Abstract

Measurement of the two-photon time distribution in a mixture of light from a He–Ne laser and a Gaussian source of the same central frequency agrees well with the prediction of coherence theory when the laser is represented by a single coherent state. The peak in the distribution near zero time difference is made up of contributions due to the second-order interference between pairs of Gaussian photons and between laser and Gaussian photons.

© 1972 Optical Society of America

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References

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  1. R. Hanbury Brown, R. Q. Twiss, Nature 177, 27 (1956).
    [CrossRef]
  2. R. Q. Twiss, A. G. Little, R. Hanbury Brown, Nature 180, 324 (1957).
    [CrossRef]
  3. G. A. Rebka, R. V. Pound, Nature 180, 1035 (1957).
    [CrossRef]
  4. V. Brannen, H. I. Ferguson, W. Wehlau, Can. J. Phys. 36, 871 (1958).
    [CrossRef]
  5. W. Martienssen, E. Spiller, Am. J. Phys. 32, 919 (1964).
    [CrossRef]
  6. J. A. Armstrong, A. W. Smith, Phys. Rev. Lett. 14, 68 (1965); Phys. Lett. 16, 38 (1965); Phys. Rev. 140, A155 (1965).
    [CrossRef]
  7. B. L. Morgan, L. Mandel, Phys. Rev. Lett. 16, 1012 (1966).
    [CrossRef]
  8. F. T. Arecchi, E. Gatti, A. Sona, Phys. Lett. 20, 27 (1966).
    [CrossRef]
  9. F. Davidson, L. Mandel, Phys. Lett. 25A, 700 (1967).
  10. D. T. Phillips, H. Kleiman, S. P. Davis, Phys. Rev. 153, 113 (1967).
    [CrossRef]
  11. D. B. Scarl, Phys. Rev. Lett. 17, 663 (1966); Phys. Rev. 175, 1661 (1968).
    [CrossRef]
  12. C. Bendjaballah, Compt. Rend. 268, 1719 (1969).
  13. H. Morawitz, Phys. Rev. 139, A1072 (1965).
    [CrossRef]
  14. L. Mandel, E. Wolf, Phys. Rev. 149, 1033 (1966).
    [CrossRef]
  15. C. D. Cantrell, Phys. Rev. A3, 728 (1971) and references therein.
  16. F. T. Arecchi, A. Berne, P. Bulamacchi, Phys. Rev. Lett. 16, 32 (1966).
    [CrossRef]
  17. W. Martienssen, E. Spiller, Phys. Rev. 145, 285 (1966).
    [CrossRef]
  18. C. Freed, H. A. Haus, Phys. Rev. 141, 287 (1966); Phys. Rev. Lett. 15, 943 (1965).
    [CrossRef]
  19. A. W. Smith, J. A. Armstrong, Phys. Lett. 19, 650 (1965); Phys. Rev. Lett. 16, 1169 (1966).
  20. R. J. Magill, R. P. Soni, Phys. Rev. Lett. 16, 911 (1966).
    [CrossRef]
  21. F. T. Arecchi, G. S. Rodari, A. Sona, Phys. Lett. 25A, 59 (1967).
  22. R. F. Chang, R. W. Detenbeck, V. Korenman, C. O. Alley, U. Hochuli, Phys. Lett. 25A, 272 (1967); R. F. Chang, V. Korenman, C. O. Alley, R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
    [CrossRef]
  23. R. J. Glauber, Phys. Rev. 131, 2766 (1963); in Quantum Optics and Electronics, C. DeWitt et al., Ed. (Gordon & Breach, New York, 1965).
    [CrossRef]

1971

C. D. Cantrell, Phys. Rev. A3, 728 (1971) and references therein.

1969

C. Bendjaballah, Compt. Rend. 268, 1719 (1969).

1967

F. Davidson, L. Mandel, Phys. Lett. 25A, 700 (1967).

D. T. Phillips, H. Kleiman, S. P. Davis, Phys. Rev. 153, 113 (1967).
[CrossRef]

F. T. Arecchi, G. S. Rodari, A. Sona, Phys. Lett. 25A, 59 (1967).

R. F. Chang, R. W. Detenbeck, V. Korenman, C. O. Alley, U. Hochuli, Phys. Lett. 25A, 272 (1967); R. F. Chang, V. Korenman, C. O. Alley, R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[CrossRef]

