Abstract

We introduce and theoretically investigate a scheme for teleportation of two-frequency entangled optical images in which the quantum channel is formed by four-frequency multimode states, generated in a single nonlinear photonic crystal by coupled parametric interactions. We study in detail the performance of the scheme. Namely, we evaluate its fidelity and the spatial-frequency spectra of the quadrature components characterizing the deterioration of the entanglement in the initial images due to the teleportation process. We analyze the influence of the spatial bandwidth of entanglement on the fidelity of teleportation. We investigate the performance of the scheme both in the near and the far diffraction field. Our analysis suggests that bandwidth matching of the quantum channel field with that of the images is generally necessary for high-quality teleportation. We show that entangled images are more fragile and more difficult to teleport than their coherent counterparts.

© 2012 Optical Society of America

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  1. C. Bennett, G. Brassad, C. Crepeau, R. Jozsa, A. Peres, and W. Wotters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
    [CrossRef]
  2. L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A 49, 1473–1476 (1994).
    [CrossRef]
  3. S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
    [CrossRef]
  4. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
    [CrossRef]
  5. A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
    [CrossRef]
  6. X. Jia, X. Su, Q. Pan, J. Gao, C. Xie, and K. Peng, “Experimental demonstration of unconditional entanglement swapping for continuous variables,” Phys. Rev. Lett. 93, 250503 (2004).
    [CrossRef]
  7. N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
    [CrossRef]
  8. I. V. Sokolov, M. I. Kolobov, A. Gatti, and L. A. Lugiato, “Quantum holographic teleportation,” Opt. Commun. 193, 175–180 (2001).
    [CrossRef]
  9. A. Gatti, I. V. Sokolov, M. I. Kolobov, and L. A. Lugiato, “Quantum fluctuations in holographic teleportation of optical images,” Euro. Phys. J. D 30, 123–135 (2004).
    [CrossRef]
  10. L. V. Magdenko, I. V. Sokolov, and M. I. Kolobov, “Quantum teleportation of optical images with frequency conversion,” Opt. Spectrosc. 103, 62–66 (2007).
    [CrossRef]
  11. A. Furusawa and N. Takei, “Quantum teleportation for continuous variables and related quantum information processing,” Phys. Rep. 443, 97–119 (2007).
    [CrossRef]
  12. S. L. Braunstein and A. K. Pati, Quantum Information with Continuous Variables (Springer, 2003).
  13. N. J. Cerf, G. Leuchs, and E. S. Polzik, Quantum Information with Continuous Variables of Atoms and Light (World Scientific, 2007).
  14. M. I. Kolobov, Quantum Imaging (Springer, 2007).
  15. A. V. Rodionov and A. S. Chirkin, “Entangled photon states in consecutive nonlinear optical interactions,” J. Exp. Theor. Phys. Lett. 79, 253–256 (2004), translated from Pis’ma v Z. Eksp. Teor. Fiz. 79, 311314 (2004).
    [CrossRef]
  16. A. Ferraro, M. Paris, M. Bondani, A. Allevi, E. Puddi, and A. Adreoni, “Three-mode entanglement by interlinked nonlinear interactions in optical χ(2) media,” J. Opt. Soc. Am. B 21, 1241–1249 (2004).
    [CrossRef]
  17. A. S. Chirkin and M. Yu. Saigin, “Statistic and information characterization of tripartite entangled states,” J. Russ. Laser Res. 28, 505–515 (2007).
    [CrossRef]
  18. C. Pannarun, A. Bradley, and M. Olsen, “Tripartite entanglement and threshold properties of coupled intracavity down-conversion and sum-frequency generation,” Phys. Rev. A 76, 063812 (2007).
    [CrossRef]
  19. A. S. Chirkin, M. Yu. Saygin, and I. V. Shutov, “Parametric amplification at low-frequency pumping and generation of four-mode entangled states,” J. Russ. Laser Res. 29, 336–346 (2008).
    [CrossRef]
  20. A. S. Chirkin and M. Yu. Saigin, “Four-mode entangled states in coupled nonlinear optical processes and teleportation of two-mode entangled CV state,” Phys. Scr. T135, 014029 (2009).
    [CrossRef]
  21. A. S. Chirkin and I. V. Shutov, “On the possibility of the nondegenerate parametric amplification of optical waves at low-frequency pumping,” J. Exp. Theor. Phys. Lett. 86, 693–697 (2008), translated from Pis’ma v Z. Eksp. Teor. Fiz. 86, 803807 (2007);
    [CrossRef]
  22. A. S. Chirkin and I. V. Shutov, “Parametric amplification of light waves at low-frequency pumping in aperiodic nonlinear photonic crystals,” J. Exp. Theor. Phys. 109, 547–556 (2009), translated from Z. Eksp. Teor. Fiz. 136, 639649 (2009).
    [CrossRef]
  23. L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
    [CrossRef]
  24. M. Yu. Saygin and A. S. Chirkin, “Simultaneous parametric generation and up-conversion of entangled optical images,” J. Exp. Theor. Phys. 111, 11–21 (2010), translated from Pis’ma v Z. Eksp. Teor. Fiz. 138, 16–27 (2010).
    [CrossRef]
  25. M. Yu. Saygin and A. S. Chirkin, “Quantum properties of optical images in coupled nondegenerate parametric processes,” Opt. Spectrosc. 110, 97–104 (2011), translated from Opt. Spektrosk. 110, 102110 (2011).
    [CrossRef]

