu, H. Caglayan, K. Aydin, and E. Ozbay, “Compact size highly directive antennas based on the SRR metamaterial medium,” New J. Phys. 7, 223 (2005).
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I. Bulu, H. Caglayan, K. Aydin, and E. Ozbay, “Compact size highly directive antennas based on the SRR metamaterial medium,” New J. Phys. 7, 223 (2005).
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H.-T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials,” Nat. Photonics 2(5), 295–298 (2008).
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X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1 Pt 2), 016608 (2004).
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Cirac, J. I.

E. Moreno, F. J. García-Vidal, D. Erni, J. I. Cirac, and L. Martín-Moreno, “Theory of plasmon-assisted transmission of entangled photons,” Phys. Rev. Lett. 92(23), 236801 (2004).
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T. H. Hand and S. A. Cummer, “Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings,” J. Appl. Phys. 103(6), 066105 (2008).
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D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
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Dickson, W.

C. García-Meca, J. Hurtado, J. Martí, A. Martínez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phys. Rev. Lett. 106(6), 067402 (2011).
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Du, B.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
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Du, F.-F.

Erni, D.

E. Moreno, F. J. García-Vidal, D. Erni, J. I. Cirac, and L. Martín-Moreno, “Theory of plasmon-assisted transmission of entangled photons,” Phys. Rev. Lett. 92(23), 236801 (2004).
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B. J. Lawrie, P. G. Evans, and R. C. Pooser, “Extraordinary optical transmission of multimode quantum correlations via localized surface plasmons,” Phys. Rev. Lett. 110(15), 156802 (2013).
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C. García-Meca, J. Hurtado, J. Martí, A. Martínez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phys. Rev. Lett. 106(6), 067402 (2011).
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E. Moreno, F. J. García-Vidal, D. Erni, J. I. Cirac, and L. Martín-Moreno, “Theory of plasmon-assisted transmission of entangled photons,” Phys. Rev. Lett. 92(23), 236801 (2004).
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D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
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J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
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Gisin, N.

P. G. Kwiat, S. Barraza-Lopez, A. Stefanov, and N. Gisin, “Experimental entanglement distillation and ‘hidden’ non-locality,” Nature 409(6823), 1014–1017 (2001).
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Gong, L.-Y.

Gorkunov, M.

M. Lapine, D. Powell, M. Gorkunov, I. Shadrivov, R. Marques, and Y. Kivshar, “Structural tunability in metamaterials,” Appl. Phys. Lett. 95(8), 084105 (2009).
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M. V. Gorkunov and M. A. Osipov, “Tunability of wire-grid metamaterial immersed into nematic liquid crystal,” J. Appl. Phys. 103(3), 036101 (2008).
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S. Arslanagic, T. V. Hansen, N. A. Mortensen, A. H. Gregersen, O. Sigmund, R. W. Ziolkowski, and O. Breinbjerg, “A review of the scattering-parameter extraction method with clarification of ambiguity issues in relation to metamaterial homogenization,” IEEE Antenn. Propag. M. 55(2), 91–106 (2013).
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Grzegorczyk, T. M.

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1 Pt 2), 016608 (2004).
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B. Gu, D. Quan, and S. Xiao, “Multi-photon entanglement concentration protocol for partially entangled W states with projection measurement,” Int. J. Theor. Phys. 51(9), 2966–2973 (2012).
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B. Gu, “Single-photon-assisted entanglement concentration of partially entangled multiphoton W states with linear optics,” J. Opt. Soc. Am. B 29, 1685–1689 (2012).

Güney, D. O.