1966

L. Mandel, E. Wolf, Phys. Rev. 149, 1033 (1966).
[CrossRef]

R. J. Magill, R. P. Soni, Phys. Rev. Lett. 16, 911 (1966).
[CrossRef]

D. B. Scarl, Phys. Rev. Lett. 17, 663 (1966); Phys. Rev. 175, 1661 (1968).
[CrossRef]

F. T. Arecchi, A. Berne, P. Bulamacchi, Phys. Rev. Lett. 16, 32 (1966).
[CrossRef]

W. Martienssen, E. Spiller, Phys. Rev. 145, 285 (1966).
[CrossRef]

C. Freed, H. A. Haus, Phys. Rev. 141, 287 (1966); Phys. Rev. Lett. 15, 943 (1965).
[CrossRef]

B. L. Morgan, L. Mandel, Phys. Rev. Lett. 16, 1012 (1966).
[CrossRef]

F. T. Arecchi, E. Gatti, A. Sona, Phys. Lett. 20, 27 (1966).
[CrossRef]

1965

J. A. Armstrong, A. W. Smith, Phys. Rev. Lett. 14, 68 (1965); Phys. Lett. 16, 38 (1965); Phys. Rev. 140, A155 (1965).
[CrossRef]

A. W. Smith, J. A. Armstrong, Phys. Lett. 19, 650 (1965); Phys. Rev. Lett. 16, 1169 (1966).

H. Morawitz, Phys. Rev. 139, A1072 (1965).
[CrossRef]

1964

W. Martienssen, E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

1963

R. J. Glauber, Phys. Rev. 131, 2766 (1963); in Quantum Optics and Electronics, C. DeWitt et al., Ed. (Gordon & Breach, New York, 1965).
[CrossRef]

1958

V. Brannen, H. I. Ferguson, W. Wehlau, Can. J. Phys. 36, 871 (1958).
[CrossRef]

1957

R. Q. Twiss, A. G. Little, R. Hanbury Brown, Nature 180, 324 (1957).
[CrossRef]

G. A. Rebka, R. V. Pound, Nature 180, 1035 (1957).
[CrossRef]

1956

R. Hanbury Brown, R. Q. Twiss, Nature 177, 27 (1956).
[CrossRef]

Alley, C. O.

R. F. Chang, R. W. Detenbeck, V. Korenman, C. O. Alley, U. Hochuli, Phys. Lett. 25A, 272 (1967); R. F. Chang, V. Korenman, C. O. Alley, R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[CrossRef]

Arecchi, F. T.

F. T. Arecchi, G. S. Rodari, A. Sona, Phys. Lett. 25A, 59 (1967).

F. T. Arecchi, E. Gatti, A. Sona, Phys. Lett. 20, 27 (1966).
[CrossRef]

F. T. Arecchi, A. Berne, P. Bulamacchi, Phys. Rev. Lett. 16, 32 (1966).
[CrossRef]

Armstrong, J. A.

A. W. Smith, J. A. Armstrong, Phys. Lett. 19, 650 (1965); Phys. Rev. Lett. 16, 1169 (1966).

J. A. Armstrong, A. W. Smith, Phys. Rev. Lett. 14, 68 (1965); Phys. Lett. 16, 38 (1965); Phys. Rev. 140, A155 (1965).
[CrossRef]

Bendjaballah, C.

C. Bendjaballah, Compt. Rend. 268, 1719 (1969).

Berne, A.

F. T. Arecchi, A. Berne, P. Bulamacchi, Phys. Rev. Lett. 16, 32 (1966).
[CrossRef]

Brannen, V.

V. Brannen, H. I. Ferguson, W. Wehlau, Can. J. Phys. 36, 871 (1958).
[CrossRef]

Bulamacchi, P.

F. T. Arecchi, A. Berne, P. Bulamacchi, Phys. Rev. Lett. 16, 32 (1966).
[CrossRef]

Cantrell, C. D.

C. D. Cantrell, Phys. Rev. A3, 728 (1971) and references therein.

Chang, R. F.

R. F. Chang, R. W. Detenbeck, V. Korenman, C. O. Alley, U. Hochuli, Phys. Lett. 25A, 272 (1967); R. F. Chang, V. Korenman, C. O. Alley, R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[CrossRef]

Davidson, F.