2011 (2)

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[CrossRef]

M. Yu. Saygin and A. S. Chirkin, “Quantum properties of optical images in coupled nondegenerate parametric processes,” Opt. Spectrosc. 110, 97–104 (2011), translated from Opt. Spektrosk. 110, 102110 (2011).
[CrossRef]

2010 (1)

M. Yu. Saygin and A. S. Chirkin, “Simultaneous parametric generation and up-conversion of entangled optical images,” J. Exp. Theor. Phys. 111, 11–21 (2010), translated from Pis’ma v Z. Eksp. Teor. Fiz. 138, 16–27 (2010).
[CrossRef]

2009 (2)

A. S. Chirkin and I. V. Shutov, “Parametric amplification of light waves at low-frequency pumping in aperiodic nonlinear photonic crystals,” J. Exp. Theor. Phys. 109, 547–556 (2009), translated from Z. Eksp. Teor. Fiz. 136, 639649 (2009).
[CrossRef]

A. S. Chirkin and M. Yu. Saigin, “Four-mode entangled states in coupled nonlinear optical processes and teleportation of two-mode entangled CV state,” Phys. Scr. T135, 014029 (2009).
[CrossRef]

2008 (2)

A. S. Chirkin and I. V. Shutov, “On the possibility of the nondegenerate parametric amplification of optical waves at low-frequency pumping,” J. Exp. Theor. Phys. Lett. 86, 693–697 (2008), translated from Pis’ma v Z. Eksp. Teor. Fiz. 86, 803807 (2007);
[CrossRef]

A. S. Chirkin, M. Yu. Saygin, and I. V. Shutov, “Parametric amplification at low-frequency pumping and generation of four-mode entangled states,” J. Russ. Laser Res. 29, 336–346 (2008).
[CrossRef]

2007 (4)

L. V. Magdenko, I. V. Sokolov, and M. I. Kolobov, “Quantum teleportation of optical images with frequency conversion,” Opt. Spectrosc. 103, 62–66 (2007).
[CrossRef]

A. Furusawa and N. Takei, “Quantum teleportation for continuous variables and related quantum information processing,” Phys. Rep. 443, 97–119 (2007).
[CrossRef]

A. S. Chirkin and M. Yu. Saigin, “Statistic and information characterization of tripartite entangled states,” J. Russ. Laser Res. 28, 505–515 (2007).
[CrossRef]

C. Pannarun, A. Bradley, and M. Olsen, “Tripartite entanglement and threshold properties of coupled intracavity down-conversion and sum-frequency generation,” Phys. Rev. A 76, 063812 (2007).
[CrossRef]

2004 (4)

A. V. Rodionov and A. S. Chirkin, “Entangled photon states in consecutive nonlinear optical interactions,” J. Exp. Theor. Phys. Lett. 79, 253–256 (2004), translated from Pis’ma v Z. Eksp. Teor. Fiz. 79, 311314 (2004).
[CrossRef]

A. Gatti, I. V. Sokolov, M. I. Kolobov, and L. A. Lugiato, “Quantum fluctuations in holographic teleportation of optical images,” Euro. Phys. J. D 30, 123–135 (2004).
[CrossRef]

X. Jia, X. Su, Q. Pan, J. Gao, C. Xie, and K. Peng, “Experimental demonstration of unconditional entanglement swapping for continuous variables,” Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

A. Ferraro, M. Paris, M. Bondani, A. Allevi, E. Puddi, and A. Adreoni, “Three-mode entanglement by interlinked nonlinear interactions in optical χ(2) media,” J. Opt. Soc. Am. B 21, 1241–1249 (2004).
[CrossRef]

2001 (1)

I. V. Sokolov, M. I. Kolobov, A. Gatti, and L. A. Lugiato, “Quantum holographic teleportation,” Opt. Commun. 193, 175–180 (2001).
[CrossRef]

2000 (1)

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

1998 (2)

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[CrossRef]

1997 (1)

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

1994 (1)

L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A 49, 1473–1476 (1994).
[CrossRef]

1993 (1)

C. Bennett, G. Brassad, C. Crepeau, R. Jozsa, A. Peres, and W. Wotters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

Adreoni, A.

Allevi, A.

Benichi, H.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[CrossRef]

Bennett, C.

C. Bennett, G. Brassad, C. Crepeau, R. Jozsa, A. Peres, and W. Wotters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

Bondani, M.

Bouwmeester, D.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

Bradley, A.

