Abstract

It has long been known that the interference produced by two light beams is related both to their mutual coherence and also to the intrinsic indistinguishability of the photon paths. With the help of a decomposition of the density operator it is shown that the degree of indistinguishability equals the degree of coherence. This provides the fundamental link between the wave and the particle descriptions.

© 1991 Optical Society of America

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References

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  1. F. Zernike, Physica 5, 785 (1975).
    [CrossRef]
  2. See, for example, M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 10.
  3. E. Wolf, Nuovo Cimento 13, 1165 (1959).
    [CrossRef]
  4. M. O. Scully, B.-G. Englert, H. Walther, Nature 351, 111 (1991).
    [CrossRef]
  5. A. G. Zajonc, L. J. Wang, X. Y. Zou, L. Mandel, “Quantum interference and the quantum error,” Nature (to be published).
  6. X. Y. Zou, L. J. Wang, L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
    [CrossRef] [PubMed]

1991 (2)

M. O. Scully, B.-G. Englert, H. Walther, Nature 351, 111 (1991).
[CrossRef]

X. Y. Zou, L. J. Wang, L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
[CrossRef] [PubMed]

1975 (1)

F. Zernike, Physica 5, 785 (1975).
[CrossRef]

1959 (1)

E. Wolf, Nuovo Cimento 13, 1165 (1959).
[CrossRef]

Born, M.

See, for example, M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 10.

Englert, B.-G.

M. O. Scully, B.-G. Englert, H. Walther, Nature 351, 111 (1991).
[CrossRef]

Mandel, L.

X. Y. Zou, L. J. Wang, L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
[CrossRef] [PubMed]

A. G. Zajonc, L. J. Wang, X. Y. Zou, L. Mandel, “Quantum interference and the quantum error,” Nature (to be published).

Scully, M. O.

M. O. Scully, B.-G. Englert, H. Walther, Nature 351, 111 (1991).
[CrossRef]

Walther, H.

M. O. Scully, B.-G. Englert, H. Walther, Nature 351, 111 (1991).
[CrossRef]

Wang, L. J.

X. Y. Zou, L. J. Wang, L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
[CrossRef] [PubMed]

A. G. Zajonc, L. J. Wang, X. Y. Zou, L. Mandel, “Quantum interference and the quantum error,” Nature (to be published).

Wolf, E.

E. Wolf, Nuovo Cimento 13, 1165 (1959).
[CrossRef]

See, for example, M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 10.

Zajonc, A. G.

A. G. Zajonc, L. J. Wang, X. Y. Zou, L. Mandel, “Quantum interference and the quantum error,” Nature (to be published).

Zernike, F.

F. Zernike, Physica 5, 785 (1975).
[CrossRef]

Zou, X. Y.

X. Y. Zou, L. J. Wang, L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
[CrossRef] [PubMed]

A. G. Zajonc, L. J. Wang, X. Y. Zou, L. Mandel, “Quantum interference and the quantum error,” Nature (to be published).

Nature (1)

M. O. Scully, B.-G. Englert, H. Walther, Nature 351, 111 (1991).
[CrossRef]

Nuovo Cimento (1)

E. Wolf, Nuovo Cimento 13, 1165 (1959).
[CrossRef]

Phys. Rev. Lett. (1)

X. Y. Zou, L. J. Wang, L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
[CrossRef] [PubMed]

Physica (1)

F. Zernike, Physica 5, 785 (1975).
[CrossRef]

Other (2)

See, for example, M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Chap. 10.

A. G. Zajonc, L. J. Wang, X. Y. Zou, L. Mandel, “Quantum interference and the quantum error,” Nature (to be published).

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Figures (2)

Fig. 1
Fig. 1

Outline of the interference experiment under consideration.

Fig. 2
Fig. 2

Illustration of the decomposition (5) in terms of Bloch vectors.

Equations (20)

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ψ = α 1 1 0 2 + β 0 1 1 2             ( α 2 + β 2 = 1 ) ,
ρ ^ ID = α 2 1 1 0 2 2 0 1 1 + β 2 0 1 1 2 2 1 1 0 + α β * 1 1 0 2 2 1 1 0 + h . c . ,
ρ ^ D = α 2 1 1 0 2 2 0 1 1 + β 2 0 1 1 2 2 1 1 0 ,
ρ ^ = ρ 11 1 1 0 2 2 0 1 1 + ρ 22 0 1 1 2 2 1 1 0 + ( ρ 12 1 1 0 2 2 1 1 0 + h . c . ) .
ρ ^ = P ID ρ ^ ID + P D ρ ^ D             ( P ID + P D = 1 ) ,
ρ 11 = α 2 ,
ρ 22 = β 2 ,
ρ 12 = P ID α β * ,
α β * = ( ρ 11 ρ 22 ) 1 / 2 exp ( i arg ρ 12 ) ,
P ID = [ ρ 12 / ( ρ 11 ρ 22 ) 1 / 2 ] exp ( - i arg ρ 12 ) = ρ 12 / ( ρ 11 ρ 22 ) 1 / 2 .
E ^ ( + ) ( r j ) = K a ^ j             ( j = 1 , 2 ) ,
Γ 12 ( 1 , 1 ) E ^ ( - ) ( r 1 ) E ^ ( + ) ( r 2 ) = K 2 Tr ( a ^ 1 a ^ 2 ρ ^ ) = K 2 ρ 21 ,
Γ 11 ( 1 , 1 ) = K 2 ρ 11 = K 2 α 2 , Γ 22 ( 1 , 1 ) = K 2 ρ 22 = K 2 β 2 .
γ 12 ( 1 , 1 ) Γ 12 ( 1 , 1 ) / [ Γ 11 ( 1 , 1 ) Γ 22 ( 1 , 1 ) ] 1 / 2 = ρ 21 / ( ρ 11 ρ 22 ) 1 / 2 .
γ 12 ( 1 , 1 ) = P ID ,
E ^ ( + ) a ^ 1 exp ( i ϕ 1 ) + a ^ 2 exp ( i ϕ 2 ) ,
Tr [ E ^ ( - ) E ^ ( + ) ρ ^ ] = Tr [ n ^ 1 + n ^ 2 + a ^ 1 a ^ 2 exp i ( ϕ 2 - ϕ 1 ) + h . c . ] ρ ^ = ρ 11 + ρ 22 + ρ 21 exp i ( ϕ 2 - ϕ 1 ) + c . c .
v = 2 ρ 21 / ( ρ 11 + ρ 22 ) = 2 ρ 21 = 2 γ 12 ( 1 , 1 ) ( ρ 11 ρ 22 ) 1 / 2 .
( ρ 11 ρ 22 ) 1 / 2 ( 1 / 2 ) ( ρ 11 + ρ 22 ) = ( 1 / 2 ) ,
v γ 12 ( 1 , 1 ) , v P ID ,

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