F. Davidson, L. Mandel, Phys. Lett. 25A, 700 (1967).

Davis, S. P.

D. T. Phillips, H. Kleiman, S. P. Davis, Phys. Rev. 153, 113 (1967).
[CrossRef]

Detenbeck, R. W.

R. F. Chang, R. W. Detenbeck, V. Korenman, C. O. Alley, U. Hochuli, Phys. Lett. 25A, 272 (1967); R. F. Chang, V. Korenman, C. O. Alley, R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[CrossRef]

Ferguson, H. I.

V. Brannen, H. I. Ferguson, W. Wehlau, Can. J. Phys. 36, 871 (1958).
[CrossRef]

Freed, C.

C. Freed, H. A. Haus, Phys. Rev. 141, 287 (1966); Phys. Rev. Lett. 15, 943 (1965).
[CrossRef]

Gatti, E.

F. T. Arecchi, E. Gatti, A. Sona, Phys. Lett. 20, 27 (1966).
[CrossRef]

Glauber, R. J.

R. J. Glauber, Phys. Rev. 131, 2766 (1963); in Quantum Optics and Electronics, C. DeWitt et al., Ed. (Gordon & Breach, New York, 1965).
[CrossRef]

Hanbury Brown, R.

R. Q. Twiss, A. G. Little, R. Hanbury Brown, Nature 180, 324 (1957).
[CrossRef]

R. Hanbury Brown, R. Q. Twiss, Nature 177, 27 (1956).
[CrossRef]

Haus, H. A.

C. Freed, H. A. Haus, Phys. Rev. 141, 287 (1966); Phys. Rev. Lett. 15, 943 (1965).
[CrossRef]

Hochuli, U.

R. F. Chang, R. W. Detenbeck, V. Korenman, C. O. Alley, U. Hochuli, Phys. Lett. 25A, 272 (1967); R. F. Chang, V. Korenman, C. O. Alley, R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[CrossRef]

Kleiman, H.

D. T. Phillips, H. Kleiman, S. P. Davis, Phys. Rev. 153, 113 (1967).
[CrossRef]

Korenman, V.

R. F. Chang, R. W. Detenbeck, V. Korenman, C. O. Alley, U. Hochuli, Phys. Lett. 25A, 272 (1967); R. F. Chang, V. Korenman, C. O. Alley, R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[CrossRef]

Little, A. G.

R. Q. Twiss, A. G. Little, R. Hanbury Brown, Nature 180, 324 (1957).
[CrossRef]

Magill, R. J.

R. J. Magill, R. P. Soni, Phys. Rev. Lett. 16, 911 (1966).
[CrossRef]

Mandel, L.

F. Davidson, L. Mandel, Phys. Lett. 25A, 700 (1967).

B. L. Morgan, L. Mandel, Phys. Rev. Lett. 16, 1012 (1966).
[CrossRef]

L. Mandel, E. Wolf, Phys. Rev. 149, 1033 (1966).
[CrossRef]

Martienssen, W.

W. Martienssen, E. Spiller, Phys. Rev. 145, 285 (1966).
[CrossRef]

W. Martienssen, E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Morawitz, H.

H. Morawitz, Phys. Rev. 139, A1072 (1965).
[CrossRef]

Morgan, B. L.

B. L. Morgan, L. Mandel, Phys. Rev. Lett. 16, 1012 (1966).
[CrossRef]

Phillips, D. T.

D. T. Phillips, H. Kleiman, S. P. Davis, Phys. Rev. 153, 113 (1967).
[CrossRef]

Pound, R. V.

G. A. Rebka, R. V. Pound, Nature 180, 1035 (1957).
[CrossRef]

Rebka, G. A.

G. A. Rebka, R. V. Pound, Nature 180, 1035 (1957).
[CrossRef]

Rodari, G. S.

F. T. Arecchi, G. S. Rodari, A. Sona, Phys. Lett. 25A, 59 (1967).

Scarl, D. B.

D. B. Scarl, Phys. Rev. Lett. 17, 663 (1966); Phys. Rev. 175, 1661 (1968).
[CrossRef]

Smith, A. W.

