Abstract

Based on the linearization approximation, a unified approach to the quantum effects of soliton propagation is developed. The new formulation provides a clearer picture. The real and imaginary parts of the perturbation field are expanded in different basis sets. Orthogonality relations are used to project out the soliton parameters. The new formulation also provides a general numerical approach to the calculation of detection noise. Numerical analyses of fiber ring gyros that use squeezed solitons are presented.

© 1993 Optical Society of America

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References

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  1. H. Takahashi, Adv. Commun. Syst. 1, 227 (1965).
  2. D. Stoler, “Photon antibunching and possible ways to observe it,” Phys. Rev. Lett. 33, 1397 (1974).
    [CrossRef]
  3. H. P. Yuen, “Two-photon coherent states of the radiation field,” Phys. Rev. A 13, 2226 (1976).
    [CrossRef]
  4. J. N. Hollenhorst, “Quantum limits on resonant-mass gravitational-radiation detectors,” Phys. Rev. D 19, 1669 (1979).
    [CrossRef]
  5. C. M. Caves, K. S. Thorne, K. W. P. Drever, V. D. Sandberg, and M. Zimmermann, “On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I,” Rev. Mod. Phys. 52, 341 (1980).
    [CrossRef]
  6. R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409 (1985).
    [CrossRef] [PubMed]
  7. R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broadband parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1986).
    [CrossRef] [PubMed]
  8. L. W. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520 (1986).
    [CrossRef] [PubMed]
  9. M. G. Raizen, L. A. Orozco, M. Xiao, T. L. Boyd, and H. J. Kimble, “Squeezed state generation by normal modes of a coupled system,” Phys. Rev. Lett. 59, 198 (1987).
    [CrossRef] [PubMed]
  10. M. W. Maeda, P. Kumar, and J. H. Shapiro, “Observation of squeezed noise produced by forward four-wave mixing in sodium vapor,” Opt. Lett. 12, 161 (1987).
    [CrossRef] [PubMed]
  11. S. Machida, Y. Yamamoto, and Y. Itaya, “Ultrabroadband amplitude squeezing in a semiconductor laser,” Phys. Rev. Lett. 60, 792 (1988).
    [CrossRef] [PubMed]
  12. R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, “Pulsed squeezed light,” Phys. Rev. Lett. 59, 2566 (1987).
    [CrossRef] [PubMed]
  13. T. Hirano and M. Matsuoka, “Broadband squeezing of light by pulse excitation,” Opt. Lett. 15, 1153 (1990).
    [CrossRef] [PubMed]
  14. K. Bergman and H. A. Haus, “Squeezing in fibers with optical pulses,” Opt. Lett. 16, 663 (1991).
    [CrossRef] [PubMed]
  15. M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett. 66, 153 (1991).
    [CrossRef] [PubMed]
  16. S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, “Squeezing of quantum solitons,” Phys. Rev. Lett. 58, 1841 (1987).
    [CrossRef] [PubMed]
  17. P. D. Drummond and S. J. Carter, “Quantum field theory of squeezing in solitons,” J. Opt. Soc. Am. B 4, 1565 (1987).
    [CrossRef]
  18. S. J. Carter, P. D. Drummond, and R. M. Shelby, “Time dependence of quantum fluctuations in solitons,” Opt. Lett. 14, 373 (1989).
    [CrossRef] [PubMed]
  19. H. A. Haus and Y. Lai, “Quantum theory of soliton squeezing—a linearized approach,” J. Opt. Soc. Am. B 7, 386 (1990).
    [CrossRef]
  20. Y. Lai and H. A. Haus, “Quantum theory of self-induced transparency solitons: a linearization approach,” Phys. Rev. A 42, 2925 (1990).
    [CrossRef] [PubMed]
  21. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  22. V. Zakharov and A. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62 (1972).
  23. D. J. Kaup, “Perturbation theory for solitons in optical fibers,” Phys. Rev. A 42, 5689 (1990).
    [CrossRef] [PubMed]
  24. R. S. Bondurant, “Response of ideal photodetectors to photon flux and/or energy flux,” Phys. Rev. A 32, 2797 (1985).
    [CrossRef] [PubMed]
  25. B. Yurke, “Wideband photon counting and homodyne detection,” Phys. Rev. A 32, 311 (1985).
    [CrossRef] [PubMed]
  26. A. M. Weiner, J. P. Heritage, and E. M. Kirschner, “High resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563 (1988).
    [CrossRef]
  27. K. Bergman, H. A. Haus, and Y. Lai, “Fiber gyros using squeezed pulses,” J. Opt. Soc. Am. B 8, 1952 (1991).
  28. J. P. Gordon and H. A. Haus, “Random walk of coherent amplified solitons in optical fiber transmission,” Opt. Lett. 11, 665 (1986).
    [CrossRef] [PubMed]
  29. H. A. Haus, “Quantum noise in a solitonlike repeater system,” J. Opt. Soc. Am. B 8, 1122 (1991).
    [CrossRef]
  30. A. Mecozzi, J. D. Moores, H. A. Haus, and Y. Lai, “Soliton transmission control,” Opt. Lett. 16, 1841 (1991).
    [CrossRef] [PubMed]
  31. Y. Kodama and A. Hasegawa, “Generation of asymptotically stable optical solitons and suppression of Gordon–Haus effect,” Opt. Lett. 17, 31 (1992).
    [CrossRef] [PubMed]
  32. D. Marcuse, “Simulations to demonstrate reduction of the Gordon–Haus effect,” Opt. Lett. 17, 34 (1992).
    [CrossRef] [PubMed]
  33. Y. Lai, “Noise analysis of soliton communication systems—a new approach,” IEEE J. Lightwave Technol. (to be published).

