Abstract

A two-photon wave packet (a biphoton) produced by type-II parametric downconversion is studied in a simple beam-splitting experiment for its natural shape in space–time. The measured triangular shape of a two-photon correlation function is the signature of a rectangular-shaped biphoton. Inserting a birefringent sample into the beam causes a displacement of the vertex of the notch pattern, which can be used to measure the optical delay between the ordinary and the extraordinary rays in the sample with femtosecond resolution.

© 1995 Optical Society of America

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References

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  1. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
    [CrossRef]
  2. J. S. Bell, Physics 1, 195 (1964).
  3. D. N. Klyshko, Photons and Nonlinear Optics (Gordon & Breach, New York, 1988).
  4. A. Yariv, Quantum Electronics (Wiley, New York, 1967).
  5. Y. H. Shih and C. O. Alley, Phys. Rev. Lett. 61, 2921 (1988).
    [CrossRef] [PubMed]
  6. Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 61, 50 (1988).
    [CrossRef] [PubMed]
  7. C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
    [CrossRef] [PubMed]
  8. Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 61, 54 (1988);P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 47, 2472 (1993).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. Y. H. Shih and A. V. Sergienko, Phys. Lett. A 186, 29 (1994).
    [CrossRef]
  12. Y. H. Shih and A. V. Sergienko, Phys. Rev. A 50, 2564 (1994).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 1903 (1987).
    [CrossRef]
  15. J. G. Rarity and P. R. Tapster, J. Opt. Soc. Am. B 6, 1221 (1989).
    [CrossRef]

1994 (2)

Y. H. Shih and A. V. Sergienko, Phys. Lett. A 186, 29 (1994).
[CrossRef]

Y. H. Shih and A. V. Sergienko, Phys. Rev. A 50, 2564 (1994).
[CrossRef] [PubMed]

1993 (2)

A M. Steinberg, P. G. Kwiat, and R. Y. Chiao, Phys. Rev. Lett. 71, 708 (1993).
[CrossRef] [PubMed]

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, Phys. Rev. Lett. 71, 3893 (1993).
[CrossRef] [PubMed]

1991 (1)

J. Brendel, E. Mohler, and W. Martienssen, Phys. Rev. Lett. 66, 1142 (1991);T. S. Larchuk, R. A. Campos, J. G. Rarity, P. R. Tapster, E. Jakeman, B. E. A. Saleh, and M. C. Teich, Phys. Rev. Lett. 70, 1603 (1993).
[CrossRef] [PubMed]

1989 (1)

1988 (3)

Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 61, 54 (1988);P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 47, 2472 (1993).
[CrossRef] [PubMed]

Y. H. Shih and C. O. Alley, Phys. Rev. Lett. 61, 2921 (1988).
[CrossRef] [PubMed]

Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 61, 50 (1988).
[CrossRef] [PubMed]

1987 (2)

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[CrossRef] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 1903 (1987).
[CrossRef]

1964 (1)

J. S. Bell, Physics 1, 195 (1964).

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
[CrossRef]

Alley, C. O.

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, Phys. Rev. Lett. 71, 3893 (1993).
[CrossRef] [PubMed]

Y. H. Shih and C. O. Alley, Phys. Rev. Lett. 61, 2921 (1988).
[CrossRef] [PubMed]

Bell, J. S.

J. S. Bell, Physics 1, 195 (1964).

Brendel, J.

J. Brendel, E. Mohler, and W. Martienssen, Phys. Rev. Lett. 66, 1142 (1991);T. S. Larchuk, R. A. Campos, J. G. Rarity, P. R. Tapster, E. Jakeman, B. E. A. Saleh, and M. C. Teich, Phys. Rev. Lett. 70, 1603 (1993).
[CrossRef] [PubMed]

Chiao, R. Y.

A M. Steinberg, P. G. Kwiat, and R. Y. Chiao, Phys. Rev. Lett. 71, 708 (1993).
[CrossRef] [PubMed]

Einstein, A.

