Abstract

In this Letter we study spontaneous generation of triple photon states in optical fibers by third order spontaneous downconversion. Using a semiclassical approach we derive an explicit expression for the triple photons generation efficiency as a function of fiber parameters. We show that optical fibers with well suited index profiles and standard outer diameters could be the key component of future triple photons sources.

© 2011 Optical Society of America

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References

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2011

K. Tarnowski, B. Kibler, C. Finot, and W. Urbanczyk, IEEE J. Quantum Electron. 47, 622 (2011).
[CrossRef]

M. Corona, K. Garay-Palmett, and A. B. U’ren, Opt. Lett. 36, 190 (2011).
[CrossRef] [PubMed]

2010

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

2008

2007

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

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, C. R. Physique 8, 206 (2007).
[CrossRef]

2005

2004

1990

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

1968

R. L. Byer and S. E. Harris, Phys. Rev. 168, 1064 (1968).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed.(Academic, 2001).

Bachor, H.-A.

H.-A. Bachor and T. Ralph, eds., A Guide to Experiments in Quantum Optics (Wiley-VCH, 2004).
[CrossRef]

Bencheikh, K.

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, C. R. Physique 8, 206 (2007).
[CrossRef]

Bétourné, A.

Birks, T.

Boulanger, B.

Bouwmans, G.

Bouwmeester, D.

D. Bouwmeester, A. Ekert, and A. Zeilinger, eds., The Physics of Quantum Information (Springer, 2000).

Bufetov, I. A.

Byer, R. L.

R. L. Byer and S. E. Harris, Phys. Rev. 168, 1064 (1968).
[CrossRef]

Corona, M.

Dianov, E. M.

Douady, J.

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, C. R. Physique 8, 206 (2007).
[CrossRef]

J. Douady and B. Boulanger, Opt. Lett. 29, 2794 (2004).
[CrossRef] [PubMed]

Douay, M.

Duligall, J.

Dvoyrin, V. V.

Ekert, A.

D. Bouwmeester, A. Ekert, and A. Zeilinger, eds., The Physics of Quantum Information (Springer, 2000).

Fedrizzi, A.

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

Feinberg, J.

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

Finot, C.

K. Tarnowski, B. Kibler, C. Finot, and W. Urbanczyk, IEEE J. Quantum Electron. 47, 622 (2011).
[CrossRef]

Fulconis, J.

Garay-Palmett, K.

Gravier, F.

F. Gravier and B. Boulanger, J. Opt. Soc. Am. B 25, 98(2008).
[CrossRef]

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, C. R. Physique 8, 206 (2007).
[CrossRef]

Greenberger, D. M.

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

Grubsky, V.

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

Guryanov, A. N.

Hamel, D. R.

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

Harris, S. E.

R. L. Byer and S. E. Harris, Phys. Rev. 168, 1064 (1968).
[CrossRef]

Horne, M. A.

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

Hübel, H.

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

Jennewein, T.

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

Khopin, V. F.

Kibler, B.

K. Tarnowski, B. Kibler, C. Finot, and W. Urbanczyk, IEEE J. Quantum Electron. 47, 622 (2011).
[CrossRef]

Leon-Saval, S.

Levenson, J. A.

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, C. R. Physique 8, 206 (2007).
[CrossRef]

Mashinsky, V. M.

Mason, M.

Medvedkov, O. I.

Neustruev, V. B.

Quiquempois, Y.

Ralph, T.

H.-A. Bachor and T. Ralph, eds., A Guide to Experiments in Quantum Optics (Wiley-VCH, 2004).
[CrossRef]

Ramelow, S.

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

Rarity, J.

Resch, K. J.

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

Russell, P.

Russell, P. St.J.

Salgansky, M. Y.

Shimony, A.

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

Shubin, A. V.

Tarnowski, K.

K. Tarnowski, B. Kibler, C. Finot, and W. Urbanczyk, IEEE J. Quantum Electron. 47, 622 (2011).
[CrossRef]

U’ren, A. B.

Urbanczyk, W.