A. Vora, J. Gwamuri, N. Pala, A. Kulkarni, J. M. Pearce, and D. O. Güney, “Exchanging Ohmic losses in metamaterial absorbers with useful optical absorption for photovoltaics,” Sci Rep 4, 4901 (2014).
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M. I. Aslam and D. O. Güney, “On negative index metamaterial spacers and their unusual optical properties,” Prog. Electromagn. Res. B 47, 203–217 (2013).
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H. Odabasi, F. Teixeira, and D. O. Güney, “Electrically small, complementary electric-field-coupled resonator antennas,” J. Appl. Phys. 113(8), 084903 (2013).
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M. I. Aslam and D. O. Güney, “Dual band double-negative polarization independent metamaterial for the visible spectrum,” J. Opt. Soc. Am. B 29(10), 2839–2847 (2012).
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M. I. Aslam and D. O. Güney, “Surface plasmon driven scalable low-loss negative-index metamaterial in the visible spectrum,” Phys. Rev. B 84(19), 195465 (2011).
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D. O. Güney, Th. Koschny, and C. M. Soukoulis, “Surface plasmon driven electric and magnetic resonators for metamaterials,” Phys. Rev. B 83(4), 045107 (2011).
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D. O. Güney, T. Koschny, and C. M. Soukoulis, “Intra-connected three-dimensionally isotropic bulk negative index photonic metamaterial,” Opt. Express 18(12), 12348–12353 (2010).
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D. O. Güney, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Connected bulk negative index photonic metamaterials,” Opt. Lett. 34(4), 506–508 (2009).
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D. O. Güney and D. A. Meyer, “Negative refraction gives rise to the Klein paradox,” Phys. Rev. A 79(6), 063834 (2009).
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D. O. Güney and D. A. Meyer, “Creation of entanglement and implementation of quantum logic gate operations using a three-dimensional photonic crystal single-mode cavity,” J. Opt. Soc. Am. B 24(2), 283–294 (2007).
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D. O. Güney and D. A. Meyer, “Integrated conditional teleportation and readout circuit based on a photonic crystal single chip,” J. Opt. Soc. Am. B 24(2), 391–397 (2007).
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Gwamuri, J.

A. Vora, J. Gwamuri, N. Pala, A. Kulkarni, J. M. Pearce, and D. O. Güney, “Exchanging Ohmic losses in metamaterial absorbers with useful optical absorption for photovoltaics,” Sci Rep 4, 4901 (2014).
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Hand, T. H.

T. H. Hand and S. A. Cummer, “Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings,” J. Appl. Phys. 103(6), 066105 (2008).
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Hansen, T. V.

S. Arslanagic, T. V. Hansen, N. A. Mortensen, A. H. Gregersen, O. Sigmund, R. W. Ziolkowski, and O. Breinbjerg, “A review of the scattering-parameter extraction method with clarification of ambiguity issues in relation to metamaterial homogenization,” IEEE Antenn. Propag. M. 55(2), 91–106 (2013).
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P. He, P. V. Parimi, Y. He, V. G. Harris, and C. Vittoria, “Tunable negative refractive index metamaterial phase shifter,” Electron. Lett. 43(25), 1440–1441 (2007).
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T. Yamamoto, K. Hayashi, S. K. Özdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat. Photonics 2(8), 488–491 (2008).
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P. He, P. V. Parimi, Y. He, V. G. Harris, and C. Vittoria, “Tunable negative refractive index metamaterial phase shifter,” Electron. Lett. 43(25), 1440–1441 (2007).
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P. He, P. V. Parimi, Y. He, V. G. Harris, and C. Vittoria, “Tunable negative refractive index metamaterial phase shifter,” Electron. Lett. 43(25), 1440–1441 (2007).
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Hurtado, J.

C. García-Meca, J. Hurtado, J. Martí, A. Martínez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phys. Rev. Lett. 106(6), 067402 (2011).
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Imoto, N.

Ş. K. Özdemir, E. Matsunaga, T. Tashima, T. Yamamoto, M. Koashi, and N. Imoto, “An optical fusion gate for W-states,” New J. Phys. 13(10), 103003 (2011).
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T. Tashima, T. Kitano, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Demonstration of local expansion toward large-scale entangled webs,” Phys. Rev. Lett. 105(21), 210503 (2010).
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T. Tashima, T. Wakatsuki, S. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon w state,” Phys. Rev. Lett. 102(13), 130502 (2009).
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T. Tashima, S. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local expansion of photonic W state using a polarization-dependent beamsplitter,” New J. Phys. 11(2), 023024 (2009).
[Crossref]

T. Yamamoto, K. Hayashi, S. K. Özdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat. Photonics 2(8), 488–491 (2008).
[Crossref]

T. Yamamoto, M. Koashi, S. K. Özdemir, and N. Imoto, “Experimental extraction of an entangled photon pair from two identically decohered pairs,” Nature 421(6921), 343–346 (2003).
[Crossref] [PubMed]

Jost, J. D.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443(7113), 838–841 (2006).
[Crossref] [PubMed]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
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Kadlec, C.