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
[CrossRef]

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[CrossRef] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 1903 (1987).
[CrossRef]

Kiess, T. E.

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, Phys. Rev. Lett. 71, 3893 (1993).
[CrossRef] [PubMed]

Klyshko, D. N.

D. N. Klyshko, Photons and Nonlinear Optics (Gordon & Breach, New York, 1988).

Kwiat, P. G.

A M. Steinberg, P. G. Kwiat, and R. Y. Chiao, Phys. Rev. Lett. 71, 708 (1993).
[CrossRef] [PubMed]

Mandel, L.

Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 61, 50 (1988).
[CrossRef] [PubMed]

Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 61, 54 (1988);P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 47, 2472 (1993).
[CrossRef] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[CrossRef] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 1903 (1987).
[CrossRef]

Martienssen, W.

J. Brendel, E. Mohler, and W. Martienssen, Phys. Rev. Lett. 66, 1142 (1991);T. S. Larchuk, R. A. Campos, J. G. Rarity, P. R. Tapster, E. Jakeman, B. E. A. Saleh, and M. C. Teich, Phys. Rev. Lett. 70, 1603 (1993).
[CrossRef] [PubMed]

Mohler, E.

J. Brendel, E. Mohler, and W. Martienssen, Phys. Rev. Lett. 66, 1142 (1991);T. S. Larchuk, R. A. Campos, J. G. Rarity, P. R. Tapster, E. Jakeman, B. E. A. Saleh, and M. C. Teich, Phys. Rev. Lett. 70, 1603 (1993).
[CrossRef] [PubMed]

Ou, Z. Y.

Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 61, 54 (1988);P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 47, 2472 (1993).
[CrossRef] [PubMed]

Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 61, 50 (1988).
[CrossRef] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[CrossRef] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 1903 (1987).
[CrossRef]

Podolsky, B.

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
[CrossRef]

Rarity, J. G.

Rosen, N.

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
[CrossRef]

Sergienko, A. V.

Y. H. Shih and A. V. Sergienko, Phys. Lett. A 186, 29 (1994).
[CrossRef]

Y. H. Shih and A. V. Sergienko, Phys. Rev. A 50, 2564 (1994).
[CrossRef] [PubMed]

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, Phys. Rev. Lett. 71, 3893 (1993).
[CrossRef] [PubMed]

Shih, Y. H.

Y. H. Shih and A. V. Sergienko, Phys. Rev. A 50, 2564 (1994).
[CrossRef] [PubMed]

Y. H. Shih and A. V. Sergienko, Phys. Lett. A 186, 29 (1994).
[CrossRef]

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, Phys. Rev. Lett. 71, 3893 (1993).
[CrossRef] [PubMed]

Y. H. Shih and C. O. Alley, Phys. Rev. Lett. 61, 2921 (1988).
[CrossRef] [PubMed]

Steinberg, A M.

A M. Steinberg, P. G. Kwiat, and R. Y. Chiao, Phys. Rev. Lett. 71, 708 (1993).
[CrossRef] [PubMed]

Tapster, P. R.

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1967).

J. Opt. Soc. Am. B (1)

Phys. Lett. A (1)

Y. H. Shih and A. V. Sergienko, Phys. Lett. A 186, 29 (1994).
[CrossRef]

Phys. Rev. (1)

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
[CrossRef]

Phys. Rev. A (1)

Y. H. Shih and A. V. Sergienko, Phys. Rev. A 50, 2564 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (8)

A M. Steinberg, P. G. Kwiat, and R. Y. Chiao, Phys. Rev. Lett. 71, 708 (1993).
[CrossRef] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 1903 (1987).
[CrossRef]

Y. H. Shih and C. O. Alley, Phys. Rev. Lett. 61, 2921 (1988).
[CrossRef] [PubMed]

Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 61, 50 (1988).
[CrossRef] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987).
[CrossRef] [PubMed]

