Abstract

Photon-emission sequences in nonclassical light beams generated by an optical parametric oscillator are studied. Exact photon-counting and waiting time distributions are derived by using a generating function technique based on the positive-P representation. This approach is used to present a simple physical picture of photon emissions from this nonclassical light source.

© 1989 Optical Society of America

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References

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  1. See the special issue on squeezed states of light, J. Opt. Soc. Am. B 4, 1450 (1987).
  2. L. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
    [CrossRef] [PubMed]
  3. H. P. Yuen, Phys. Rev. A 13, 2226 (1976); J. Huang, P. Kumar, Bull. Am. Phys. Soc. 33, 1671 (1988).
    [CrossRef]
  4. P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1980).
    [CrossRef]
  5. H. J. Carmichael, M. J. Wolinsky, in Quantum Optics IV, J. D. Harvey, D. F. Walls, eds. (Springer-Verlag, Berlin, 1986), pp. 208–220; M. J. Wolinsky, H. J. Carmichael, Phys. Rev. Lett. 60, 1836 (1988).
    [CrossRef] [PubMed]
  6. D. Slepian, Bell Syst. Tech. J. 37, 163 (1958).
  7. R. Vyas, S. Singh, in Coherence and Quantum Optics VI, J. H. Eberly, L. Mandel, E. Wolf, eds. (Plenum, New York, 1989); “Photon-counting statistics of the degenerate optical parametric oscillator,” submitted to Phys. Rev. A.
  8. R. Vyas, S. Singh, Phys. Rev. A 38, 2423 (1988); H. J. Carmichael, S. Singh, R. Vyas, P. R. Rice, Phys. Rev. A 39, 1200 (1989).
    [CrossRef] [PubMed]
  9. M. R. Young, S. Singh, Opt. Lett. 13, 21 (1988).
    [CrossRef] [PubMed]

1988

R. Vyas, S. Singh, Phys. Rev. A 38, 2423 (1988); H. J. Carmichael, S. Singh, R. Vyas, P. R. Rice, Phys. Rev. A 39, 1200 (1989).
[CrossRef] [PubMed]

M. R. Young, S. Singh, Opt. Lett. 13, 21 (1988).
[CrossRef] [PubMed]

1987

See the special issue on squeezed states of light, J. Opt. Soc. Am. B 4, 1450 (1987).

1986

L. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

1980

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1980).
[CrossRef]

1976

H. P. Yuen, Phys. Rev. A 13, 2226 (1976); J. Huang, P. Kumar, Bull. Am. Phys. Soc. 33, 1671 (1988).
[CrossRef]

1958

D. Slepian, Bell Syst. Tech. J. 37, 163 (1958).

Carmichael, H. J.

H. J. Carmichael, M. J. Wolinsky, in Quantum Optics IV, J. D. Harvey, D. F. Walls, eds. (Springer-Verlag, Berlin, 1986), pp. 208–220; M. J. Wolinsky, H. J. Carmichael, Phys. Rev. Lett. 60, 1836 (1988).
[CrossRef] [PubMed]

Drummond, P. D.

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1980).
[CrossRef]

Hall, J. L.

L. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

Kimble, H. J.

L. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

McNeil, K. J.

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1980).
[CrossRef]

Singh, S.

R. Vyas, S. Singh, Phys. Rev. A 38, 2423 (1988); H. J. Carmichael, S. Singh, R. Vyas, P. R. Rice, Phys. Rev. A 39, 1200 (1989).
[CrossRef] [PubMed]

M. R. Young, S. Singh, Opt. Lett. 13, 21 (1988).
[CrossRef] [PubMed]

R. Vyas, S. Singh, in Coherence and Quantum Optics VI, J. H. Eberly, L. Mandel, E. Wolf, eds. (Plenum, New York, 1989); “Photon-counting statistics of the degenerate optical parametric oscillator,” submitted to Phys. Rev. A.

Slepian, D.

D. Slepian, Bell Syst. Tech. J. 37, 163 (1958).

Vyas, R.

R. Vyas, S. Singh, Phys. Rev. A 38, 2423 (1988); H. J. Carmichael, S. Singh, R. Vyas, P. R. Rice, Phys. Rev. A 39, 1200 (1989).
[CrossRef] [PubMed]

R. Vyas, S. Singh, in Coherence and Quantum Optics VI, J. H. Eberly, L. Mandel, E. Wolf, eds. (Plenum, New York, 1989); “Photon-counting statistics of the degenerate optical parametric oscillator,” submitted to Phys. Rev. A.