F. Dominec, C. Kadlec, H. Němec, P. Kužel, and F. Kadlec, “Transition between metamaterial and photonic-crystal behavior in arrays of dielectric rods,” Opt. Express 22(25), 30492–30503 (2014).
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F. Dominec, C. Kadlec, H. Němec, P. Kužel, and F. Kadlec, “Transition between metamaterial and photonic-crystal behavior in arrays of dielectric rods,” Opt. Express 22(25), 30492–30503 (2014).
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H. Nemec, P. Kuzel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, “Tunable terahertz metamaterials with negative permeability,” Phys. Rev. B 79(24), 241108 (2009).
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Kafesaki, M.

D. O. Güney, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Connected bulk negative index photonic metamaterials,” Opt. Lett. 34(4), 506–508 (2009).
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J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B 80(3), 035109 (2009).
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Kang, L.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
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Khoo, I.-C.

Kildishev, A. V.

Kim, M. S.

K. R. McEnery, M. S. Tame, S. A. Maier, and M. S. Kim, “Tunable negative permeability in a quantum plasmonic metamaterial,” Phys. Rev. A 89(1), 013822 (2014).
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M. S. Tame, K. R. McEnery, S. K. Ozdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
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D. Ballester, M. S. Tame, and M. S. Kim, “Quantum theory of surface-plasmon polariton scattering,” Phys. Rev. A 82(1), 012325 (2010).
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D. Ballester, M. S. Tame, C. Lee, J. Lee, and M. S. Kim, “Long-range surface plasmon-polariton excitation at the quantum level,” Phys. Rev. A 79(5), 053845 (2009).
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M. S. Tame, C. Lee, J. Lee, D. Ballester, M. Paternostro, A. V. Zayats, and M. S. Kim, “Single-photon excitation of surface plasmon polaritons,” Phys. Rev. Lett. 101(19), 190504 (2008).
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Kitano, T.

T. Tashima, T. Kitano, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Demonstration of local expansion toward large-scale entangled webs,” Phys. Rev. Lett. 105(21), 210503 (2010).
[Crossref] [PubMed]

Kivshar, Y.

M. Lapine, D. Powell, M. Gorkunov, I. Shadrivov, R. Marques, and Y. Kivshar, “Structural tunability in metamaterials,” Appl. Phys. Lett. 95(8), 084105 (2009).
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Knill, E.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443(7113), 838–841 (2006).
[Crossref] [PubMed]

Koashi, M.

Ş. K. Özdemir, E. Matsunaga, T. Tashima, T. Yamamoto, M. Koashi, and N. Imoto, “An optical fusion gate for W-states,” New J. Phys. 13(10), 103003 (2011).
[Crossref]

T. Tashima, T. Kitano, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Demonstration of local expansion toward large-scale entangled webs,” Phys. Rev. Lett. 105(21), 210503 (2010).
[Crossref] [PubMed]

T. Tashima, S. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local expansion of photonic W state using a polarization-dependent beamsplitter,” New J. Phys. 11(2), 023024 (2009).
[Crossref]

T. Tashima, T. Wakatsuki, S. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon w state,” Phys. Rev. Lett. 102(13), 130502 (2009).
[Crossref] [PubMed]

T. Yamamoto, K. Hayashi, S. K. Özdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat. Photonics 2(8), 488–491 (2008).
[Crossref]

T. Yamamoto, M. Koashi, S. K. Özdemir, and N. Imoto, “Experimental extraction of an entangled photon pair from two identically decohered pairs,” Nature 421(6921), 343–346 (2003).
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M. S. Tame, C. Lee, J. Lee, D. Ballester, M. Paternostro, A. V. Zayats, and M. S. Kim, “Single-photon excitation of surface plasmon polaritons,” Phys. Rev. Lett. 101(19), 190504 (2008).
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Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
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T. Tashima, T. Kitano, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Demonstration of local expansion toward large-scale entangled webs,” Phys. Rev. Lett. 105(21), 210503 (2010).
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M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater. 7(7), 543–546 (2008).
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D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(3), 036617 (2005).
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T. Yamamoto, K. Hayashi, S. K. Özdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat. Photonics 2(8), 488–491 (2008).
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T. Yamamoto, M. Koashi, S. K. Özdemir, and N. Imoto, “Experimental extraction of an entangled photon pair from two identically decohered pairs,” Nature 421(6921), 343–346 (2003).
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Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
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Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
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P. He, P. V. Parimi, Y. He, V. G. Harris, and C. Vittoria, “Tunable negative refractive index metamaterial phase shifter,” Electron. Lett. 43(25), 1440–1441 (2007).
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IEEE Antenn. Propag. M. (1)

