Abstract

A two-photon state can be selected by coincidence detection of photon pairs created in parametric downconversion. We demonstrate a reduction in the coincidence-count rate when pairs of photons are combined in a beam splitter. This reduction occurs only when photon wave functions overlap and can permit accurate (subpicosecond) relative timing measurements. We relate the width of the coincidence reduction to the bandwidth of the downconverted light and thence to the detailed phase-matching conditions in the parametric downconversion crystal. We also demonstrate that the loss of coincidences is associated with an increased probability of detection of photon pairs in each output of the beam splitter.

© 1989 Optical Society of America

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References

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  1. Z. Y. Ou, C. K. Hong, L. Mandel, “Relation between input and output states for a beamsplitter,” Opt. Commun. 63, 118–122 (1987).
    [CrossRef]
  2. H. Fearn, R. Loudon, “Quantum theory for the lossless beamsplitter,” Opt. Commun. 64, 485–490 (1987).
    [CrossRef]
  3. S. Prasad, M. O. Scully, W. Martienssen, “A quantum description of the beamsplitter,” Opt. Commun. 62, 139–145 (1987).
    [CrossRef]
  4. J. Brendel, S. Schutrumpf, R. Lange, W. Martienssen, M. O. Scully, “A beam splitting experiment with correlated photons,” Europhys. Lett. 5, 223–228 (1988).
    [CrossRef]
  5. B. R. Mollow, “Photon correlations in the parametric frequency splitting of light,” Phys. Rev. A 8, 2684–2694 (1973).
    [CrossRef]
  6. C. K. Hong, Z. Y. Ou, L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
    [CrossRef] [PubMed]
  7. J. G. Rarity, P. R. Tapster, “Non classical effects in parametric downconversion,” in Photons and Quantum Fluctuations, E. R. Pike, H. Walther, eds. (Hilger, London, 1988), pp. 122–150.
  8. A. Yariv, Introduction to Quantum Electronics (Holt, Rinehart and Winston, San Francisco, 1976), Chaps. 16 and 17.
  9. Z. Y. Ou, “Quantum theory of fourth order interference,” Phys. Rev. A 37, 1607–1619 (1988).
    [CrossRef] [PubMed]
  10. R. G. W. Brown, R. Jones, J. G. Rarity, K. D. Ridley, “Characterization of silicon avalanche photodiodes for photon correlation measurements. 2: Active quenching,” Appl. Opt. 26, 2383–2389 (1987).
    [CrossRef] [PubMed]
  11. Z. Y. Ou, L. Mandel, “Observation of spatial quantum beating with separated photodetectors,” Phys. Rev. Lett. 61, 54–57 (1988).
    [CrossRef] [PubMed]
  12. S. Sarkar, E. R. Pike, “Power law tails of single-photon states in parametric down-conversion,” Europhys. Lett. 7, 581–585 (1988).
    [CrossRef]
  13. Z. Y. Ou, 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]

1988 (5)

J. Brendel, S. Schutrumpf, R. Lange, W. Martienssen, M. O. Scully, “A beam splitting experiment with correlated photons,” Europhys. Lett. 5, 223–228 (1988).
[CrossRef]

Z. Y. Ou, “Quantum theory of fourth order interference,” Phys. Rev. A 37, 1607–1619 (1988).
[CrossRef] [PubMed]

Z. Y. Ou, L. Mandel, “Observation of spatial quantum beating with separated photodetectors,” Phys. Rev. Lett. 61, 54–57 (1988).
[CrossRef] [PubMed]

S. Sarkar, E. R. Pike, “Power law tails of single-photon states in parametric down-conversion,” Europhys. Lett. 7, 581–585 (1988).
[CrossRef]

Z. Y. Ou, 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]

1987 (5)

R. G. W. Brown, R. Jones, J. G. Rarity, K. D. Ridley, “Characterization of silicon avalanche photodiodes for photon correlation measurements. 2: Active quenching,” Appl. Opt. 26, 2383–2389 (1987).
[CrossRef] [PubMed]

Z. Y. Ou, C. K. Hong, L. Mandel, “Relation between input and output states for a beamsplitter,” Opt. Commun. 63, 118–122 (1987).
[CrossRef]

H. Fearn, R. Loudon, “Quantum theory for the lossless beamsplitter,” Opt. Commun. 64, 485–490 (1987).
[CrossRef]

S. Prasad, M. O. Scully, W. Martienssen, “A quantum description of the beamsplitter,” Opt. Commun. 62, 139–145 (1987).
[CrossRef]

C. K. Hong, Z. Y. Ou, L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

1973 (1)

B. R. Mollow, “Photon correlations in the parametric frequency splitting of light,” Phys. Rev. A 8, 2684–2694 (1973).
[CrossRef]

Brendel, J.