Z. Y. Ou and L. Mandel, Phys. Rev. Lett. 61, 54 (1988);P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev. A 47, 2472 (1993).
[CrossRef] [PubMed]

J. Brendel, E. Mohler, and W. Martienssen, Phys. Rev. Lett. 66, 1142 (1991);T. S. Larchuk, R. A. Campos, J. G. Rarity, P. R. Tapster, E. Jakeman, B. E. A. Saleh, and M. C. Teich, Phys. Rev. Lett. 70, 1603 (1993).
[CrossRef] [PubMed]

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, Phys. Rev. Lett. 71, 3893 (1993).
[CrossRef] [PubMed]

Physics (1)

J. S. Bell, Physics 1, 195 (1964).

Other (2)

D. N. Klyshko, Photons and Nonlinear Optics (Gordon & Breach, New York, 1988).

A. Yariv, Quantum Electronics (Wiley, New York, 1967).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the experimental setup. BS, beam splitter; f1, f2, spectral filters; D1, D2, single-photon detector packages; Nc, coincidence count.

Fig. 2
Fig. 2

Schematic of the Π(t) part of a two-photon wave function.

Fig. 3
Fig. 3

Observation of a V-shaped correlation function and measurement of optical delay in a 2.4-mm-thick sample of crystal quartz.

Equations (16)

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ω 1 + ω 2 = ω p , k 1 + k 2 = k p ,
| Ψ = d ω 1 δ ( ω 1 + ω 2 ω p ) ψ ( k 1 + k 2 k p ) a o [ ω 1 ( k 1 ) ] × a e [ ω 2 ( k 2 ) ] | 0 ,
ψ ( Δ k ) = [ 1 exp ( i Δ k L ) ] / ( i Δ k L ) ,
k 1 = k o + ν ( d k o / d Ω o ) = k o + ν / u o , k 2 = k e ν ( d k e / d Ω e ) = k e ν / u e ,
ψ ( ν ) = [ 1 exp ( i ν D L ) ] / i ν D ,
E 1 ( + ) ( t ) = α t d ω exp [ i ω ( t τ 1 ) ] j ê 1 ê j a j ( ω ) , E 2 ( + ) ( t ) = α r d ω exp [ i ω ( t τ 2 ) ] j ê 2 ê j a j ( ω ) ,
R c = ( 1 / T ) 0 T d T 1 d T 2 | Ψ ( t 1 , t 2 ) | 2 ,
Ψ ( t 1 , t 2 ) = 0 | E 1 ( + ) E 2 ( + ) | Ψ .
Ψ ( t 1 , t 2 ) = α t α r υ ( t 1 + t 2 ) [ u ( t 1 t 2 ) u ( t 1 + t 2 ) ] ,
υ ( t ) = υ 0 exp ( i ω p t / 2 ) ,
u ( t ) = u 0 exp ( i ω d t / 2 ) d ν [ 1 exp ( ν D L ) ] / ( i ν D L ) × exp ( i ν t ) = exp ( i ω d t / 2 ) Π ( t ) .
Π ( t ) = { u 0 D L > t > 0 0 otherwise ,
Ψ ( t 1 , t 2 ) = υ 0 exp ( σ 2 ( t 1 + t 2 ) 2 / 8 ) Π ( t 1 t 2 ) exp ( i Ω o t 1 ) × exp ( i Ω o t 2 ) .
Ψ ( T 1 , T 2 ) = α t α r υ ( T 1 + T 2 ϕ ) [ u ( T 1 T 2 + δ ) u ( T 1 + T 2 + δ ) ] ,
R c = R c 0 [ 1 ρ ( δ ) ] ,
ρ = { 0 < δ < 0 κ δ 0 < δ D L / 2 1 κ ( δ D 1 / 2 ) D L / 2 δ < D L 0 D L < δ < ,

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