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IEEE J. Sel. Top. Quantum Electron. (1)

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quantum Electron. 16(2), 367–375 (2010).
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Int. J. Theor. Phys. (1)

B. Gu, D. Quan, and S. Xiao, “Multi-photon entanglement concentration protocol for partially entangled W states with projection measurement,” Int. J. Theor. Phys. 51(9), 2966–2973 (2012).
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M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater. 7(7), 543–546 (2008).
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T. Yamamoto, K. Hayashi, S. K. Özdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat. Photonics 2(8), 488–491 (2008).
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T. Tashima, S. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local expansion of photonic W state using a polarization-dependent beamsplitter,” New J. Phys. 11(2), 023024 (2009).
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Phys. Rev. B (5)

H. Nemec, P. Kuzel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, “Tunable terahertz metamaterials with negative permeability,” Phys. Rev. B 79(24), 241108 (2009).
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Prog. Electromagn. Res. B (1)

M. I. Aslam and D. O. Güney, “On negative index metamaterial spacers and their unusual optical properties,” Prog. Electromagn. Res. B 47, 203–217 (2013).
[Crossref]

Sci Rep (1)

A. Vora, J. Gwamuri, N. Pala, A. Kulkarni, J. M. Pearce, and D. O. Güney, “Exchanging Ohmic losses in metamaterial absorbers with useful optical absorption for photovoltaics,” Sci Rep 4, 4901 (2014).
[Crossref] [PubMed]

Science (1)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 (a) Distillation of partially entangled photons using (b) appropriately designed plasmonic metamaterials.
Fig. 2
Fig. 2 Two different views of the unit cell of a plasmonic metamaterial structure. The unit cell consists of a gold thin film in the middle and two gold nano-patterned structures on both sides of the thin film. The nano-patterned structures are the same on both sides except that they are diagonally shifted by a/ 2 in their planes with respect to each other where ais the unit cell size for the square lattice. The metamaterial is designed to be functional under normally incident light indicated by wave vector k and polarizations |0 and |1. The metamaterial can be designed as polarization-independent (or polarization dependent) by choosing the strip widths w 0 and w 1 equal (or slightly different).
Fig. 3
Fig. 3 (a) Reflectance (R), transmittance (T), and absorbance (A) of a polarization independent plasmonic metamaterial. Retrieved effective (b) refractive index, (c) relative electrical permittivity ( ε r = ε r +i ε r ) and relative magnetic permeability ( μ r = μ r +i μ r ). The strip widths w 0 = w 1 =40nm. The lattice constant a=80nm. The thicknesses of the thin film and the strips are 5nm and 11nm, respectively. The strips are separated from the thin film in the middle by 8nm. The thickness of the unit cell along the direction of propagation is 100nm. The dashed green line in (b) indicates the first Brillouin zone edge.
Fig. 4
Fig. 4 Transmittance for horizontally and vertically polarized light. w 0 =39nm, w 1 =45nm. Other parameters are the same as in Fig. 3.
Fig. 5
Fig. 5 Distillation of partially entangled Bell states | Φ 2 . The first photon (i.e., Photon 1) in the partially entangled state travels through the metamaterial of Design I and the second photon (i.e., Photon 2) travels through the metamaterial of Design I*. The transmittance of the metamaterial with Design I is | α | for the horizontal polarization |0 and | β | for the vertical polarization |1. The metamaterial of Design I* is obtained by rotating the Design I around k by π/2 . For example, for | α |=0.6 and | β |=0.8, Design I refers to the metamaterial structure operating at 396THz, considered in Fig. 4.
Fig. 6
Fig. 6 Distillation of partially entangled 3-photon W states | Φ 3 . The first photon (i.e., Photon 1) in the partially entangled state travels through the metamaterial of Design I2, the second (i.e., Photon 2) and third photons (i.e., Photon 3) travel through polarization-independent metamaterials of Design II. The transmittance of the metamaterial with Design I2 is | α | 2 for the horizontal polarization |0 and | β | 2 for the vertical polarization |1 (i.e., compare the required transmittances for Design I and Design I2 for the naming). The metamaterial with Design II has polarization independent transmittance | γ | 2 . For example, for | α | 2 =0.8 and | β | 2 =0.2, Design I2 refers to the metamaterial structure operating at 418THz, considered in Fig. 4, while Design II refers to the polarization independent metamaterial structure considered in Fig. 3, operating at the same frequency.

