Abstract

The wave–particle duality of a photon in emission is demonstrated by measuring the interference between spontaneous emissions in nearly opposite directions from a thin layer of organic dye. The interference is the product of a single photon from a single-emission process. It is shown that the Heisenberg uncertainty relation requires that the interference generated by the spontaneously emitted photon and the recoil transferred to the molecule by the emission cannot be observed simultaneously.

© 1992 Optical Society of America

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References

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  1. A. Einstein, “On the quantum theory of radiation,” in Source of Quantum Mechanics, B. L. Van Der Waerden, ed. (Dover, New York, 1968).
  2. O. R. Frisch, Z. Phys. 86, 42 (1933).
    [CrossRef]
  3. J.-L. Picqué, J.-L. Vialle, Opt. Commun. 5, 402 (1972).
    [CrossRef]
  4. R. Schieder, H. Walther, L. Wöste, Opt. Commun. 5, 337 (1972).
    [CrossRef]
  5. P. W. Milonni, “Wave–particle duality of light: a current perspective,” in The Wave–Particle Dualism, S. Diner, D. Fargue, G. Lochak, F. Selleri, eds. (Reidel, Boston, Mass., 1983).
  6. J. F. Clauser, Phys. Rev. D 9, 853 (1974).
    [CrossRef]
  7. M. O. Scully, Phys. Rev. A 35, 452 (1987).
    [CrossRef] [PubMed]
  8. M. Lai, J.-C. Diels, Am. J. Phys. 58, 928 (1990).
    [CrossRef]
  9. G. I. Taylor, Proc. Cambridge Philos. Soc. 15, 114 (1909);G. T. Geynolds, K. Spartalian, D. B. Scarl, Nuovo Cimento 61B, 355 (1969).
  10. T. Okoshi, A. Hirose, K. Kimura, Opt. Commun. 72, 7 (1989).
    [CrossRef]
  11. W. Heitler, The Quantum Theory of Radiation (Dover, New York, 1976).
  12. P. W. Milonni, Am. J. Phys. 52, 340 (1984).
    [CrossRef]
  13. R. P. Feynman, Quantum Electrodynamics (BenjaminCummings, Reading, Mass., 1962).
  14. N. M. Kroll, “Quantum theory of radiation,” in Quantum Optics and Electronics, C. Dewitt-Norette, A. Blendin, C. Cohen-Tannoudji, eds. (Gordon & Breach, New York, 1965).
  15. M. Lai, J.-C. Diels, Phys. Rev. A 42, 536 (1990).
    [CrossRef] [PubMed]
  16. M. Lai, J.-C. Diels, Phys. Rev. A 43, 2464 (1991).
    [CrossRef] [PubMed]

1991 (1)

M. Lai, J.-C. Diels, Phys. Rev. A 43, 2464 (1991).
[CrossRef] [PubMed]

1990 (2)

M. Lai, J.-C. Diels, Phys. Rev. A 42, 536 (1990).
[CrossRef] [PubMed]

M. Lai, J.-C. Diels, Am. J. Phys. 58, 928 (1990).
[CrossRef]

1989 (1)

T. Okoshi, A. Hirose, K. Kimura, Opt. Commun. 72, 7 (1989).
[CrossRef]

1987 (1)

M. O. Scully, Phys. Rev. A 35, 452 (1987).
[CrossRef] [PubMed]

1984 (1)

P. W. Milonni, Am. J. Phys. 52, 340 (1984).
[CrossRef]

1974 (1)

J. F. Clauser, Phys. Rev. D 9, 853 (1974).
[CrossRef]

1972 (2)

J.-L. Picqué, J.-L. Vialle, Opt. Commun. 5, 402 (1972).
[CrossRef]

R. Schieder, H. Walther, L. Wöste, Opt. Commun. 5, 337 (1972).
[CrossRef]

1933 (1)

O. R. Frisch, Z. Phys. 86, 42 (1933).
[CrossRef]

1909 (1)

G. I. Taylor, Proc. Cambridge Philos. Soc. 15, 114 (1909);G. T. Geynolds, K. Spartalian, D. B. Scarl, Nuovo Cimento 61B, 355 (1969).

Clauser, J. F.

J. F. Clauser, Phys. Rev. D 9, 853 (1974).
[CrossRef]

Diels, J.-C.

