Abstract

We present a consistent multimode theory that describes the coupling of single photons generated by collinear Type-I parametric down-conversion into single-mode optical fibers. We have calculated an analytic expression for the fiber diameter which maximizes the pair photon count rate. For a given focal length and wavelength, a lower limit of the fiber diameter for satisfactory coupling is obtained.

© 2004 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

J. Lightwave Technol.

J. Opt. B: Quantum semiclass. Opt.

R. Andrews, E. R. Pike and Sarben Sarkar, ???Photon correlations and interference in type-I optical parametric down-conversion,??? J. Opt. B: Quantum semiclass. Opt. 1, 588-597 (1999).
[CrossRef]

Nature

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

A. Mair, A. Vaziri, G. Weihs and A. Zeilinger, ???Entanglement of the orbital angular momentum states of photons,??? Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Opt. Commun.

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. D. Giuseppe, and A. V. Sergienko, ???Effective fiber coupling of entangled photons for quantum communication,??? Opt. Commun. 227, 343-348 (2003).
[CrossRef]

Phys. Rev. A

L. Vaidman, ???Teleportation of quantum states,??? Phys. Rev. A 49, 1473-1476 (1994).
[CrossRef] [PubMed]

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, ???High-efficiency entangled photon pair collection in type-II parametric fluorescence,??? Phys. Rev. A 64, 023802 (2001).
[CrossRef]

Z. Y. Ou, X. Y. Zou, L. J. Wang and L. Mandel, ???Experiment on nonclassical fourth-order interference,??? Phys. Rev. A 42, 2957-2965 (1990).
[CrossRef] [PubMed]

C. K. Hong and L. Mandel, ??????Theory of parametric frequency down-conversion of light,?????? Phys. Rev. A 31, 2409-2418 (1985).
[CrossRef] [PubMed]

A. L. Migdall, D. Branning, and S. Castelleto, ???Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source,??? Phys. Rev. A, 66, 053805-1-053805-4 (2002).
[CrossRef]

Phys. Rev. Lett.

Z. Y. Ou and L. Mandel, ???Violation of Bell???s inequality and classical probability in a two-photon correlation experiment,??? Phys. Rev. Lett. 61, 50-53 (1988)
[CrossRef] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, ???Teleporting an unknown quantum state via classical and Einstein-Podolsky-Rosen channels,??? Phys. Rev. Lett. 70, 1895-1899 (1993).
[CrossRef] [PubMed]

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

J-W Pan, D. Bouwmeester, H. Weinfurter and A. Zeilinger, ???Experimental entanglement swapping : Entangling photons that never interacted,??? Phys. Rev. Lett. 80, 3891-3894 (1998).
[CrossRef]

D. Bouwmeester, J-W Pan, M. Daniell, H. Weinfurter and A. Zeilinger, Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef]

A. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, ???Practical quantum cryptography based on twophoton interferometry,??? Phys. Rev. Lett. 69 (9), 1293-1295 (1992).
[CrossRef] [PubMed]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, ???Quantum cryptography using entangled photons in energytime Bell states,??? Phys. Rev. Lett. 84 (20), 4737-4740, 2000.
[CrossRef] [PubMed]

D. C. Burnham and D. L. Weinberg, ???Observation of simultaneity in parametric production of optical photon pairs,??? Phys. Rev. Lett. 25, 84-87 (1970).
[CrossRef]

Other

S. Castelletto, I. P. Degiovanni, M. Ware, and A. Migdall, ???Coupling efficiencies in single photon on-demand sources,??? ArXiv:quant-ph/0311099 (2003).

E. R. Pike and S. Sarkar, The Quantum Theory of Radiation, Oxford University Press (1995).

A. Yariv, Optical Electronics in Modern Communications (5th Edition, Oxford Series in Electrical and Computer Engineering).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), chaps. 7 and 8.

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Figures (1)

Fig. 1.
Fig. 1.

Schematic of the experimental setup to determine pair photon coupling in fibers

Equations (18)

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A ( 2 ) = E H + ( r 1 , t 1 ) E H + ( r 2 , t 2 )
d 3 r 3 d 3 k 1 d 3 k 2 U k 1 λ 1 * ( r 3 ) U k 2 λ 2 * ( r 3 ) U k 0 λ 0 ( r 3 ) f p ( r 3 ) ( ω k 0 2 ε 0 ) 1 2 ( ω k 1 2 ε 0 ) 1 2 ( ω k 2 2 ε 0 ) 1 2
× α k 0 , 0 E I ( + ) ( r 2 , t 2 ) E I ( + ) ( r 1 , t 1 ) ω k 0 , k 1 , k 2 δ ( ω k 1 ω k 2 ω k 0 )
E + ( r , t ) = i λ λ d 3 k d 3 k ( ω k 2 ε 0 ) 1 2 ε k λ β k λ , k λ U k λ f ( r ) e i ω t a k λ
β k λ k λ = d x d y U k λ in ( x , y ) U k λ f * ( x , y )
d 3 k 1 d 3 k 2 f ˜ p ( k 1 t + k 2 t ) sin c ( Δ k 1 z k 2 z d 2 ) β k 1 λ 1 β k 2 λ 2 U f ( r 1 ) U f ( r 2 )
× ( ω k 1 2 ε 0 ) 1 2 ( ω k 2 2 ε 0 ) 1 2 e i ω k 1 t 1 e i ω k 2 t 2 δ ( ω k 0 ω k 1 ω k 2 )
f ( r t ) exp ( x 2 + y 2 w p )
f ˜ p ( k 1 t + k 2 t ) exp ( 1 4 w p 2 v 2 ( ω k 1 ω k 2 ) 2 sin 2 θ * )
U k λ in ( x , y ) = 1 i k d e i k ( d + d ) e i k 2 d ( x 2 + y 2 ) 0 2 π 0 R r d θ d r ( e i ( k 2 d k 2 f ) r 2 e i k ( x cos θ d + y sin θ d ) r )
U f ( x , y ) = 1 w 0 π exp ( x 2 + y 2 2 w 0 2 )
β k λ w 0 2 d 2 + i k w 0 4 d k d w 0 ( d 2 + k 2 w 0 4 ) ( 1 e ( A k + i B k ) R 2 ) ( A k + i B k )
A k = k 2 w 0 2 2 ( d 2 + k 2 w 0 4 )
B k = ( 1 2 d 1 2 f ) k k 3 w 0 4 2 d ( d 2 + k 2 w 0 4 )
A ( 2 ) e i τ x x 2 Δ 2 ( 1 e ( a + b x ) ) 2 d x
a = ( k * 2 w 0 2 2 f 2 i k * 3 w 0 4 2 f 3 ) R 2
b = ( k * w 0 2 n g c f 2 i 3 2 n g k * 2 w 0 4 2 c f 3 ) R 2
C ( 1 4 e y + 6 e 2 y 4 e 3 y + e 4 y )

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