Equations (31)

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Q( |ψ )= 4 n j=1 n D( μ j ( 0 )|ψ, μ j ( 1 )|ψ ).
D( |u,|v )=  x<y | u x v y u y v x | 2
μ j ( b )| b 1   b n =  δ b b j | b 1   b j ^   b n .
| W n = 1 n ( |1 1 |0 2 |0 3 ... |0 n + |0 1 |1 2 |0 3 ... |0 n + |0 1 |0 2 |1 3 ... |0 n +...+ |0 1 |0 2 |0 3 ... |1 n ).
| W n = 1 n ( t ( 1 ) |1 1 |0 2 |0 3 ... |0 n + t ( 2 ) |0 1 |1 2 |0 3 ... |0 n + t ( 3 ) |0 1 |0 2 |1 3 ... |0 n +...+ t ( n ) |0 1 |0 2 |0 3 ... |1 n ),
t ( i ) = t 01 t 02   t 1i t 0n Z . 
Q( | W n )= 8 i<j | t [ i ] | 2 | t [ j ] | 2   n ( i=1 n | t [ i ] | 2 ) 2    ,
t [ i ] = t ( i ) Z= t 01 t 02   t 1i t 0n
Q( | W 3 )= 8 3 ( | t [ 1 ] | 2 | t [ 2 ] | 2 + | t [ 1 ] | 2 | t [ 3 ] | 2 + | t [ 2 ] | 2 | t [ 3 ] | 2 ) ( | t [ 1 ] | 2 + | t [ 2 ] | 2 + | t [ 3 ] | 2 ) 2  
Q( | W n )=Q( | W n )= 4( n1 ) n 2 .  
| Φ n =α |1 1 |0 2 |0 3 ... |0 n +β( |0 1 |1 2 |0 3 ... |0 n + |0 1 |0 2 |1 3 ... |0 n +...+ |0 1 |0 2 |0 3 ... |1 n ),
| α | 2 +( n1 ) | β | 2 =1.
| Φ n =α t ( 1 ) |1 1 |0 2 |0 3 ... |0 n +β( t ( 2 ) |0 1 |1 2 |0 3 ... |0 n + t ( 3 ) |0 1 |0 2 |1 3 ... |0 n +...+ t ( n ) |0 1 |0 2 |0 3 ... |1 n ).
Q( | Φ n )= 8 n ( | αβ t ( 1 ) | 2 i=2 n | t ( i ) | 2 + | β | 4 i=2 n i<j  | t ( i ) t ( j ) | 2 ).  
Q( | Φ 2 )= 4 | αβ | 2 τ 1 ( | α | 2 + | β | 2 τ 1 ) 2 ,
| t 01 |=| t 12 |= | α | ,
| t 11 |=| t 02 |= | β | .
Q( | Φ 3 )= 8 3 | αβ | 2 τ 2 + | β | 4 τ 3 2 ( | α | 2 + | β | 2 τ 2 ) 2 , 
τ 2 = ( | t [ 2 ] | 2 + | t [ 3 ] | 2 ) | t [ 1 ] | 2   ,
τ 3 = | t [ 2 ] || t [ 3 ] | | t [ 1 ] | 2 . 
τ 2 = u 2 + v 2 ,
τ 3 =uv,
u= | t [ 2 ] | | t [ 1 ] |  ,
v= | t [ 3 ] | | t [ 1 ] | .
u= τ 2 cosθ ,
v= τ 2 sinθ ,
Q( | Φ 3 )= 8 3 | αβ | 2 τ 2 + | β | 4 ( τ 2 2 sin( 2θ ) ) 2 ( | α | 2 + | β | 2 τ 2 ) 2 . 
u=v= | α | | β | .    
| t 02 | = | t 03 | = | t 12 |=| t 13 |,
| t 01 |=| α |,
| t 11 |=| β |, 

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