Abstract

We investigate quantum fluctuations in coherent solitons propagating in a dispersive nonlinear waveguide. Optimal squeezing or noise reduction occurs for a local oscillator width near the soliton width in time, i.e., the quantum fluctuations are localized.

© 1989 Optical Society of America

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References

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  1. T. E. Stern, IEEE Trans. Inf. Theory IT-6, 435 (1960); J. P. Gordon, Proc. IRE 50, 1898 (1962); D. S. Levedev, L. B. Levitin, Sov. Phys. Dokl. 8, 377 (1963); H. Takahashi, in Advances in Communications Systems, A. V. Balakrishnan, ed. (Academic, New York, 1965); C. Y. She, IEEE Trans. Inf. Theory IT-14, 32 (1968).
    [CrossRef]
  2. See, e.g., R. E. Slusher, B. Yurke, P. Grangier, A. LaPorta, D. F. Walls, M. Reid, J. Opt. Soc. Am. B 4, 1453 (1987); L.-A. Wu, M. Xiao, H. J. Kimble, J. Opt. Soc. Am. B 4, 1465 (1987); G. J. Milburn, M. D. Levenson, R. M. Shelby, S. H. Perlmutter, R. G. DeVoe, D. F. Walls, J. Opt. Soc. Am. B 4, 1476 (1987); L. A. Orozco, M. G. Raizen, M. Xiao, R. J. Brecha, H. J. Kimble, J. Opt. Soc. Am. B 4, 1490 (1987); M. W. Maeda, P. Kumar, J. H. Shapiro, J. Opt. Soc. Am. B 4, 1501 (1987).
    [CrossRef]
  3. H. P. Yuen, Phys. Rev. Lett 51, 719 (1983); also see Y. Yamamoto, H. A. Haus, Rev. Mod. Phys. 58, 1001 (1986).
    [CrossRef]
  4. R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. S. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986).
    [CrossRef] [PubMed]
  5. R. E. Slusher, P. Grangier, A. La Porta, B. Yurke, M. J. Potasek, Phys. Rev. Lett. 59, 2566 (1987).
    [CrossRef] [PubMed]
  6. S. Machida, Y. Yamamoto, Y. Itaya, Phys. Rev. Lett. 58, 1000 (1987).
    [CrossRef] [PubMed]
  7. S. J. Carter, P. D. Drummond, M. D. Reid, R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987); P. D. Drummond, S. J. Carter, J. Opt. Soc. Am. B. 4, 1565 (1987).
    [CrossRef] [PubMed]
  8. M. Hillery, L. D. Mlodinow, Phys. Rev. A 30, 1860 (1984).
    [CrossRef]
  9. L. F. Mollenauer, Philos. Trans. R. Soc. London Ser. A 315, 435 (1985).
  10. P. D. Drummond, Phys. Rev. A 35, 4253 (1987).
    [CrossRef] [PubMed]
  11. R. J. Glauber, Phys. Rev. 130, 2529 (1963).
    [CrossRef]
  12. Similar normally ordered calculations for the case of time-independent local oscillators are used by Z. Y. Ou, C. K. Hong, L. Mandel, J. Opt. Soc. Am. B 4, 1574 (1987) and H. J. Carmichael, J. Opt. Soc. Am. B 4, 1588 (1987).
    [CrossRef]
  13. This term is also obtained in the balanced homodyne detection scheme reported by B. Yurke, P. Grangier, R. E. Slusher, M. J. Potasek, Phys. Rev. A 35, 3586 (1987).
    [CrossRef] [PubMed]

1987

1986

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. S. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

1985

L. F. Mollenauer, Philos. Trans. R. Soc. London Ser. A 315, 435 (1985).

1984

M. Hillery, L. D. Mlodinow, Phys. Rev. A 30, 1860 (1984).
[CrossRef]

1983

H. P. Yuen, Phys. Rev. Lett 51, 719 (1983); also see Y. Yamamoto, H. A. Haus, Rev. Mod. Phys. 58, 1001 (1986).
[CrossRef]

1963

R. J. Glauber, Phys. Rev. 130, 2529 (1963).
[CrossRef]

1960

T. E. Stern, IEEE Trans. Inf. Theory IT-6, 435 (1960); J. P. Gordon, Proc. IRE 50, 1898 (1962); D. S. Levedev, L. B. Levitin, Sov. Phys. Dokl. 8, 377 (1963); H. Takahashi, in Advances in Communications Systems, A. V. Balakrishnan, ed. (Academic, New York, 1965); C. Y. She, IEEE Trans. Inf. Theory IT-14, 32 (1968).
[CrossRef]

Carter, S. J.

