Abstract

We present an experimental proposal for the generation of photon triplets based on third-order spontaneous parametric downconversion in thin optical fibers. Our analysis includes expressions for the quantum state, which describes the photon triplets and for the generation rate in terms of all experimental parameters. We also present, for a specific source design, numerically calculated generation rates.

© 2011 Optical Society of America

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References

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  1. M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, IEEE Photonics Technol. Lett. 14, 983 (2002).
  2. T. Felbinger, S. Schiller, and J. Mlynek, Phys. Rev. Lett. 80, 492 (1998).
  3. M. V. Chekhova, O. A. Ivanova, V. Berardi, and A. Garuccio, Phys. Rev. A 72, 023818 (2005).
  4. J. Douady and B. Boulanger, Opt. Lett. 29, 2794 (2004).
    [PubMed]
  5. J. Persson, T. Aichele, V. Zwiller, L. Samuelson, and O. Benson, Phys. Rev. B 69, 233314 (2004).
  6. T. E. Keller, M. H. Rubin, and Y. Shih, Phys. Rev. A 57, 2076 (1998).
  7. J. G. Rarity and P. R. Tapster, Phys. Rev. A 59, R35 (1999).
  8. H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, Nature 466, 601 (2010).
    [PubMed]
  9. D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).
  10. M. Corona, K. Garay-Palmett, and A. B. U’Ren are preparing a manuscript to be called “Theory for the process of third-order spontaneous parametric downconversion in optical fibers.”
  11. V. Grubsky and J. Feinberg, Opt. Commun. 274, 447 (2007).
  12. W. P. Grice and I. A. Walmsley, Phys. Rev. A 56, 1627 (1997).
  13. S. G. Leon-Saval, T. Birks, W. J. Wadsworth, P. St. J. Russell, and M. W. Mason, Opt. Express 12, 2864 (2004).
    [PubMed]
  14. K. Garay-Palmett, A. B. U’Ren, and R. Rangel-Rojo, Phys. Rev. A 82, 043809 (2010).
  15. For example: K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, Opt. Lett. 31, 1905 (2006).
    [PubMed]

2010 (2)

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, Nature 466, 601 (2010).
[PubMed]

K. Garay-Palmett, A. B. U’Ren, and R. Rangel-Rojo, Phys. Rev. A 82, 043809 (2010).

2007 (1)

V. Grubsky and J. Feinberg, Opt. Commun. 274, 447 (2007).

2006 (1)

2005 (1)

M. V. Chekhova, O. A. Ivanova, V. Berardi, and A. Garuccio, Phys. Rev. A 72, 023818 (2005).

2004 (3)

2002 (1)

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, IEEE Photonics Technol. Lett. 14, 983 (2002).

1999 (1)

J. G. Rarity and P. R. Tapster, Phys. Rev. A 59, R35 (1999).

1998 (2)

T. Felbinger, S. Schiller, and J. Mlynek, Phys. Rev. Lett. 80, 492 (1998).

T. E. Keller, M. H. Rubin, and Y. Shih, Phys. Rev. A 57, 2076 (1998).

1997 (1)

W. P. Grice and I. A. Walmsley, Phys. Rev. A 56, 1627 (1997).

1990 (1)

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).

Aichele, T.

J. Persson, T. Aichele, V. Zwiller, L. Samuelson, and O. Benson, Phys. Rev. B 69, 233314 (2004).

Benson, O.

J. Persson, T. Aichele, V. Zwiller, L. Samuelson, and O. Benson, Phys. Rev. B 69, 233314 (2004).

Berardi, V.

M. V. Chekhova, O. A. Ivanova, V. Berardi, and A. Garuccio, Phys. Rev. A 72, 023818 (2005).

Birks, T.

Boulanger, B.

Chekhova, M. V.

M. V. Chekhova, O. A. Ivanova, V. Berardi, and A. Garuccio, Phys. Rev. A 72, 023818 (2005).

Chen, J.

Corona, M.

M. Corona, K. Garay-Palmett, and A. B. U’Ren are preparing a manuscript to be called “Theory for the process of third-order spontaneous parametric downconversion in optical fibers.”