M. Lai, J.-C. Diels, Phys. Rev. A 43, 2464 (1991).
[CrossRef] [PubMed]

M. Lai, J.-C. Diels, Phys. Rev. A 42, 536 (1990).
[CrossRef] [PubMed]

M. Lai, J.-C. Diels, Am. J. Phys. 58, 928 (1990).
[CrossRef]

Einstein, A.

A. Einstein, “On the quantum theory of radiation,” in Source of Quantum Mechanics, B. L. Van Der Waerden, ed. (Dover, New York, 1968).

Feynman, R. P.

R. P. Feynman, Quantum Electrodynamics (BenjaminCummings, Reading, Mass., 1962).

Frisch, O. R.

O. R. Frisch, Z. Phys. 86, 42 (1933).
[CrossRef]

Heitler, W.

W. Heitler, The Quantum Theory of Radiation (Dover, New York, 1976).

Hirose, A.

T. Okoshi, A. Hirose, K. Kimura, Opt. Commun. 72, 7 (1989).
[CrossRef]

Kimura, K.

T. Okoshi, A. Hirose, K. Kimura, Opt. Commun. 72, 7 (1989).
[CrossRef]

Kroll, N. M.

N. M. Kroll, “Quantum theory of radiation,” in Quantum Optics and Electronics, C. Dewitt-Norette, A. Blendin, C. Cohen-Tannoudji, eds. (Gordon & Breach, New York, 1965).

Lai, M.

M. Lai, J.-C. Diels, Phys. Rev. A 43, 2464 (1991).
[CrossRef] [PubMed]

M. Lai, J.-C. Diels, Phys. Rev. A 42, 536 (1990).
[CrossRef] [PubMed]

M. Lai, J.-C. Diels, Am. J. Phys. 58, 928 (1990).
[CrossRef]

Milonni, P. W.

P. W. Milonni, Am. J. Phys. 52, 340 (1984).
[CrossRef]

P. W. Milonni, “Wave–particle duality of light: a current perspective,” in The Wave–Particle Dualism, S. Diner, D. Fargue, G. Lochak, F. Selleri, eds. (Reidel, Boston, Mass., 1983).

Okoshi, T.

T. Okoshi, A. Hirose, K. Kimura, Opt. Commun. 72, 7 (1989).
[CrossRef]

Picqué, J.-L.

J.-L. Picqué, J.-L. Vialle, Opt. Commun. 5, 402 (1972).
[CrossRef]

Schieder, R.

R. Schieder, H. Walther, L. Wöste, Opt. Commun. 5, 337 (1972).
[CrossRef]

Scully, M. O.

M. O. Scully, Phys. Rev. A 35, 452 (1987).
[CrossRef] [PubMed]

Taylor, G. I.

G. I. Taylor, Proc. Cambridge Philos. Soc. 15, 114 (1909);G. T. Geynolds, K. Spartalian, D. B. Scarl, Nuovo Cimento 61B, 355 (1969).

Vialle, J.-L.

J.-L. Picqué, J.-L. Vialle, Opt. Commun. 5, 402 (1972).
[CrossRef]

Walther, H.

R. Schieder, H. Walther, L. Wöste, Opt. Commun. 5, 337 (1972).
[CrossRef]

Wöste, L.

R. Schieder, H. Walther, L. Wöste, Opt. Commun. 5, 337 (1972).
[CrossRef]

Am. J. Phys. (2)

M. Lai, J.-C. Diels, Am. J. Phys. 58, 928 (1990).
[CrossRef]

P. W. Milonni, Am. J. Phys. 52, 340 (1984).
[CrossRef]

Opt. Commun. (3)

T. Okoshi, A. Hirose, K. Kimura, Opt. Commun. 72, 7 (1989).
[CrossRef]

J.-L. Picqué, J.-L. Vialle, Opt. Commun. 5, 402 (1972).
[CrossRef]

R. Schieder, H. Walther, L. Wöste, Opt. Commun. 5, 337 (1972).
[CrossRef]

Phys. Rev. A (3)

M. O. Scully, Phys. Rev. A 35, 452 (1987).
[CrossRef] [PubMed]

M. Lai, J.-C. Diels, Phys. Rev. A 42, 536 (1990).
[CrossRef] [PubMed]

M. Lai, J.-C. Diels, Phys. Rev. A 43, 2464 (1991).
[CrossRef] [PubMed]

Phys. Rev. D (1)

J. F. Clauser, Phys. Rev. D 9, 853 (1974).
[CrossRef]

Proc. Cambridge Philos. Soc. (1)

G. I. Taylor, Proc. Cambridge Philos. Soc. 15, 114 (1909);G. T. Geynolds, K. Spartalian, D. B. Scarl, Nuovo Cimento 61B, 355 (1969).