J. Brendel, S. Schutrumpf, R. Lange, W. Martienssen, M. O. Scully, “A beam splitting experiment with correlated photons,” Europhys. Lett. 5, 223–228 (1988).
[CrossRef]

Brown, R. G. W.

Fearn, H.

H. Fearn, R. Loudon, “Quantum theory for the lossless beamsplitter,” Opt. Commun. 64, 485–490 (1987).
[CrossRef]

Hong, C. K.

C. K. Hong, Z. Y. Ou, L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

Z. Y. Ou, C. K. Hong, L. Mandel, “Relation between input and output states for a beamsplitter,” Opt. Commun. 63, 118–122 (1987).
[CrossRef]

Jones, R.

Lange, R.

J. Brendel, S. Schutrumpf, R. Lange, W. Martienssen, M. O. Scully, “A beam splitting experiment with correlated photons,” Europhys. Lett. 5, 223–228 (1988).
[CrossRef]

Loudon, R.

H. Fearn, R. Loudon, “Quantum theory for the lossless beamsplitter,” Opt. Commun. 64, 485–490 (1987).
[CrossRef]

Mandel, L.

Z. Y. Ou, 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]

Z. Y. Ou, L. Mandel, “Observation of spatial quantum beating with separated photodetectors,” Phys. Rev. Lett. 61, 54–57 (1988).
[CrossRef] [PubMed]

Z. Y. Ou, C. K. Hong, L. Mandel, “Relation between input and output states for a beamsplitter,” Opt. Commun. 63, 118–122 (1987).
[CrossRef]

C. K. Hong, Z. Y. Ou, L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

Martienssen, W.

J. Brendel, S. Schutrumpf, R. Lange, W. Martienssen, M. O. Scully, “A beam splitting experiment with correlated photons,” Europhys. Lett. 5, 223–228 (1988).
[CrossRef]

S. Prasad, M. O. Scully, W. Martienssen, “A quantum description of the beamsplitter,” Opt. Commun. 62, 139–145 (1987).
[CrossRef]

Mollow, B. R.

B. R. Mollow, “Photon correlations in the parametric frequency splitting of light,” Phys. Rev. A 8, 2684–2694 (1973).
[CrossRef]

Ou, Z. Y.

Z. Y. Ou, L. Mandel, “Observation of spatial quantum beating with separated photodetectors,” Phys. Rev. Lett. 61, 54–57 (1988).
[CrossRef] [PubMed]

Z. Y. Ou, “Quantum theory of fourth order interference,” Phys. Rev. A 37, 1607–1619 (1988).
[CrossRef] [PubMed]

Z. Y. Ou, 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]

C. K. Hong, Z. Y. Ou, L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

Z. Y. Ou, C. K. Hong, L. Mandel, “Relation between input and output states for a beamsplitter,” Opt. Commun. 63, 118–122 (1987).
[CrossRef]

Pike, E. R.

S. Sarkar, E. R. Pike, “Power law tails of single-photon states in parametric down-conversion,” Europhys. Lett. 7, 581–585 (1988).
[CrossRef]

Prasad, S.

S. Prasad, M. O. Scully, W. Martienssen, “A quantum description of the beamsplitter,” Opt. Commun. 62, 139–145 (1987).
[CrossRef]

Rarity, J. G.

R. G. W. Brown, R. Jones, J. G. Rarity, K. D. Ridley, “Characterization of silicon avalanche photodiodes for photon correlation measurements. 2: Active quenching,” Appl. Opt. 26, 2383–2389 (1987).
[CrossRef] [PubMed]

J. G. Rarity, P. R. Tapster, “Non classical effects in parametric downconversion,” in Photons and Quantum Fluctuations, E. R. Pike, H. Walther, eds. (Hilger, London, 1988), pp. 122–150.

Ridley, K. D.

Sarkar, S.

S. Sarkar, E. R. Pike, “Power law tails of single-photon states in parametric down-conversion,” Europhys. Lett. 7, 581–585 (1988).
[CrossRef]

Schutrumpf, S.

J. Brendel, S. Schutrumpf, R. Lange, W. Martienssen, M. O. Scully, “A beam splitting experiment with correlated photons,” Europhys. Lett. 5, 223–228 (1988).
[CrossRef]

Scully, M. O.

J. Brendel, S. Schutrumpf, R. Lange, W. Martienssen, M. O. Scully, “A beam splitting experiment with correlated photons,” Europhys. Lett. 5, 223–228 (1988).
[CrossRef]

S. Prasad, M. O. Scully, W. Martienssen, “A quantum description of the beamsplitter,” Opt. Commun. 62, 139–145 (1987).
[CrossRef]

Tapster, P. R.

J. G. Rarity, P. R. Tapster, “Non classical effects in parametric downconversion,” in Photons and Quantum Fluctuations, E. R. Pike, H. Walther, eds. (Hilger, London, 1988), pp. 122–150.