Douady, J.

Fedrizzi, A.

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, Nature 466, 601 (2010).
[PubMed]

Feinberg, J.

V. Grubsky and J. Feinberg, Opt. Commun. 274, 447 (2007).

Felbinger, T.

T. Felbinger, S. Schiller, and J. Mlynek, Phys. Rev. Lett. 80, 492 (1998).

Fiorentino, M.

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, IEEE Photonics Technol. Lett. 14, 983 (2002).

Garay-Palmett, K.

K. Garay-Palmett, A. B. U’Ren, and R. Rangel-Rojo, Phys. Rev. A 82, 043809 (2010).

M. Corona, K. Garay-Palmett, and A. B. U’Ren are preparing a manuscript to be called “Theory for the process of third-order spontaneous parametric downconversion in optical fibers.”

Garuccio, A.

M. V. Chekhova, O. A. Ivanova, V. Berardi, and A. Garuccio, Phys. Rev. A 72, 023818 (2005).

Greenberger, D. M.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).

Grice, W. P.

W. P. Grice and I. A. Walmsley, Phys. Rev. A 56, 1627 (1997).

Grubsky, V.

V. Grubsky and J. Feinberg, Opt. Commun. 274, 447 (2007).

Hamel, D. R.

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, Nature 466, 601 (2010).
[PubMed]

Horne, M. A.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).

Hübel, H.

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, Nature 466, 601 (2010).
[PubMed]

Ivanova, O. A.

M. V. Chekhova, O. A. Ivanova, V. Berardi, and A. Garuccio, Phys. Rev. A 72, 023818 (2005).

Jennewein, T.

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, Nature 466, 601 (2010).
[PubMed]

Keller, T. E.

T. E. Keller, M. H. Rubin, and Y. Shih, Phys. Rev. A 57, 2076 (1998).

Kumar, P.

For example: K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, Opt. Lett. 31, 1905 (2006).
[PubMed]

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, IEEE Photonics Technol. Lett. 14, 983 (2002).

Lee, K. F.

Leon-Saval, S. G.

Li, X.

Liang, C.

Mason, M. W.

Mlynek, J.

T. Felbinger, S. Schiller, and J. Mlynek, Phys. Rev. Lett. 80, 492 (1998).

Persson, J.

J. Persson, T. Aichele, V. Zwiller, L. Samuelson, and O. Benson, Phys. Rev. B 69, 233314 (2004).

Ramelow, S.

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, Nature 466, 601 (2010).
[PubMed]

Rangel-Rojo, R.

K. Garay-Palmett, A. B. U’Ren, and R. Rangel-Rojo, Phys. Rev. A 82, 043809 (2010).

Rarity, J. G.

J. G. Rarity and P. R. Tapster, Phys. Rev. A 59, R35 (1999).

Resch, K. J.

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, Nature 466, 601 (2010).
[PubMed]

Rubin, M. H.

T. E. Keller, M. H. Rubin, and Y. Shih, Phys. Rev. A 57, 2076 (1998).

Russell, P. St. J.

Samuelson, L.

J. Persson, T. Aichele, V. Zwiller, L. Samuelson, and O. Benson, Phys. Rev. B 69, 233314 (2004).

Schiller, S.

T. Felbinger, S. Schiller, and J. Mlynek, Phys. Rev. Lett. 80, 492 (1998).

Sharping, J. E.

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, IEEE Photonics Technol. Lett. 14, 983 (2002).

Shih, Y.

T. E. Keller, M. H. Rubin, and Y. Shih, Phys. Rev. A 57, 2076 (1998).

Shimony, A.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).

Tapster, P. R.

J. G. Rarity and P. R. Tapster, Phys. Rev. A 59, R35 (1999).

U’Ren, A. B.

K. Garay-Palmett, A. B. U’Ren, and R. Rangel-Rojo, Phys. Rev. A 82, 043809 (2010).

M. Corona, K. Garay-Palmett, and A. B. U’Ren are preparing a manuscript to be called “Theory for the process of third-order spontaneous parametric downconversion in optical fibers.”