A. W. Smith, J. A. Armstrong, Phys. Lett. 19, 650 (1965); Phys. Rev. Lett. 16, 1169 (1966).

J. A. Armstrong, A. W. Smith, Phys. Rev. Lett. 14, 68 (1965); Phys. Lett. 16, 38 (1965); Phys. Rev. 140, A155 (1965).
[CrossRef]

Sona, A.

F. T. Arecchi, G. S. Rodari, A. Sona, Phys. Lett. 25A, 59 (1967).

F. T. Arecchi, E. Gatti, A. Sona, Phys. Lett. 20, 27 (1966).
[CrossRef]

Soni, R. P.

R. J. Magill, R. P. Soni, Phys. Rev. Lett. 16, 911 (1966).
[CrossRef]

Spiller, E.

W. Martienssen, E. Spiller, Phys. Rev. 145, 285 (1966).
[CrossRef]

W. Martienssen, E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Twiss, R. Q.

R. Q. Twiss, A. G. Little, R. Hanbury Brown, Nature 180, 324 (1957).
[CrossRef]

R. Hanbury Brown, R. Q. Twiss, Nature 177, 27 (1956).
[CrossRef]

Wehlau, W.

V. Brannen, H. I. Ferguson, W. Wehlau, Can. J. Phys. 36, 871 (1958).
[CrossRef]

Wolf, E.

L. Mandel, E. Wolf, Phys. Rev. 149, 1033 (1966).
[CrossRef]

Am. J. Phys.

W. Martienssen, E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Can. J. Phys.

V. Brannen, H. I. Ferguson, W. Wehlau, Can. J. Phys. 36, 871 (1958).
[CrossRef]

Compt. Rend.

C. Bendjaballah, Compt. Rend. 268, 1719 (1969).

Nature

R. Hanbury Brown, R. Q. Twiss, Nature 177, 27 (1956).
[CrossRef]

R. Q. Twiss, A. G. Little, R. Hanbury Brown, Nature 180, 324 (1957).
[CrossRef]

G. A. Rebka, R. V. Pound, Nature 180, 1035 (1957).
[CrossRef]

Phys. Lett.

F. T. Arecchi, E. Gatti, A. Sona, Phys. Lett. 20, 27 (1966).
[CrossRef]

F. Davidson, L. Mandel, Phys. Lett. 25A, 700 (1967).

A. W. Smith, J. A. Armstrong, Phys. Lett. 19, 650 (1965); Phys. Rev. Lett. 16, 1169 (1966).

F. T. Arecchi, G. S. Rodari, A. Sona, Phys. Lett. 25A, 59 (1967).

R. F. Chang, R. W. Detenbeck, V. Korenman, C. O. Alley, U. Hochuli, Phys. Lett. 25A, 272 (1967); R. F. Chang, V. Korenman, C. O. Alley, R. W. Detenbeck, Phys. Rev. 178, 612 (1969).
[CrossRef]

Phys. Rev.

R. J. Glauber, Phys. Rev. 131, 2766 (1963); in Quantum Optics and Electronics, C. DeWitt et al., Ed. (Gordon & Breach, New York, 1965).
[CrossRef]

W. Martienssen, E. Spiller, Phys. Rev. 145, 285 (1966).
[CrossRef]

C. Freed, H. A. Haus, Phys. Rev. 141, 287 (1966); Phys. Rev. Lett. 15, 943 (1965).
[CrossRef]

H. Morawitz, Phys. Rev. 139, A1072 (1965).
[CrossRef]

L. Mandel, E. Wolf, Phys. Rev. 149, 1033 (1966).
[CrossRef]

C. D. Cantrell, Phys. Rev. A3, 728 (1971) and references therein.

D. T. Phillips, H. Kleiman, S. P. Davis, Phys. Rev. 153, 113 (1967).
[CrossRef]

Phys. Rev. Lett.

D. B. Scarl, Phys. Rev. Lett. 17, 663 (1966); Phys. Rev. 175, 1661 (1968).
[CrossRef]

J. A. Armstrong, A. W. Smith, Phys. Rev. Lett. 14, 68 (1965); Phys. Lett. 16, 38 (1965); Phys. Rev. 140, A155 (1965).
[CrossRef]

B. L. Morgan, L. Mandel, Phys. Rev. Lett. 16, 1012 (1966).
[CrossRef]

F. T. Arecchi, A. Berne, P. Bulamacchi, Phys. Rev. Lett. 16, 32 (1966).
[CrossRef]

R. J. Magill, R. P. Soni, Phys. Rev. Lett. 16, 911 (1966).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

The experimental arrangement.

