Abstract

It is shown that, in principle, there exists a light source giving a higher information rate per symbol in an optical communication channel than a single-mode laser. Such a source emits a definite number of photons per symbol. A possible form for this source is suggested, and the corresponding information rates are compared.

© 1976 Optical Society of America

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References

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  1. T. E. Stern, Trans. I. R. E. IT-6, 435 (1960).
  2. J. P. Gordon, in Advances in Quantum Electronics, edited by J. R. Singer (Columbia University, New York, 1961), p. 509; also G. J. Lasher, ibid. p. 520;J. P. Gordon, Proc. I. R. E. 50, 1898 (1962), and in Quantum Electronics and Coherent Light, edited by C. H. Townes and P. A. Miles (Academic, New York, 1962), p. 156.
    [Crossref]
  3. L. P. Bolgiano and L. F. Jelsma, Proc. I. E. E. E. 52, 218 (1964); B. E. Goodwin and L. P. Bolgiano, Proc. I. E. E. E. 53, 1745 (1965).
  4. G. Toraldo di Francis, Opt. Acta 2, 5 (1955).
    [Crossref]
  5. R. C. Jones, J. Opt. Soc. Am. 50, 1166 (1960); J. Opt. Soc. Am. 52, 493 (1962).
    [Crossref]
  6. E. Hisdal, J. Opt. Soc. Am. 55, 1446 (1963); J. Opt. Soc. Am. 57, 35 (1967); J. Opt. Soc. Am. 59, 921 (1969).
    [Crossref]
  7. G. L. Fillmore and G. Lachs, I. E. E. E. Trans. IT-15, 465 (1969).
  8. R. Jodoin and L. Mandel, J. Opt. Soc. Am. 61, 191 (1971).
    [Crossref]
  9. C. Bendjaballah, Opt. Commun. 17, 55 (1976).
    [Crossref]
  10. We identify Hilbert space operators for the quantum field by the caret, ^.
  11. See, for example, L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965); R. J. Glauber, in Quantum Optics and Electronics, edited by C. DeWitt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1965), p. 63.
    [Crossref]
  12. E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963); R. J. Glauber, Phys. Rev. 131, 2766 (1963); J. R. Klauder, Phys. Rev. Lett. 16, 534 (1966).
    [Crossref]

1976 (1)

C. Bendjaballah, Opt. Commun. 17, 55 (1976).
[Crossref]

1971 (1)

1969 (1)

G. L. Fillmore and G. Lachs, I. E. E. E. Trans. IT-15, 465 (1969).

1965 (1)

See, for example, L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965); R. J. Glauber, in Quantum Optics and Electronics, edited by C. DeWitt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1965), p. 63.
[Crossref]

1964 (1)

L. P. Bolgiano and L. F. Jelsma, Proc. I. E. E. E. 52, 218 (1964); B. E. Goodwin and L. P. Bolgiano, Proc. I. E. E. E. 53, 1745 (1965).

1963 (2)

E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963); R. J. Glauber, Phys. Rev. 131, 2766 (1963); J. R. Klauder, Phys. Rev. Lett. 16, 534 (1966).
[Crossref]

E. Hisdal, J. Opt. Soc. Am. 55, 1446 (1963); J. Opt. Soc. Am. 57, 35 (1967); J. Opt. Soc. Am. 59, 921 (1969).
[Crossref]

1960 (2)

1955 (1)

G. Toraldo di Francis, Opt. Acta 2, 5 (1955).
[Crossref]

Bendjaballah, C.

C. Bendjaballah, Opt. Commun. 17, 55 (1976).
[Crossref]

Bolgiano, L. P.

L. P. Bolgiano and L. F. Jelsma, Proc. I. E. E. E. 52, 218 (1964); B. E. Goodwin and L. P. Bolgiano, Proc. I. E. E. E. 53, 1745 (1965).

Fillmore, G. L.

G. L. Fillmore and G. Lachs, I. E. E. E. Trans. IT-15, 465 (1969).

Gordon, J. P.

J. P. Gordon, in Advances in Quantum Electronics, edited by J. R. Singer (Columbia University, New York, 1961), p. 509; also G. J. Lasher, ibid. p. 520;J. P. Gordon, Proc. I. R. E. 50, 1898 (1962), and in Quantum Electronics and Coherent Light, edited by C. H. Townes and P. A. Miles (Academic, New York, 1962), p. 156.
[Crossref]

Hisdal, E.

Jelsma, L. F.