C. Pannarun, A. Bradley, and M. Olsen, “Tripartite entanglement and threshold properties of coupled intracavity down-conversion and sum-frequency generation,” Phys. Rev. A 76, 063812 (2007).
[CrossRef]

Brassad, G.

C. Bennett, G. Brassad, C. Crepeau, R. Jozsa, A. Peres, and W. Wotters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

Braunstein, S. L.

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[CrossRef]

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

S. L. Braunstein and A. K. Pati, Quantum Information with Continuous Variables (Springer, 2003).

Cerf, N. J.

N. J. Cerf, G. Leuchs, and E. S. Polzik, Quantum Information with Continuous Variables of Atoms and Light (World Scientific, 2007).

Chirkin, A. S.

M. Yu. Saygin and A. S. Chirkin, “Quantum properties of optical images in coupled nondegenerate parametric processes,” Opt. Spectrosc. 110, 97–104 (2011), translated from Opt. Spektrosk. 110, 102110 (2011).
[CrossRef]

M. Yu. Saygin and A. S. Chirkin, “Simultaneous parametric generation and up-conversion of entangled optical images,” J. Exp. Theor. Phys. 111, 11–21 (2010), translated from Pis’ma v Z. Eksp. Teor. Fiz. 138, 16–27 (2010).
[CrossRef]

A. S. Chirkin and M. Yu. Saigin, “Four-mode entangled states in coupled nonlinear optical processes and teleportation of two-mode entangled CV state,” Phys. Scr. T135, 014029 (2009).
[CrossRef]

A. S. Chirkin and I. V. Shutov, “Parametric amplification of light waves at low-frequency pumping in aperiodic nonlinear photonic crystals,” J. Exp. Theor. Phys. 109, 547–556 (2009), translated from Z. Eksp. Teor. Fiz. 136, 639649 (2009).
[CrossRef]

A. S. Chirkin and I. V. Shutov, “On the possibility of the nondegenerate parametric amplification of optical waves at low-frequency pumping,” J. Exp. Theor. Phys. Lett. 86, 693–697 (2008), translated from Pis’ma v Z. Eksp. Teor. Fiz. 86, 803807 (2007);
[CrossRef]

A. S. Chirkin, M. Yu. Saygin, and I. V. Shutov, “Parametric amplification at low-frequency pumping and generation of four-mode entangled states,” J. Russ. Laser Res. 29, 336–346 (2008).
[CrossRef]

A. S. Chirkin and M. Yu. Saigin, “Statistic and information characterization of tripartite entangled states,” J. Russ. Laser Res. 28, 505–515 (2007).
[CrossRef]

A. V. Rodionov and A. S. Chirkin, “Entangled photon states in consecutive nonlinear optical interactions,” J. Exp. Theor. Phys. Lett. 79, 253–256 (2004), translated from Pis’ma v Z. Eksp. Teor. Fiz. 79, 311314 (2004).
[CrossRef]

Cirac, J. I.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

Crepeau, C.

C. Bennett, G. Brassad, C. Crepeau, R. Jozsa, A. Peres, and W. Wotters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

Duan, L.-M.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

Eibl, M.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

Ferraro, A.

Fuchs, C. A.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

Furusawa, A.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[CrossRef]

A. Furusawa and N. Takei, “Quantum teleportation for continuous variables and related quantum information processing,” Phys. Rep. 443, 97–119 (2007).
[CrossRef]

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

Gao, J.

X. Jia, X. Su, Q. Pan, J. Gao, C. Xie, and K. Peng, “Experimental demonstration of unconditional entanglement swapping for continuous variables,” Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

Gatti, A.

A. Gatti, I. V. Sokolov, M. I. Kolobov, and L. A. Lugiato, “Quantum fluctuations in holographic teleportation of optical images,” Euro. Phys. J. D 30, 123–135 (2004).
[CrossRef]

I. V. Sokolov, M. I. Kolobov, A. Gatti, and L. A. Lugiato, “Quantum holographic teleportation,” Opt. Commun. 193, 175–180 (2001).
[CrossRef]

Giedke, G.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

Huntington, E.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[CrossRef]

Jia, X.

X. Jia, X. Su, Q. Pan, J. Gao, C. Xie, and K. Peng, “Experimental demonstration of unconditional entanglement swapping for continuous variables,” Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

Jozsa, R.

C. Bennett, G. Brassad, C. Crepeau, R. Jozsa, A. Peres, and W. Wotters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

Kimble, H. J.

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[CrossRef]

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

Kolobov, M. I.

L. V. Magdenko, I. V. Sokolov, and M. I. Kolobov, “Quantum teleportation of optical images with frequency conversion,” Opt. Spectrosc. 103, 62–66 (2007).
[CrossRef]

A. Gatti, I. V. Sokolov, M. I. Kolobov, and L. A. Lugiato, “Quantum fluctuations in holographic teleportation of optical images,” Euro. Phys. J. D 30, 123–135 (2004).
[CrossRef]

I. V. Sokolov, M. I. Kolobov, A. Gatti, and L. A. Lugiato, “Quantum holographic teleportation,” Opt. Commun. 193, 175–180 (2001).
[CrossRef]

M. I. Kolobov, Quantum Imaging (Springer, 2007).

Lee, N.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[CrossRef]

Leuchs, G.