Yariv, A.

A. Yariv, Introduction to Quantum Electronics (Holt, Rinehart and Winston, San Francisco, 1976), Chaps. 16 and 17.

Appl. Opt. (1)

Europhys. Lett. (2)

S. Sarkar, E. R. Pike, “Power law tails of single-photon states in parametric down-conversion,” Europhys. Lett. 7, 581–585 (1988).
[CrossRef]

J. Brendel, S. Schutrumpf, R. Lange, W. Martienssen, M. O. Scully, “A beam splitting experiment with correlated photons,” Europhys. Lett. 5, 223–228 (1988).
[CrossRef]

Opt. Commun. (3)

Z. Y. Ou, C. K. Hong, L. Mandel, “Relation between input and output states for a beamsplitter,” Opt. Commun. 63, 118–122 (1987).
[CrossRef]

H. Fearn, R. Loudon, “Quantum theory for the lossless beamsplitter,” Opt. Commun. 64, 485–490 (1987).
[CrossRef]

S. Prasad, M. O. Scully, W. Martienssen, “A quantum description of the beamsplitter,” Opt. Commun. 62, 139–145 (1987).
[CrossRef]

Phys. Rev. A (2)

Z. Y. Ou, “Quantum theory of fourth order interference,” Phys. Rev. A 37, 1607–1619 (1988).
[CrossRef] [PubMed]

B. R. Mollow, “Photon correlations in the parametric frequency splitting of light,” Phys. Rev. A 8, 2684–2694 (1973).
[CrossRef]

Phys. Rev. Lett. (3)

C. K. Hong, Z. Y. Ou, L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

Z. Y. Ou, L. Mandel, “Observation of spatial quantum beating with separated photodetectors,” Phys. Rev. Lett. 61, 54–57 (1988).
[CrossRef] [PubMed]

Z. Y. Ou, 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]

Other (2)

J. G. Rarity, P. R. Tapster, “Non classical effects in parametric downconversion,” in Photons and Quantum Fluctuations, E. R. Pike, H. Walther, eds. (Hilger, London, 1988), pp. 122–150.

A. Yariv, Introduction to Quantum Electronics (Holt, Rinehart and Winston, San Francisco, 1976), Chaps. 16 and 17.

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Figures (10)

Fig. 1
Fig. 1

Schematic of the beam splitter (BS) showing inputs 1 and 2 and outputs 3 and 4.

Fig. 2
Fig. 2

Schematic showing the optical distance X′ from a point R in a KDP crystal to an aperture P in air. This distance is equivalent to the physical distance RP, where R′ is the apparent (viewed from P) position of point R. Also defined here are internal angle θi, the external angle θ, the crystal center 0 and the apparent center 0′, and the optical distance from the crystal center to the aperture, X.

Fig. 3
Fig. 3

Beam splitter BS with finite size detectors. and 3 are 4 angular displacements across the detector surfaces. Note that reflection at the beam splitter changes the sign of these angles at the crystal.

Fig. 4
Fig. 4

Block diagram of the photon-localization apparatus. A1 and A2 are apertures. Prism P1 is mounted upon a micrometer-driven translation stage to allow path-length difference δx to be varied. Prism P2 is fixed. The 50/50 beam splitter (S) combines the two beams, which are detected by photon-counting detectors D3 and D4.

Fig. 5
Fig. 5

The measured coincidence rate as a function of prism position δx with narrow-band interference filters in front of detectors.

Fig. 6
Fig. 6

The measured coincidence rate as a function of prism position δx with narrow-band interference filters removed. Aperture of diameter 0.8-mm placed 500 mm from the crystal.

Fig. 7
Fig. 7

Modification of the apparatus used to investigate the enhancement of the coincidence rate across a second beam splitter.

Fig. 8
Fig. 8

The measured enhancement of the coincidence rate across a second beam splitter as a function of prism position δx. Aperture diameter 0.8 mm.

Fig. 9
Fig. 9

The measured coincidence rate as a function, of prism position δx with narrow-band interference filters removed. Aperture of diameter 3.0 mm placed 500 mm from the crystal.

Fig. 10
Fig. 10

Geometry of beam-splitter tilt, showing the equivalence of a tilt angle δ to translation of the pump beam by a distance 2.