K. Tarnowski, B. Kibler, C. Finot, and W. Urbanczyk, IEEE J. Quantum Electron. 47, 622 (2011).
[CrossRef]

Vasiliev, S. A.

Wadsworth, W.

Zeilinger, A.

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

D. Bouwmeester, A. Ekert, and A. Zeilinger, eds., The Physics of Quantum Information (Springer, 2000).

Am. J. Phys.

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

C. R. Physique

K. Bencheikh, F. Gravier, J. Douady, J. A. Levenson, and B. Boulanger, C. R. Physique 8, 206 (2007).
[CrossRef]

IEEE J. Quantum Electron.

K. Tarnowski, B. Kibler, C. Finot, and W. Urbanczyk, IEEE J. Quantum Electron. 47, 622 (2011).
[CrossRef]

J. Opt. Soc. Am. B

Nature

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

Opt. Commun.

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

Opt. Express

Opt. Lett.

Phys. Rev.

R. L. Byer and S. E. Harris, Phys. Rev. 168, 1064 (1968).
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed.(Academic, 2001).

H.-A. Bachor and T. Ralph, eds., A Guide to Experiments in Quantum Optics (Wiley-VCH, 2004).
[CrossRef]

D. Bouwmeester, A. Ekert, and A. Zeilinger, eds., The Physics of Quantum Information (Springer, 2000).

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Figures (1)

Fig. 1
Fig. 1

(a) Calculated triple photon creation spectral density d 2 Γ ( λ 3 , λ 4 ) for 1 W of input power and a 1 m long fiber of the design described in the text. (b) total triple photon creation rate as a function of the fiber length. Circles: numerical integration of (13); full line: explicit expression (21).\

Equations (21)

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

ω 1 = ω 2 + ω 3 + ω 4 .
d A 1 d z = i [ γ 11 | A 1 | 2 A 1 + 2 γ 1 A 2 A 3 A 4 e i Δ k z ] ,
d A 2 d z = i [ 2 γ 21 | A 1 | 2 A 2 + 2 γ 2 A 1 A 3 * A 4 * e i Δ k z ] ,
d A 3 d z = i [ 2 γ 31 | A 1 | 2 A 3 + 2 γ 3 A 1 A 2 * A 4 * e i Δ k z ] ,
d A 4 d z = i [ 2 γ 41 | A 1 | 2 A 4 + 2 γ 4 A 1 A 2 * A 3 * e i Δ k z ] ,
γ i j = ω i c n 2 ( r , θ ) ψ i 2 ( r , θ ) ψ j 2 ( r , θ ) r d r d θ ,
γ i = ω i c n 2 ( r , θ ) i = 1 4 ψ i ( r , θ ) r d r d θ ,
d P i v = ω i 2 π d ω i .
A 1 ( z ) = P 1 exp ( i γ 11 P 1 z ) ,
B 2 = A 2 exp ( 2 i γ 21 P 1 z ) ,
κ = Δ k + ( 2 γ 21 - γ 11 ) P 1 .
d B 2 d z = 2 i γ 2 P 1 A 3 * A 4 * e i κ z .
d 2 Γ = 4 γ 2 2 P 1 ω 2 ω 3 2 π ω 4 2 π z 2 sinc 2 ( κ z / 2 ) d ω 3 d ω 4 .
κ = κ d + b i = 2 4 ( ω i ω 0 ) 2 ,
κ d = κ pm + i = 2 4 β i ( ω 0 ) β 1 ,
b = ( d 2 β i d ω i 2 ) ω i = ω 0 , for     i = 2 , 3 , 4 ,
Γ = γ 0 2 P 1 ω 0 π 2 z 2 d ω 3 d ω 4 sinc 2 ( κ z / 2 ) ,
r cos θ = ω 3 ω 0 ,
r sin θ = ω 4 ω 0 ,
Γ = γ 0 2 P 1 ω 0 π 2 z 2 b d θ 1 1 + sin 2 θ 2 d u     sinc 2 ( u ) ,
Γ = 2 3 γ 0 2 P 1 ω 0 b z .

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