N. J. Cerf, G. Leuchs, and E. S. Polzik, Quantum Information with Continuous Variables of Atoms and Light (World Scientific, 2007).

Lugiato, L. A.

A. Gatti, I. V. Sokolov, M. I. Kolobov, and L. A. Lugiato, “Quantum fluctuations in holographic teleportation of optical images,” Euro. Phys. J. D 30, 123–135 (2004).
[CrossRef]

I. V. Sokolov, M. I. Kolobov, A. Gatti, and L. A. Lugiato, “Quantum holographic teleportation,” Opt. Commun. 193, 175–180 (2001).
[CrossRef]

Magdenko, L. V.

L. V. Magdenko, I. V. Sokolov, and M. I. Kolobov, “Quantum teleportation of optical images with frequency conversion,” Opt. Spectrosc. 103, 62–66 (2007).
[CrossRef]

Mattle, K.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

Olsen, M.

C. Pannarun, A. Bradley, and M. Olsen, “Tripartite entanglement and threshold properties of coupled intracavity down-conversion and sum-frequency generation,” Phys. Rev. A 76, 063812 (2007).
[CrossRef]

Pan, J. W.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

Pan, Q.

X. Jia, X. Su, Q. Pan, J. Gao, C. Xie, and K. Peng, “Experimental demonstration of unconditional entanglement swapping for continuous variables,” Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

Pannarun, C.

C. Pannarun, A. Bradley, and M. Olsen, “Tripartite entanglement and threshold properties of coupled intracavity down-conversion and sum-frequency generation,” Phys. Rev. A 76, 063812 (2007).
[CrossRef]

Paris, M.

Pati, A. K.

S. L. Braunstein and A. K. Pati, Quantum Information with Continuous Variables (Springer, 2003).

Peng, K.

X. Jia, X. Su, Q. Pan, J. Gao, C. Xie, and K. Peng, “Experimental demonstration of unconditional entanglement swapping for continuous variables,” Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

Peres, A.

C. Bennett, G. Brassad, C. Crepeau, R. Jozsa, A. Peres, and W. Wotters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

Polzik, E. S.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

N. J. Cerf, G. Leuchs, and E. S. Polzik, Quantum Information with Continuous Variables of Atoms and Light (World Scientific, 2007).

Puddi, E.

Rodionov, A. V.

A. V. Rodionov and A. S. Chirkin, “Entangled photon states in consecutive nonlinear optical interactions,” J. Exp. Theor. Phys. Lett. 79, 253–256 (2004), translated from Pis’ma v Z. Eksp. Teor. Fiz. 79, 311314 (2004).
[CrossRef]

Saigin, M. Yu.

A. S. Chirkin and M. Yu. Saigin, “Four-mode entangled states in coupled nonlinear optical processes and teleportation of two-mode entangled CV state,” Phys. Scr. T135, 014029 (2009).
[CrossRef]

A. S. Chirkin and M. Yu. Saigin, “Statistic and information characterization of tripartite entangled states,” J. Russ. Laser Res. 28, 505–515 (2007).
[CrossRef]

Saygin, M. Yu.

M. Yu. Saygin and A. S. Chirkin, “Quantum properties of optical images in coupled nondegenerate parametric processes,” Opt. Spectrosc. 110, 97–104 (2011), translated from Opt. Spektrosk. 110, 102110 (2011).
[CrossRef]

M. Yu. Saygin and A. S. Chirkin, “Simultaneous parametric generation and up-conversion of entangled optical images,” J. Exp. Theor. Phys. 111, 11–21 (2010), translated from Pis’ma v Z. Eksp. Teor. Fiz. 138, 16–27 (2010).
[CrossRef]

A. S. Chirkin, M. Yu. Saygin, and I. V. Shutov, “Parametric amplification at low-frequency pumping and generation of four-mode entangled states,” J. Russ. Laser Res. 29, 336–346 (2008).
[CrossRef]

Shutov, I. V.

A. S. Chirkin and I. V. Shutov, “Parametric amplification of light waves at low-frequency pumping in aperiodic nonlinear photonic crystals,” J. Exp. Theor. Phys. 109, 547–556 (2009), translated from Z. Eksp. Teor. Fiz. 136, 639649 (2009).
[CrossRef]

A. S. Chirkin and I. V. Shutov, “On the possibility of the nondegenerate parametric amplification of optical waves at low-frequency pumping,” J. Exp. Theor. Phys. Lett. 86, 693–697 (2008), translated from Pis’ma v Z. Eksp. Teor. Fiz. 86, 803807 (2007);
[CrossRef]

A. S. Chirkin, M. Yu. Saygin, and I. V. Shutov, “Parametric amplification at low-frequency pumping and generation of four-mode entangled states,” J. Russ. Laser Res. 29, 336–346 (2008).
[CrossRef]

Sokolov, I. V.