Z. Phys. (1)

O. R. Frisch, Z. Phys. 86, 42 (1933).
[CrossRef]

Other (5)

A. Einstein, “On the quantum theory of radiation,” in Source of Quantum Mechanics, B. L. Van Der Waerden, ed. (Dover, New York, 1968).

P. W. Milonni, “Wave–particle duality of light: a current perspective,” in The Wave–Particle Dualism, S. Diner, D. Fargue, G. Lochak, F. Selleri, eds. (Reidel, Boston, Mass., 1983).

W. Heitler, The Quantum Theory of Radiation (Dover, New York, 1976).

R. P. Feynman, Quantum Electrodynamics (BenjaminCummings, Reading, Mass., 1962).

N. M. Kroll, “Quantum theory of radiation,” in Quantum Optics and Electronics, C. Dewitt-Norette, A. Blendin, C. Cohen-Tannoudji, eds. (Gordon & Breach, New York, 1965).

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Figures (4)

Fig. 1
Fig. 1

Is the behavior of a photon wavelike in a single-emission process?

Fig. 2
Fig. 2

Experimental layout for examining the coherence of spontaneous emission in nearly opposite directions. The solid arrows refer to excitation beam, and the open arrows refer to spontaneous emission. Inset: related energy levels of the dye molecules.

Fig. 3
Fig. 3

Single-photon interference fringes made by spontaneous emission in nearly opposite directions from a thin layer of Rhodamine 6G.

Fig. 4
Fig. 4

Can we measure the photon interference and the molecular recoil simultaneously?

Equations (17)

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H = H atom + H field + H interaction = ( ω a 0 0 ω b ) + s Ω s â s + â s + s [ g s â s exp ( i φ s ) + g s * â s + exp ( i φ s ) ] ( σ + + σ ) .
p ( t ) = e r a b [ σ + ( t ) + σ ( t ) ] ,
E ( r , t ) = s s [ â s exp ( i φ s ) exp ( i k s · ( r r 0 ) + â s + exp ( i φ s ) exp ( i k s · ( r r 0 ) ] E ( + ) + E ( ) .
g s = e r a b · s exp ( i k s · r 0 ) = e r a b · s ,
â ˙ s = i Ω s â s i g s * exp ( i φ s ) ( σ + + σ ) ,
σ ˙ + + σ ˙ = i ( ω a ω b ) ( σ + σ ) ,
σ + = ( 0 1 0 0 ) , σ = ( 0 0 1 0 )
ω a b = ω a ω b ,
â ¨ s = Ω s 2 â s g s * exp ( i φ s ) × [ ( Ω s ω a b ) σ + + ( Ω s + ω a b ) σ ] .
( 2 1 c 2 2 t 2 ) â s exp ( i k s · r ) = g s * c 2 exp ( i φ s ) [ ( Ω s ω a b ) σ + + ( Ω s + ω a b ) σ ] × exp ( i k s · r ) ,
( 2 1 c 2 2 t 2 ) E ( + ) = s g s * c 2 s [ ( Ω s ω a b ) σ + + ( Ω s + ω a b ) σ ] exp ( i k s · r ) = s e c 2 r a b · s s [ ( Ω s ω a b ) σ + + ( Ω s ω a b ) σ ] exp ( i k s · r ) .
( 2 1 c 2 2 t 2 ) E ( + ) = e c 2 k 2 k ̂ × ( k ̂ × r a b ) ( k c + ω a b ) σ exp ( i k · r ) d k ,
Δ x Δ p x h .
Δ p x h / λ .
S ( τ ) ϕ | E 1 ( t , ϕ ) + E 2 ( t + τ , ϕ ) | 2 d t .
S ( τ ) | ϕ [ E 1 ( t , ϕ ) + E 2 ( t + τ , ϕ ) ] | 2 d t .
| ϕ E 1 ( t , ϕ ) | = constant .

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