S. J. Carter, P. D. Drummond, M. D. Reid, R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987); P. D. Drummond, S. J. Carter, J. Opt. Soc. Am. B. 4, 1565 (1987).
[CrossRef] [PubMed]

DeVoe, R. S.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. S. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

Drummond, P. D.

S. J. Carter, P. D. Drummond, M. D. Reid, R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987); P. D. Drummond, S. J. Carter, J. Opt. Soc. Am. B. 4, 1565 (1987).
[CrossRef] [PubMed]

P. D. Drummond, Phys. Rev. A 35, 4253 (1987).
[CrossRef] [PubMed]

Glauber, R. J.

R. J. Glauber, Phys. Rev. 130, 2529 (1963).
[CrossRef]

Grangier, P.

Hillery, M.

M. Hillery, L. D. Mlodinow, Phys. Rev. A 30, 1860 (1984).
[CrossRef]

Hong, C. K.

Itaya, Y.

S. Machida, Y. Yamamoto, Y. Itaya, Phys. Rev. Lett. 58, 1000 (1987).
[CrossRef] [PubMed]

La Porta, A.

R. E. Slusher, P. Grangier, A. La Porta, B. Yurke, M. J. Potasek, Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

LaPorta, A.

Levenson, M. D.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. S. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

Machida, S.

S. Machida, Y. Yamamoto, Y. Itaya, Phys. Rev. Lett. 58, 1000 (1987).
[CrossRef] [PubMed]

Mandel, L.

Mlodinow, L. D.

M. Hillery, L. D. Mlodinow, Phys. Rev. A 30, 1860 (1984).
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer, Philos. Trans. R. Soc. London Ser. A 315, 435 (1985).

Ou, Z. Y.

Perlmutter, S. H.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. S. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

Potasek, M. J.

R. E. Slusher, P. Grangier, A. La Porta, B. Yurke, M. J. Potasek, Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

This term is also obtained in the balanced homodyne detection scheme reported by B. Yurke, P. Grangier, R. E. Slusher, M. J. Potasek, Phys. Rev. A 35, 3586 (1987).
[CrossRef] [PubMed]

Reid, M.

Reid, M. D.

S. J. Carter, P. D. Drummond, M. D. Reid, R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987); P. D. Drummond, S. J. Carter, J. Opt. Soc. Am. B. 4, 1565 (1987).
[CrossRef] [PubMed]

Shelby, R. M.

S. J. Carter, P. D. Drummond, M. D. Reid, R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987); P. D. Drummond, S. J. Carter, J. Opt. Soc. Am. B. 4, 1565 (1987).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. S. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

Slusher, R. E.

Stern, T. E.

T. E. Stern, IEEE Trans. Inf. Theory IT-6, 435 (1960); J. P. Gordon, Proc. IRE 50, 1898 (1962); D. S. Levedev, L. B. Levitin, Sov. Phys. Dokl. 8, 377 (1963); H. Takahashi, in Advances in Communications Systems, A. V. Balakrishnan, ed. (Academic, New York, 1965); C. Y. She, IEEE Trans. Inf. Theory IT-14, 32 (1968).
[CrossRef]

Walls, D. F.

Yamamoto, Y.

S. Machida, Y. Yamamoto, Y. Itaya, Phys. Rev. Lett. 58, 1000 (1987).
[CrossRef] [PubMed]

Yuen, H. P.

H. P. Yuen, Phys. Rev. Lett 51, 719 (1983); also see Y. Yamamoto, H. A. Haus, Rev. Mod. Phys. 58, 1001 (1986).
[CrossRef]

Yurke, B.

IEEE Trans. Inf. Theory

T. E. Stern, IEEE Trans. Inf. Theory IT-6, 435 (1960); J. P. Gordon, Proc. IRE 50, 1898 (1962); D. S. Levedev, L. B. Levitin, Sov. Phys. Dokl. 8, 377 (1963); H. Takahashi, in Advances in Communications Systems, A. V. Balakrishnan, ed. (Academic, New York, 1965); C. Y. She, IEEE Trans. Inf. Theory IT-14, 32 (1968).
[CrossRef]

J. Opt. Soc. Am. B

Philos. Trans. R. Soc. London Ser. A

L. F. Mollenauer, Philos. Trans. R. Soc. London Ser. A 315, 435 (1985).

Phys. Rev.