1992 (2)

1991 (5)

1990 (4)

D. J. Kaup, “Perturbation theory for solitons in optical fibers,” Phys. Rev. A 42, 5689 (1990).
[CrossRef] [PubMed]

T. Hirano and M. Matsuoka, “Broadband squeezing of light by pulse excitation,” Opt. Lett. 15, 1153 (1990).
[CrossRef] [PubMed]

H. A. Haus and Y. Lai, “Quantum theory of soliton squeezing—a linearized approach,” J. Opt. Soc. Am. B 7, 386 (1990).
[CrossRef]

Y. Lai and H. A. Haus, “Quantum theory of self-induced transparency solitons: a linearization approach,” Phys. Rev. A 42, 2925 (1990).
[CrossRef] [PubMed]

1989 (1)

1988 (2)

A. M. Weiner, J. P. Heritage, and E. M. Kirschner, “High resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563 (1988).
[CrossRef]

S. Machida, Y. Yamamoto, and Y. Itaya, “Ultrabroadband amplitude squeezing in a semiconductor laser,” Phys. Rev. Lett. 60, 792 (1988).
[CrossRef] [PubMed]

1987 (5)

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, “Pulsed squeezed light,” Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

M. G. Raizen, L. A. Orozco, M. Xiao, T. L. Boyd, and H. J. Kimble, “Squeezed state generation by normal modes of a coupled system,” Phys. Rev. Lett. 59, 198 (1987).
[CrossRef] [PubMed]

M. W. Maeda, P. Kumar, and J. H. Shapiro, “Observation of squeezed noise produced by forward four-wave mixing in sodium vapor,” Opt. Lett. 12, 161 (1987).
[CrossRef] [PubMed]

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, “Squeezing of quantum solitons,” Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

P. D. Drummond and S. J. Carter, “Quantum field theory of squeezing in solitons,” J. Opt. Soc. Am. B 4, 1565 (1987).
[CrossRef]

1986 (3)

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broadband parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

L. W. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

J. P. Gordon and H. A. Haus, “Random walk of coherent amplified solitons in optical fiber transmission,” Opt. Lett. 11, 665 (1986).
[CrossRef] [PubMed]

1985 (3)

R. S. Bondurant, “Response of ideal photodetectors to photon flux and/or energy flux,” Phys. Rev. A 32, 2797 (1985).
[CrossRef] [PubMed]

B. Yurke, “Wideband photon counting and homodyne detection,” Phys. Rev. A 32, 311 (1985).
[CrossRef] [PubMed]

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409 (1985).
[CrossRef] [PubMed]

1980 (1)

C. M. Caves, K. S. Thorne, K. W. P. Drever, V. D. Sandberg, and M. Zimmermann, “On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I,” Rev. Mod. Phys. 52, 341 (1980).
[CrossRef]

1979 (1)

J. N. Hollenhorst, “Quantum limits on resonant-mass gravitational-radiation detectors,” Phys. Rev. D 19, 1669 (1979).
[CrossRef]

1976 (1)

H. P. Yuen, “Two-photon coherent states of the radiation field,” Phys. Rev. A 13, 2226 (1976).
[CrossRef]

1974 (1)

D. Stoler, “Photon antibunching and possible ways to observe it,” Phys. Rev. Lett. 33, 1397 (1974).
[CrossRef]

1972 (1)

V. Zakharov and A. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62 (1972).

1965 (1)

H. Takahashi, Adv. Commun. Syst. 1, 227 (1965).

Bergman, K.