L. V. Magdenko, I. V. Sokolov, and M. I. Kolobov, “Quantum teleportation of optical images with frequency conversion,” Opt. Spectrosc. 103, 62–66 (2007).
[CrossRef]

A. Gatti, I. V. Sokolov, M. I. Kolobov, and L. A. Lugiato, “Quantum fluctuations in holographic teleportation of optical images,” Euro. Phys. J. D 30, 123–135 (2004).
[CrossRef]

I. V. Sokolov, M. I. Kolobov, A. Gatti, and L. A. Lugiato, “Quantum holographic teleportation,” Opt. Commun. 193, 175–180 (2001).
[CrossRef]

Sørensen, J. L.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

Su, X.

X. Jia, X. Su, Q. Pan, J. Gao, C. Xie, and K. Peng, “Experimental demonstration of unconditional entanglement swapping for continuous variables,” Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

Takeda, S.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[CrossRef]

Takei, N.

A. Furusawa and N. Takei, “Quantum teleportation for continuous variables and related quantum information processing,” Phys. Rep. 443, 97–119 (2007).
[CrossRef]

Takeno, Y.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[CrossRef]

Vaidman, L.

L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A 49, 1473–1476 (1994).
[CrossRef]

Webb, J.

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
[CrossRef]

Weinfurter, H.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

Wotters, W.

C. Bennett, G. Brassad, C. Crepeau, R. Jozsa, A. Peres, and W. Wotters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

Xie, C.

X. Jia, X. Su, Q. Pan, J. Gao, C. Xie, and K. Peng, “Experimental demonstration of unconditional entanglement swapping for continuous variables,” Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

Zeilinger, A.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

Zoller, P.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

Euro. Phys. J. D (1)

A. Gatti, I. V. Sokolov, M. I. Kolobov, and L. A. Lugiato, “Quantum fluctuations in holographic teleportation of optical images,” Euro. Phys. J. D 30, 123–135 (2004).
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A. S. Chirkin and I. V. Shutov, “Parametric amplification of light waves at low-frequency pumping in aperiodic nonlinear photonic crystals,” J. Exp. Theor. Phys. 109, 547–556 (2009), translated from Z. Eksp. Teor. Fiz. 136, 639649 (2009).
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M. Yu. Saygin and A. S. Chirkin, “Simultaneous parametric generation and up-conversion of entangled optical images,” J. Exp. Theor. Phys. 111, 11–21 (2010), translated from Pis’ma v Z. Eksp. Teor. Fiz. 138, 16–27 (2010).
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J. Exp. Theor. Phys. Lett. (2)

A. S. Chirkin and I. V. Shutov, “On the possibility of the nondegenerate parametric amplification of optical waves at low-frequency pumping,” J. Exp. Theor. Phys. Lett. 86, 693–697 (2008), translated from Pis’ma v Z. Eksp. Teor. Fiz. 86, 803807 (2007);
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A. V. Rodionov and A. S. Chirkin, “Entangled photon states in consecutive nonlinear optical interactions,” J. Exp. Theor. Phys. Lett. 79, 253–256 (2004), translated from Pis’ma v Z. Eksp. Teor. Fiz. 79, 311314 (2004).
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J. Opt. Soc. Am. B (1)

J. Russ. Laser Res. (2)

A. S. Chirkin and M. Yu. Saigin, “Statistic and information characterization of tripartite entangled states,” J. Russ. Laser Res. 28, 505–515 (2007).
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A. S. Chirkin, M. Yu. Saygin, and I. V. Shutov, “Parametric amplification at low-frequency pumping and generation of four-mode entangled states,” J. Russ. Laser Res. 29, 336–346 (2008).
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Nature (1)

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

Opt. Commun. (1)

I. V. Sokolov, M. I. Kolobov, A. Gatti, and L. A. Lugiato, “Quantum holographic teleportation,” Opt. Commun. 193, 175–180 (2001).
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L. V. Magdenko, I. V. Sokolov, and M. I. Kolobov, “Quantum teleportation of optical images with frequency conversion,” Opt. Spectrosc. 103, 62–66 (2007).
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M. Yu. Saygin and A. S. Chirkin, “Quantum properties of optical images in coupled nondegenerate parametric processes,” Opt. Spectrosc. 110, 97–104 (2011), translated from Opt. Spektrosk. 110, 102110 (2011).
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A. Furusawa and N. Takei, “Quantum teleportation for continuous variables and related quantum information processing,” Phys. Rep. 443, 97–119 (2007).
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Phys. Rev. A (2)

C. Pannarun, A. Bradley, and M. Olsen, “Tripartite entanglement and threshold properties of coupled intracavity down-conversion and sum-frequency generation,” Phys. Rev. A 76, 063812 (2007).
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Phys. Rev. Lett. (4)