Walls, D. F.

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1980).
[CrossRef]

Wolinsky, M. J.

H. J. Carmichael, M. J. Wolinsky, in Quantum Optics IV, J. D. Harvey, D. F. Walls, eds. (Springer-Verlag, Berlin, 1986), pp. 208–220; M. J. Wolinsky, H. J. Carmichael, Phys. Rev. Lett. 60, 1836 (1988).
[CrossRef] [PubMed]

Wu, H.

L. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

Wu, L.

L. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

Young, M. R.

Yuen, H. P.

H. P. Yuen, Phys. Rev. A 13, 2226 (1976); J. Huang, P. Kumar, Bull. Am. Phys. Soc. 33, 1671 (1988).
[CrossRef]

Bell Syst. Tech. J.

D. Slepian, Bell Syst. Tech. J. 37, 163 (1958).

J. Opt. Soc. Am. B

See the special issue on squeezed states of light, J. Opt. Soc. Am. B 4, 1450 (1987).

Opt. Acta

P. D. Drummond, K. J. McNeil, D. F. Walls, Opt. Acta 28, 211 (1980).
[CrossRef]

Opt. Lett.

Phys. Rev. A

H. P. Yuen, Phys. Rev. A 13, 2226 (1976); J. Huang, P. Kumar, Bull. Am. Phys. Soc. 33, 1671 (1988).
[CrossRef]

R. Vyas, S. Singh, Phys. Rev. A 38, 2423 (1988); H. J. Carmichael, S. Singh, R. Vyas, P. R. Rice, Phys. Rev. A 39, 1200 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett.

L. Wu, H. J. Kimble, J. L. Hall, H. Wu, Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

Other

H. J. Carmichael, M. J. Wolinsky, in Quantum Optics IV, J. D. Harvey, D. F. Walls, eds. (Springer-Verlag, Berlin, 1986), pp. 208–220; M. J. Wolinsky, H. J. Carmichael, Phys. Rev. Lett. 60, 1836 (1988).
[CrossRef] [PubMed]

R. Vyas, S. Singh, in Coherence and Quantum Optics VI, J. H. Eberly, L. Mandel, E. Wolf, eds. (Plenum, New York, 1989); “Photon-counting statistics of the degenerate optical parametric oscillator,” submitted to Phys. Rev. A.

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Figures (2)

Fig. 1
Fig. 1

(a) Photon-counting distribution for 2γT = 150 and n ¯ = 0.02. The upper dotted curve is from relation (8a), and the lower dotted curve is from relation (8b). (b) The waiting time distribution for photons emitted by the cavity for n ¯ = 0.02.

Fig. 2
Fig. 2

(a) Counting distribution for 2γT = 20 and n ¯ = 10. (b) The waiting time distribution for photons emitted by the cavity for n ¯ = 10.

Equations (10)

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H ˆ = 1 2 i ћ κ ( a ˆ 2 b ˆ a ˆ 2 b ˆ ) + i ћ Γ ( b ˆ b ˆ ) + H ˆ loss ,
α ˙ = γ α + κ α * + κ ξ 1 ( t ) , α ˙ * = γ α * + κ α + κ ξ 2 ( t ) ,
u i ( t ) u j ( t ) = 1 4 κ λ i δ i j exp ( λ i | t t | ) ,
G ( s , T ) = T : exp [ s η 0 T I ˆ ( t ) d t ] : ,
G ( s , T ) = exp [ 2 s η γ 0 T u 1 2 ( t ) d t ] × exp [ 2 s η γ 0 T u 2 2 ( t ) d t ] ,
G ( s , T ) = e γ T { [ cosh z 1 T + 1 2 ( λ 1 z 1 + z 1 λ 1 ) sinh z 1 T ] [ cosh z 2 T + 1 2 ( λ 2 z 2 + z 2 λ 2 ) sinh z 2 T ] } 1 / 2 ,
p ( m , T ) = ( 1 ) m m ! [ d m d s m G ( s , T ) ] s = 1 .
p ( 2 m , T ) [ 1 n ¯ 2 ( 1 + 2 m m ) ] × 1 m ! ( m 2 ) m exp ( m / 2 ) ,
p ( 2 m + 1 , T ) n ¯ 1 m ! ( m 2 ) m exp ( m / 2 ) ,
w ( T ) 2 γ n ¯ exp ( γ n ¯ T ) { 1 4 [ 1 + exp ( 4 γ T ) ] + 1 2 ( 3 + 1 n ¯ ) exp ( 2 γ T ) } .

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