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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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 and J.-L. Vialle, Opt. Commun. 5, 402 (1972).
    [Crossref]
  4. R. Schieder, H. Walther, and 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, and 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 and 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, and D. B. Scarl, Nuovo Cimento 61B, 355 (1969).
  10. T. Okoshi, A. Hirose, and 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, and C. Cohen-Tannoudji, eds. (Gordon & Breach, New York, 1965).
  15. M. Lai and J.-C. Diels, Phys. Rev. A 42, 536 (1990).
    [Crossref] [PubMed]
  16. M. Lai and J.-C. Diels, Phys. Rev. A 43, 2464 (1991).
    [Crossref] [PubMed]

1991 (1)

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

1990 (2)

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

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

1989 (1)

T. Okoshi, A. Hirose, and 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 and J.-L. Vialle, Opt. Commun. 5, 402 (1972).
[Crossref]

R. Schieder, H. Walther, and 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, and 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 and J.-C. Diels, Phys. Rev. A 43, 2464 (1991).
[Crossref] [PubMed]

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

M. Lai and 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, and K. Kimura, Opt. Commun. 72, 7 (1989).
[Crossref]

Kimura, K.

T. Okoshi, A. Hirose, and 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, and C. Cohen-Tannoudji, eds. (Gordon & Breach, New York, 1965).

Lai, M.

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

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

M. Lai and 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, and F. Selleri, eds. (Reidel, Boston, Mass., 1983).

Okoshi, T.

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

Picqué, J.-L.

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

Schieder, R.

R. Schieder, H. Walther, and 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, and D. B. Scarl, Nuovo Cimento 61B, 355 (1969).

Vialle, J.-L.

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

Walther, H.

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

Wöste, L.

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

Am. J. Phys. (2)

M. Lai and 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, and K. Kimura, Opt. Commun. 72, 7 (1989).
[Crossref]

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

R. Schieder, H. Walther, and 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 and J.-C. Diels, Phys. Rev. A 42, 536 (1990).
[Crossref] [PubMed]

M. Lai and 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, and 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, and 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, and C. Cohen-Tannoudji, eds. (Gordon & Breach, New York, 1965).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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)

Equations on this page are rendered with MathJax. Learn more.

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 .

Metrics