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[CrossRef]

C. Bennett, G. Brassad, C. Crepeau, R. Jozsa, A. Peres, and W. Wotters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef]

X. Jia, X. Su, Q. Pan, J. Gao, C. Xie, and K. Peng, “Experimental demonstration of unconditional entanglement swapping for continuous variables,” Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).
[CrossRef]

Phys. Scr. (1)

A. S. Chirkin and M. Yu. Saigin, “Four-mode entangled states in coupled nonlinear optical processes and teleportation of two-mode entangled CV state,” Phys. Scr. T135, 014029 (2009).
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Science (2)

N. Lee, H. Benichi, Y. Takeno, S. Takeda, J. Webb, E. Huntington, and A. Furusawa, “Teleportation of nonclassical wave packets of light,” Science 332, 330–333 (2011).
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S. L. Braunstein and A. K. Pati, Quantum Information with Continuous Variables (Springer, 2003).

N. J. Cerf, G. Leuchs, and E. S. Polzik, Quantum Information with Continuous Variables of Atoms and Light (World Scientific, 2007).

M. I. Kolobov, Quantum Imaging (Springer, 2007).

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Figures (7)

Fig. 1.
Fig. 1.

Vector diagrams of the (a) quasi-phase-matched PDC and (b) coupled parametric interactions consisting of one PDC process and two upconversion processes. Here g⃗ is the reciprocal lattice vector for the NPC, while g⃗m (m=1, 2, 3) are the reciprocal lattice vectors for the ANPC.

Fig. 2.
Fig. 2.

EPR variances [Eq. (15)] as a function of the transverse wave vector q for different values of the interaction length z: (a) 1.0 and (b) 2.0 cm. The curves are plotted for the nonlinear coupling coefficient βPDC=1cm1 and Ω=0 (λs=2.26μm, λi=0.69μm).

Fig. 3.
Fig. 3.

Teleportation scheme for entangled optical images.

Fig. 4.
Fig. 4.

EPR variances of the teleported fields Vsiout as a function of the ratio q/q0 for different values of the interaction length z: (a) zPDC=1.0cm and (b) zPDC=2.0cm. The figures are calculated for zANPC=5cm, βPDC=1cm1, and βANPC=2γANPC=1cm1 (λp=1.06μm, λ1=2.0μm, λ2=2.26μm, λ3=0.69μm, λ4=0.72μm). The thin line corresponds to case without spatial matching (s=1.0), while the bold line—with the BMD (s=2.0). The figure corresponds to the case of Fig. 2.

Fig. 5.
Fig. 5.

Fidelity of holographic teleportation as a function of Δ/δρ for the case of (a) coherent images (zPDC=0) and (b) entangled images (zPDC=1), for the pattern of four pixels shown on the right side of (a) (δρ=2π/q0). The dashed curves correspond to the case without BMD, and the solid curves correspond to the case with bandwidth matching. All parameters are the same as in Fig. 4.

Fig. 6.
Fig. 6.

EPR variances for two corresponding pixels of the initial images as a function of Δ/δρ for the case of entangled (zPDC=1cm) and coherent images (zPDC=0). All the parameters are the same as in Fig. 2.

Fig. 7.
Fig. 7.

EPR variances for two corresponding pixels of the teleported images as a function of Δ/δρ for the case of (a) coherent images (zPDC=0) and (b) entangled images (zPDC=1cm). The dashed curves correspond to the case without BMD, and the solid curves correspond to the case with bandwidth matching. All the parameters are the same as in Fig. 2.

Equations (57)