Voss, P. L.

For example: K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, Opt. Lett. 31, 1905 (2006).
[PubMed]

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, IEEE Photonics Technol. Lett. 14, 983 (2002).

Wadsworth, W. J.

Walmsley, I. A.

W. P. Grice and I. A. Walmsley, Phys. Rev. A 56, 1627 (1997).

Zeilinger, A.

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).

Zwiller, V.

J. Persson, T. Aichele, V. Zwiller, L. Samuelson, and O. Benson, Phys. Rev. B 69, 233314 (2004).

Am. J. Phys. (1)

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. 58, 1131 (1990).

IEEE Photonics Technol. Lett. (1)

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, IEEE Photonics Technol. Lett. 14, 983 (2002).

Nature (1)

H. Hübel, D. R. Hamel, A. Fedrizzi, S. Ramelow, K. J. Resch, and T. Jennewein, Nature 466, 601 (2010).
[PubMed]

Opt. Commun. (1)

V. Grubsky and J. Feinberg, Opt. Commun. 274, 447 (2007).

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (5)

M. V. Chekhova, O. A. Ivanova, V. Berardi, and A. Garuccio, Phys. Rev. A 72, 023818 (2005).

K. Garay-Palmett, A. B. U’Ren, and R. Rangel-Rojo, Phys. Rev. A 82, 043809 (2010).

W. P. Grice and I. A. Walmsley, Phys. Rev. A 56, 1627 (1997).

T. E. Keller, M. H. Rubin, and Y. Shih, Phys. Rev. A 57, 2076 (1998).

J. G. Rarity and P. R. Tapster, Phys. Rev. A 59, R35 (1999).

Phys. Rev. B (1)

J. Persson, T. Aichele, V. Zwiller, L. Samuelson, and O. Benson, Phys. Rev. B 69, 233314 (2004).

Phys. Rev. Lett. (1)

T. Felbinger, S. Schiller, and J. Mlynek, Phys. Rev. Lett. 80, 492 (1998).

Other (1)

M. Corona, K. Garay-Palmett, and A. B. U’Ren are preparing a manuscript to be called “Theory for the process of third-order spontaneous parametric downconversion in optical fibers.”

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Figures (2)

Fig. 1
Fig. 1

(a) k ( 3 ω ) and 3 k ( ω ) versus fiber radius. Plotted versus degenerate TOSPDC wavelength (b) PM radius and (c) nonlinearity γ. Transverse intensity for (d) the pump and (e) the TOSPDC photons.

Fig. 2
Fig. 2

Representation, plotted versus the three generation frequencies, of the (a) PM, (b) PSA, and (c) joint intensity functions. (d) Generated flux versus fiber length. (e) TOSPDC single-photon spectrum.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

| Ψ = | 0 r | 0 s | 0 i + ζ | Ψ 3 ,
| Ψ 3 = k r k s k i G k ( k r , k s , k i ) × a ^ ( k r ) a ^ ( k s ) a ^ ( k i ) | 0 r | 0 s | 0 i ,
ζ = [ 2 ( 2 π ) 3 / 2 ϵ 0 3 c 3 n p 3 P L 2 γ 2 2 ( ω p o ) 2 σ ] 1 / 2 ( δ k ) 3 / 2 .
γ = 3 χ ( 3 ) ω p o 4 ϵ 0 c 2 n p 2 A eff ,
ϕ ( ω r , ω s , ω i ) = sinc [ L 2 Δ k ( ω r , ω s , ω i ) ] e i L 2 Δ k ( ω r , ω s , ω i ) ,
N = lim δ k 0 k r Ψ | a ( k r ) a ( k r ) | Ψ R = 2 3 3 2 c 3 n p 3 π 2 ( ω p o ) 2 L 2 γ 2 P R σ 2 × d ω r d ω s d ω i k r ω r n r 2 k s ω s n s 2 k i ω i n i 2 | F ( ω r , ω s , ω i ) | 2 ,

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