R. J. Glauber, Phys. Rev. 130, 2529 (1963).
[CrossRef]

Phys. Rev. A

M. Hillery, L. D. Mlodinow, Phys. Rev. A 30, 1860 (1984).
[CrossRef]

P. D. Drummond, Phys. Rev. A 35, 4253 (1987).
[CrossRef] [PubMed]

This term is also obtained in the balanced homodyne detection scheme reported by B. Yurke, P. Grangier, R. E. Slusher, M. J. Potasek, Phys. Rev. A 35, 3586 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett

H. P. Yuen, Phys. Rev. Lett 51, 719 (1983); also see Y. Yamamoto, H. A. Haus, Rev. Mod. Phys. 58, 1001 (1986).
[CrossRef]

Phys. Rev. Lett.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. S. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

R. E. Slusher, P. Grangier, A. La Porta, B. Yurke, M. J. Potasek, Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

S. Machida, Y. Yamamoto, Y. Itaya, Phys. Rev. Lett. 58, 1000 (1987).
[CrossRef] [PubMed]

S. J. Carter, P. D. Drummond, M. D. Reid, R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987); P. D. Drummond, S. J. Carter, J. Opt. Soc. Am. B. 4, 1565 (1987).
[CrossRef] [PubMed]

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Figures (1)

Fig. 1
Fig. 1

Optimal squeezing variance in decibels, 10 log10[V(w)], versus the propagation distance. The phase angle is optimized for each frequency component individually; ts = t0 and width l0 = 1.

Equations (15)

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H ^ = [ 1 2 D ^ 2 ( x ) - 0 χ ( 3 ) 4 4 D ^ 4 ( x ) + 1 2 μ B ^ 2 ( x ) ] d 3 x + 0 ( D ^ 6 ) .
ζ ϕ ( τ , ζ ) = [ i 2 ( 2 τ 2 - 1 ) + i ϕ + ϕ + ( i / n ¯ ) 1 / 2 η ( τ , ζ ) ] ϕ ( τ , ζ ) ,
n ¯ = [ A c k ω 0 2 n 2 t s ] .
S i j ( ω 1 , ω 2 , ζ ) = δ ϕ i ( ω 1 , ζ ) δ ϕ j ( ω 2 , ζ ) ,
δ ϕ i ( ω ) = 1 2 π e i ω t δ ϕ i ( t ) d t .
G I ( ω ) = j e i ω ( t - t ) i 0 ( t - t j ) i 0 ( t - t j ) d t d t + j k e i ω ( t - t ) i 0 ( t - t j ) i 0 ( t - t k ) d t d t .
I ^ ( t ) = [ η 0 * ϕ ^ 0 + ( t ) + η * ϕ ^ + ( t ) ] H . c .
G I ( ω ) = ( Z e ) 2 [ I ( t ) d t + e i ω ( t - t ) G ( 2 ) ( t , t ) d t d t ] .
u ( t ) = η 0 ϕ ^ 0 ( t ) + η ϕ ^ ( t ) / I c ,
I c ( t ) = η 0 ϕ ^ 0 ( t ) + η ϕ ^ ( t ) 2 , I c = i c ( t ) d t .
G I ( ω ) = ( Ze ) 2 { I c [ 1 + 2 π : X ( - ω ) X ( ω ) : ] + 2 π [ I c ( - ω ) I c ( ω ) + I c ( - ω ) I x ( ω ) + I c ( ω ) I x ( - ω ) ] } ,
I c ( ω ) = 1 2 π I c ( t ) e i ω t d t .
X ^ ( t ) = η δ ϕ ^ ( t ) u * ( t ) + H . c . , X ^ ( ω ) = 1 2 π X ^ ( t ) e i ω t d t , I x ( t ) = η 2 [ ϕ ^ + ( t ) ϕ ^ ( t ) - ϕ ^ ( t ) 2 ] , I x ( ω ) = 1 2 π I x ( t ) e i ω t d t .
V ( ω ) = 1 + 2 π : X ^ ( - ω ) X ^ ( ω ) : .
V ( ω ) = 1 + { S 21 ( ω , - ω , ξ ) [ u ˜ ( ω - ω ) u ˜ * ( ω - ω ) + u ˜ ( - ω - ω ) u ˜ * ( ω + ω ) ] + 2 Re [ e 2 i θ S 11 ( ω , - ω , ξ ) × u ˜ * ( ω - ω ) u ˜ * ( ω - ω ) ] } d 2 ω ,

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