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ωp=ωs+ωi.
Δk(q⃗,Ω)=kpksz(q⃗,Ω)kiz(q⃗,Ω),
Δk(0,0)=mgz,
ωp=ω1+ω2,ω1+ωp=ω3,ω2+ωp=ω4.
[A^m(ρ⃗,t),A^m(ρ⃗,t)]=δmmδ(ρ⃗ρ⃗)δ(tt),[A^m(ρ⃗,t),A^m(ρ⃗,t)]=0,
a^m(q⃗,Ω)=1(2π)3A^m(ρ⃗,t)exp(i(Ωtq⃗ρ⃗))dρ⃗dt.
[a^m(q⃗,Ω),a^m(q⃗,Ω)]=1(2π)3δmmδ(q⃗+q⃗)δ(Ω+Ω).
(a^s(q⃗,Ω;z)a^i(q⃗,Ω;z))=(Us(q,Ω;z)Vs(q,Ω;z)Ui(q,Ω;z)Vi(q,Ω;z))(a^s0(q⃗,Ω)a^i0(q⃗,Ω)),
|Um(q,Ω;z)|2|Vm(q,Ω;z)|2=1,
Us(q,Ω;z)Ui*(q,Ω;z)=Vs(q,Ω;z)Vi*(q,Ω;z),
x^j(θ)=a^jeiθ+a^jeiθ2,y^j(θ)=x^(θ+π/2)=a^jeiθa^jeiθi2.
Vx(q⃗,Ω)=Var(x^1(θ1)(q⃗,Ω)x^2(θ2)(q⃗,Ω)),Vy(q⃗,Ω)=Var(y^1(θ1)(q⃗,Ω)+y^2(θ2)(q⃗,Ω)),
θ1(q⃗,Ω)=θ2(q⃗,Ω)=12arg(Us(q⃗,Ω)Vs(q⃗,Ω)).
VxVy<1.
Vx(q⃗,Ω)=Vy(q⃗,Ω)=(|Vs(q,Ω)||Vi(q,Ω)|)2.
q0=2kskiks+ki(βPDC2+π2z2)1/4,
L1[A^1(ρ⃗,t;z)]=iβANPCA^2(ρ⃗,t;z)+iγ1*A^3(ρ⃗,t;z),L2[A^2(ρ⃗,t;z)]=iβANPCA^1(ρ⃗,t;z)+iγ2*A^4(ρ⃗,t;z),L3[A^3(ρ⃗,t;z)]=iγ1A^1(ρ⃗,t;z),L4[A^4(ρ⃗,t;z)]=iγ2A^2(ρ⃗,t;z),
Lj=(z+1ujti2kjΔ).
A^j(ρ⃗,t;z)=a^j(q⃗,Ω;z)ei(Ωtq⃗ρ⃗)dq⃗dΩ.
ddz(a^1(q⃗,Ω;z)a^2(q⃗,Ω;z)a^3(q⃗,Ω;z)a^4(q⃗,Ω;z))=(iϵ1iβiγ10iβiϵ20iγ2iγ10iϵ300iγ20iϵ4)(a^1(q⃗,Ω;z)a^2(q⃗,Ω;z)a^3(q⃗,Ω;z)a^4(q⃗,Ω;z)),
ϵj=(Ωujq22kj),(j=14)
(a^1(q⃗,Ω;z)a^2(q⃗,Ω;z)a^3(q⃗,Ω;z)a^4(q⃗,Ω;z))=(Q11Q12Q13Q14Q21Q22Q23Q24Q31Q32Q33Q34Q41Q42Q43Q44)(a^10(q⃗,Ω)a^20(q⃗,Ω)a^30(q⃗,Ω)a^40(q⃗,Ω)).
m=14(1)m+lQlm(q⃗,Ω;z)Qkm*(q⃗,Ω;z)=δlk.
b^s1(q⃗)=a^1(q⃗/s)+a^sin(q⃗)2,b^s2(q⃗)=a^sin(q⃗)a^1(q⃗/s)2,b^i1(q⃗)=a^4(q⃗/s)+a^iin(q⃗)2,b^i2(q⃗)=a^iin(q⃗)a^4(q⃗/s)2,
x^s2(q⃗)=b^s2(q⃗)+b^s2(q⃗)2,y^s1(q⃗)=b^s1(q⃗)b^s1(q⃗)i2,x^i2(q⃗)=b^i2(q⃗)+b^i2(q⃗)2,y^i1(q⃗)=b^i1(q⃗)b^i1(q⃗)i2.
a^sout(q⃗)=a^sin(q⃗)+f^1(q⃗),a^iout(q⃗)=a^iin(q⃗)+f^2(q⃗),
f^1(q⃗)=a^1(q⃗/s)a^2(q⃗/s),f^2(q⃗)=a^3(q⃗/s)a^4(q⃗/s),
[a^s,iin(q⃗),f^1,2(q⃗)]=0,[a^s,iin(q⃗),f^m(q⃗)]=0.
[f^m(q⃗),f^n(q⃗)]=0(m,n=1,2),
W(ξ⃗;q⃗)=1(2π)2det(σ(q⃗))exp(12ξ⃗σ1(q⃗)ξ⃗T),
σin(q⃗)=σcoh+σent(q⃗),
σent(q⃗)=(ν(q⃗)Iν(q⃗)(1+ν(q⃗))σzν(q⃗)(1+ν(q⃗))σzν(q⃗)I),
I=(1001),σz=(1001),
σout(q⃗)=σin(q⃗)+σN(q⃗),
σN(q⃗)=(Vd(q⃗)IC(q⃗)IC(q⃗)IVu(q⃗)I).