Equations (26)

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P 34 ( τ ) A ^ 3 ( - ) ( t , X 3 ) A ^ 4 ( - ) ( t + τ , X 4 ) A ^ 4 ( + ) ( t + τ , X 4 ) A ^ 3 ( + ) ( t , X 3 ) ,
r b 2 + t b 2 = 1 ,             t b r b * + r b t b * = 0.
A ^ 3 ( + ) ( t ) = r b A ^ 1 ( + ) ( t - X T / c + τ 1 ) + t b A ^ 2 ( + ) ( t - X T / c + τ 1 + δ t ) , A ^ 4 ( + ) = t b A ^ 1 ( + ) ( t - X T / c ) + r b A ^ 2 ( + ) ( t - X T / c + δ t ) ,
X 1 + X 4 = X T ,             X 1 - X 2 = c δ t , X 2 + X 3 = X T - c ( τ 1 + δ t ) ,             X 4 - X 3 = c τ 1 ,
C ¯ - Δ T / 2 Δ T / 2 P 34 ( τ - τ 1 ) d τ .
A ^ 1 ( + ) ( t ) A ^ 2 ( + ) ( t ) 2 A ^ j ( + ) t A ^ j ( + ) 2 ,             j = 1 , 2.
C ¯ { r b 4 + t b 4 - r b 2 t b 2 × [ - g 12 * ( δ t - τ ) g 12 ( δ t + τ ) d τ - g 12 ( τ ) 2 d τ + c . c . ] } ,
g 12 ( Δ t ) A ^ 1 ( + ) ( t ¯ 1 ) A ^ 2 ( + ) ( t ¯ 2 ) ,
k 0 = k 1 + k 2 .
ω 0 = ω 1 + ω 2 ,
g 12 d ω 1 d ω 2 ω 1 ω 2 χ ( 2 ) ( ω 0 , ω 1 , ω 2 ) δ ( ω 0 - ω 1 - ω 2 ) d 3 r × exp { - i [ ω 1 ( t 1 - X 1 / c ) + ω 2 ( t 2 - X 2 / c ) ] } exp ( - i k 0 · r ) h ( r ) ,
X j = X j - r j ,             j = 1 , 2 ,
r j = ( r x , r y , r z / n j )
X j = X j - X j · r j ,             j = 1 , 2.
θ 1 = θ + 1 ,             θ 2 = - θ + 2
ω 1 = ω 0 2 + ω ,             ω 2 = ω 0 2 - ω
g 12 ( Δ t ) exp [ - i ω 0 ( t ¯ 1 + t ¯ 2 ) / 2 ] d ω ( ω 0 2 4 - ω 2 ) × χ ( 2 ) ( ω 0 , ω ) exp ( i ω Δ t ) d 3 r × exp [ - i r c ω 0 c Ψ x ( 1 , 2 , ω ) + i r z ω 0 c n 00 Ψ z ( 1 , 2 , ω ) ] h ( r ) ,
Ψ x 1 ( 1 , 2 , ω ) = 2 ω / ω 0 sin θ + cos θ [ ( 1 + 2 ) / 2 + ω / ω 0 ( 1 - 2 ) ] , Ψ z 1 ( 1 , 2 , ω ) = 2 Δ ω 2 / ω 0 cos θ + sin θ [ ( 1 - 2 ) / 2 + ω / ω 0 ( 1 + 2 ) ] + O ( D ω ) .
g 12 exp [ - i ω 0 ( t ¯ 1 + t ¯ 2 ) / 2 ] d ω exp ( i ω Δ t ) f ( ω , 1 , 2 ) , f ( ω , 1 , 2 ) = ( ω 0 2 4 - ω 2 ) χ ( 2 ) ( ω 0 , ω ) exp [ - ω 0 2 σ 2 4 c 2 Ψ x 1 2 ( 1 , 2 , ω ) ] × sinc [ ω 0 L 4 c n 00 Ψ z 1 ( 1 , 2 , ω ) ] .
C ¯ 1 - r b 2 t b 2 r b 4 + t b 4 × [ f * ( ω , 3 , 4 ) f ( - ω , - 3 , - 4 ) exp ( - i 2 ω δ t ) d ω f ( ω , 3 , 4 ) 2 d ω + c . c . ] .
f ( ω , 0 , 0 ) = K exp ( - ω 2 σ 2 sin 2 θ / c 2 ) sinc ( ω 2 D L cos θ 2 c n 00 ) .
C ¯ 1 - V exp [ - ( δ x 2 2 σ 2 sin 2 θ ) ] ,
V = r b 2 t b 2 r b 4 + t b 4 .
C ¯ 1 - V exp { - [ δ x 2 2 σ 2 sin 2 θ ( 1 + b ) ] } ,             b = π 2 σ 2 Σ 2 cos 2 θ / λ 2 ,
f ( ω ) = f ( ω ) exp { i δ ϕ X 2 c [ ( 3 + 4 ) ω 0 - 2 ( 3 - 4 ) ω ] } .
C ¯ 1 - V exp { - [ δ x 2 2 σ 2 sin 2 θ ( 1 + b ) ] } , V = V exp { - [ ω 0 2 X 2 δ ϕ 2 Σ 2 2 c 2 ( 1 + b ) ] }

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