L. P. Bolgiano and L. F. Jelsma, Proc. I. E. E. E. 52, 218 (1964); B. E. Goodwin and L. P. Bolgiano, Proc. I. E. E. E. 53, 1745 (1965).

Jodoin, R.

Jones, R. C.

Lachs, G.

G. L. Fillmore and G. Lachs, I. E. E. E. Trans. IT-15, 465 (1969).

Mandel, L.

R. Jodoin and L. Mandel, J. Opt. Soc. Am. 61, 191 (1971).
[Crossref]

See, for example, L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965); R. J. Glauber, in Quantum Optics and Electronics, edited by C. DeWitt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1965), p. 63.
[Crossref]

Stern, T. E.

T. E. Stern, Trans. I. R. E. IT-6, 435 (1960).

Sudarshan, E. C. G.

E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963); R. J. Glauber, Phys. Rev. 131, 2766 (1963); J. R. Klauder, Phys. Rev. Lett. 16, 534 (1966).
[Crossref]

Toraldo di Francis, G.

G. Toraldo di Francis, Opt. Acta 2, 5 (1955).
[Crossref]

Wolf, E.

See, for example, L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965); R. J. Glauber, in Quantum Optics and Electronics, edited by C. DeWitt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1965), p. 63.
[Crossref]

I. E. E. E. Trans. (1)

G. L. Fillmore and G. Lachs, I. E. E. E. Trans. IT-15, 465 (1969).

J. Opt. Soc. Am. (3)

Opt. Acta (1)

G. Toraldo di Francis, Opt. Acta 2, 5 (1955).
[Crossref]

Opt. Commun. (1)

C. Bendjaballah, Opt. Commun. 17, 55 (1976).
[Crossref]

Phys. Rev. Lett. (1)

E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963); R. J. Glauber, Phys. Rev. 131, 2766 (1963); J. R. Klauder, Phys. Rev. Lett. 16, 534 (1966).
[Crossref]

Proc. I. E. E. E. (1)

L. P. Bolgiano and L. F. Jelsma, Proc. I. E. E. E. 52, 218 (1964); B. E. Goodwin and L. P. Bolgiano, Proc. I. E. E. E. 53, 1745 (1965).

Rev. Mod. Phys. (1)

See, for example, L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965); R. J. Glauber, in Quantum Optics and Electronics, edited by C. DeWitt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1965), p. 63.
[Crossref]

Trans. I. R. E. (1)

T. E. Stern, Trans. I. R. E. IT-6, 435 (1960).

Other (2)

J. P. Gordon, in Advances in Quantum Electronics, edited by J. R. Singer (Columbia University, New York, 1961), p. 509; also G. J. Lasher, ibid. p. 520;J. P. Gordon, Proc. I. R. E. 50, 1898 (1962), and in Quantum Electronics and Coherent Light, edited by C. H. Townes and P. A. Miles (Academic, New York, 1962), p. 156.
[Crossref]

We identify Hilbert space operators for the quantum field by the caret, ^.

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Figures (2)

FIG. 1
FIG. 1

Outline of the geometry for an optical communications channel.

FIG. 2
FIG. 2

Comparison of the information rates per symbol for an N-atom source (N = 1000) and a single-mode laser, for a vocabulary of S = 20 and S = 5 different symbols.

Equations (15)

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I / I max x ,             0 x 1 ,
C = n = 0 0 1 d x P ( x ) ( n x ) log [ ( n x ) / 0 1 d x P ( x ) ( n x ) ] .
P ( x ) = [ a / ( 1 - e - a ) ] e - a x for 0 x 1 , = 0 otherwise ,
n ˆ ( r ) n ˆ ( n ˆ - 1 ) ( n ˆ - r + 1 ) = â r â r : n ˆ r : ,
( Δ n ˆ ) 2 = n ˆ 2 - n ˆ 2 = n ˆ + ( : n ˆ 2 : - n ˆ 2 ) .
( Δ n ˆ ) 2 = n ˆ ,
( Δ n ˆ ) 2 > n ˆ
( Δ n ˆ ) 2 < n ˆ .
( Δ n ˆ ) 2 = 0 ,
( n x ) = ( x N n ) α n ( 1 - α ) x N - n for 0 n x N , = 0 otherwise ,
D = n = 0 N i = 1 S P ( x i ) ( n x i ) × log [ ( n x i ) / j = 1 S P ( x j ) ( n x j ) ] .
Δ x D = C + log Δ x .
( n x ) = ( α x N ) n e - α x N / n ! ,
( Δ n ) 2 x = α x N ( 1 - α ) ,
( Δ n ) 2 x = α x N ,