Vd(q⃗)=Var(x^1(q⃗)x^2(q⃗))=Var(y^1(q⃗)+y^2(q⃗))=12[(Q11(q,0;z)Q12*(q,0;z))2+(Q13(q,0;z)Q14*(q,0;z))2+h.c.],Vu(q⃗)=Var(x^3(q⃗)x^4(q⃗))=Var(y^3(q⃗)+y^4(q⃗))=12[(Q13(q,0;z)+Q14(q,0;z))2+(Q33(q,0;z)Q34*(q,0;z))2+h.c.],C(q⃗)=(x^1(q⃗)x^2(q⃗))(x^3(q⃗)x^4(q⃗))=(y^1(q⃗)+y^2(q⃗))(y^3(q⃗)+y^4(q⃗))=Q11(q,0;z)(Q13*(q,0;z)+Q14*(q,0;z))+Q13(q,0;z)(Q33*(q,0;z)Q34(q,0;z))+h.c.
F(q⃗)=(2π)2Win(ξ⃗;q⃗)Wout(ξ⃗;q⃗)dξ⃗.
F(q⃗)=1det(σin(q⃗)+σout(q⃗)).
Vout(q⃗)=Vin(q⃗)+ΔV(q⃗),
ΔV(q⃗)=Vd(q⃗)+Vu(q⃗)2C(q⃗)0.
A^jout(m)=1Sρ⃗mA^jout(ρ⃗)dρ⃗,
[A^jout(m),A^lout(n)]=δmnδjl.
X^jout(m)=X^jin(m)+X^jN(m),Y^jout(m)=Y^jin(m)+Y^jN(m),
X^jN(m)=1S12ρ⃗m(f^j(q⃗)+f^j(q⃗))eiq⃗ρ⃗dq⃗dρ⃗,Y^jN(m)=1S1i2ρ⃗m(f^j(q⃗)f^j(q⃗))eiq⃗ρ⃗dq⃗dρ⃗
X^jout(m)X^lout(n)=BΔ(q⃗)x^jout(q⃗)x^lout(q⃗)cos(q⃗(ρ⃗mρ⃗n))dq⃗,Y^jout(m)Y^lout(n)=BΔ(q⃗)y^jout(q⃗)y^lout(q⃗)cos(q⃗(ρ⃗mρ⃗n))dq⃗,X^jout(m)Y^lout(n)=0,
BΔ(q⃗)=Δ24π2sinc2(qxΔ2)sinc2(qyΔ2)
σoutgr=BΔ(q⃗)σout(q⃗)P(q⃗)dq⃗.
Win/out(ξ⃗)=1(2π)2Ndet(σin/outgr)2Nexp(12ξ⃗(σin/outgr)1ξ⃗T),
F=((2π)2NWin(ξ⃗)Wout(ξ⃗)dξ⃗)1/N.
F=1det(σingr+σoutgr)2N.
Vin/outgr=BΔ(q⃗)Vin/out(q⃗)dq⃗.
Q11(q,Ω;z)=[(Γ12+γ2+ϵd2βANPC2)C2(Γ22+γ2+ϵd2βANPC2)C1+i(ϵdΓ22+2ϵdγ2+ϵuγ2+ϵd3ϵdβANPC2)S1Γ1i(ϵdΓ12+2ϵdγ2+ϵuγ2+ϵd3ϵdβANPC2)S2Γ2]/(Γ12Γ22),Q12(q,Ω;z)=iβANPC[(Γ12+2γ2+ϵd2βANPC2)S2Γ2(Γ22+2γ2+ϵd2βANPC2)S1Γ1]/(Γ12Γ22),Q13(q,Ω;z)=γ[(ϵd+ϵu)(C1C2)+i(Γ12+γ2+ϵu2+ϵdϵu+ϵd2βANPC2)S2Γ2i(Γ22+γ2+ϵu2+ϵdϵu+ϵd2βANPC2)S1Γ1]/(Γ12Γ22),Q14(q,Ω;z)=βANPCγ[(C1C2)+iϵu(S1Γ1S2Γ2)]/(Γ12Γ22),Q33(q,Ω;z)=[(Γ12+γ2+ϵu2)C2(Γ22+γ2+ϵu2)C1+i(ϵuΓ22+γ2ϵd+2γ2ϵu+ϵu3)S1Γ1i(ϵuΓ12+γ2ϵd+2γ2ϵu+ϵu3)S2Γ2]/(Γ12Γ22),Q34(q,Ω;z)=iβANPCγ2(S1Γ1S1Γ1)/(Γ12Γ22),
Γ1,2=12[(βANPC22γ2ϵd2ϵu2+(γ2ϵdϵu)2ϵu2)1/2±(βANPC22γ2ϵd2ϵu2(γ2ϵdϵu)2ϵu2)1/2]
Q22=Q11*,Q44=Q33*,Q21=Q12*,Q43=Q34*,Q13=Q31=Q24*=Q42*,Q14=Q41=Q23*=Q32*.
Us(q,Ω;z)=exp(iϵsϵi2z)(cosh(Γz)+iϵs+ϵi2Γsinh(Γz)),Vs(q,Ω;z)=iexp(iϵsϵi2z)βPDCsinh(Γz)Γ,Ui(q,Ω;z)=iexp(iϵsϵi2z)βPDCsinh(Γz)Γ,Vi(q,Ω;z)=exp(iϵsϵi2z)(cosh(Γz)iϵs+ϵi2Γsinh(Γz)),
ϵs,i=(Ωus,iq22ks,i),
Γ=βPDC2(ϵs+ϵi2)2.

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