Fig. 2
Fig. 2

The integral of spatial coherence for the interference of laser and Gaussian photons as a function of the diameter of the second circular aperture d, the diameter of the first circular aperture a, the distance between apertures L, and the wavelength λ.

Fig. 3
Fig. 3

The distribution in time between consecutive detected photons in a beam made up of 50% laser and 50% Gaussian light. The error bar indicates the statistical error and applies to all points.

Equations (27)

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W = T r ρ A ( x 1 ) A ( x 2 ) A ( x 1 ) 2 ,
W = G ( 2 ) ( x 1 , x 2 , x 2 , x 1 ) 2 .
ρ = l ρ l .
ρ l = P l ( α l ) α l > < α l d 2 α l .
P l ( α l ) = ( 1 / π n l ) exp ( - α l 2 / n l ) ,
P = ( 1 / π n ) exp ( - α 2 / n ) ,
P = δ ( 2 ) ( α - α 0 ) .
P L ( α L ) = ( 1 / π n L ) exp ( - α L - α 0 2 / n L ) ,
H L = ω L α 0 2 ,
H G ( ω L ) = ω L n L .
P = 1 π n L exp ( - α L - α 0 2 / n L ) l L 1 π n l exp ( - α l 2 / n l ) .
G ( 1 ) ( x 1 , x 2 ) = T r ρ A ( x 1 ) A ( x 2 )
G ( 2 ) ( x 1 , x 2 , x 2 , x 1 ) = G ( 1 ) ( x 1 , x 1 ) G ( 1 ) ( x 2 , x 2 ) + G ( 1 ) ( x 1 , x 2 ) G ( 1 ) ( x 2 , x 1 ) - G L ( 1 ) ( x 1 , x 2 ) G L ( 1 ) ( x 2 , x 1 ) .
G ( 1 ) = G L ( 1 ) + G G ( 1 ) ,
G L ( 1 ) = T r ρ L A ( x 1 ) A ( x 2 )
G G ( 1 ) = T r ρ G A ( x 1 ) A ( x 2 ) .
G G ( 1 ) ( x 1 , x 1 ) = G G ( 1 ) ( x 2 , x 2 ) = H G , G L ( 1 ) ( x 1 , x 1 ) = G L ( 1 ) ( x 2 , x 2 ) = H L , G G ( 1 ) ( x 1 , x 2 ) = G G * ( 1 ) ( x 2 , x 1 ) = H G q ( Δ r ) f ( Δ t ) , G L ( 1 ) ( x 1 , x 2 ) = G L * ( 1 ) ( x 2 , x 1 ) = H L exp ( i k L · Δ r ) exp ( i ω L Δ t ) .
q ( Δ r ) = 2 J 1 ( π a Δ r / λ L ) π a Δ r / λ L ,
f ( Δ t ) = exp ( i ω 0 Δ t ) exp [ - ( Δ t ) 2 / 2 σ t 2 ] ,
W = 2 H T 2 { 1 + F G 2 q 2 ( Δ r ) exp [ - ( Δ t ) 2 / σ t 2 ] + 2 F G F L q ( Δ r ) exp [ - ( Δ t ) 2 / 2 σ t 2 ] } ,
S 1 = Aperture q 2 ( Δ r ) d r 1 d r 2
S 2 = Aperture q ( Δ r ) d r 1 d r 2
R = W d t d A d A = I 2 T { 1 + C 1 exp [ - ( Δ t ) 2 / 2 σ 1 2 ] + C 2 exp [ - ( Δ t ) 2 / 2 σ 2 2 ] } .
I = I G + I L + N
C 1 = I G 2 S 1 σ t / 2 I 2 σ t , C 2 = I G I L S 2 σ t / I 2 σ 2 ,
σ 1 2 = 2 σ t 2 + σ 2 , σ 2 2 = σ t 2 + σ 2 .
R = R 0 { 1 + 0.039 exp [ - ( Δ t ) 2 / 0.65 ] + 0.121 exp [ - ( Δ t ) 2 / 0.69 ] } .

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