Bondurant, R. S.

R. S. Bondurant, “Response of ideal photodetectors to photon flux and/or energy flux,” Phys. Rev. A 32, 2797 (1985).
[CrossRef] [PubMed]

Boyd, T. L.

M. G. Raizen, L. A. Orozco, M. Xiao, T. L. Boyd, and H. J. Kimble, “Squeezed state generation by normal modes of a coupled system,” Phys. Rev. Lett. 59, 198 (1987).
[CrossRef] [PubMed]

Carter, S. J.

Caves, C. M.

C. M. Caves, K. S. Thorne, K. W. P. Drever, V. D. Sandberg, and M. Zimmermann, “On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I,” Rev. Mod. Phys. 52, 341 (1980).
[CrossRef]

DeVoe, R. G.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broadband parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

Drever, K. W. P.

C. M. Caves, K. S. Thorne, K. W. P. Drever, V. D. Sandberg, and M. Zimmermann, “On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I,” Rev. Mod. Phys. 52, 341 (1980).
[CrossRef]

Drummond, P. D.

Gordon, J. P.

Grangier, P.

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, “Pulsed squeezed light,” Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

Hall, J. L.

L. W. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

Hasegawa, A.

Haus, H. A.

Heritage, J. P.

Hirano, T.

Hollberg, L. W.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409 (1985).
[CrossRef] [PubMed]

Hollenhorst, J. N.

J. N. Hollenhorst, “Quantum limits on resonant-mass gravitational-radiation detectors,” Phys. Rev. D 19, 1669 (1979).
[CrossRef]

Itaya, Y.

S. Machida, Y. Yamamoto, and Y. Itaya, “Ultrabroadband amplitude squeezing in a semiconductor laser,” Phys. Rev. Lett. 60, 792 (1988).
[CrossRef] [PubMed]

Kaup, D. J.

D. J. Kaup, “Perturbation theory for solitons in optical fibers,” Phys. Rev. A 42, 5689 (1990).
[CrossRef] [PubMed]

Kimble, H. J.

M. G. Raizen, L. A. Orozco, M. Xiao, T. L. Boyd, and H. J. Kimble, “Squeezed state generation by normal modes of a coupled system,” Phys. Rev. Lett. 59, 198 (1987).
[CrossRef] [PubMed]

L. W. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

Kirschner, E. M.

Kodama, Y.

Kumar, P.

Lai, Y.

K. Bergman, H. A. Haus, and Y. Lai, “Fiber gyros using squeezed pulses,” J. Opt. Soc. Am. B 8, 1952 (1991).

A. Mecozzi, J. D. Moores, H. A. Haus, and Y. Lai, “Soliton transmission control,” Opt. Lett. 16, 1841 (1991).
[CrossRef] [PubMed]

H. A. Haus and Y. Lai, “Quantum theory of soliton squeezing—a linearized approach,” J. Opt. Soc. Am. B 7, 386 (1990).
[CrossRef]

Y. Lai and H. A. Haus, “Quantum theory of self-induced transparency solitons: a linearization approach,” Phys. Rev. A 42, 2925 (1990).
[CrossRef] [PubMed]

Y. Lai, “Noise analysis of soliton communication systems—a new approach,” IEEE J. Lightwave Technol. (to be published).

LaPorta, A.

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, “Pulsed squeezed light,” Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

Levenson, M. D.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broadband parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

Machida, S.

S. Machida, Y. Yamamoto, and Y. Itaya, “Ultrabroadband amplitude squeezing in a semiconductor laser,” Phys. Rev. Lett. 60, 792 (1988).
[CrossRef] [PubMed]

Maeda, M. W.

Marcuse, D.

Matsuoka, M.

Mecozzi, A.

Mertz, J. C.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409 (1985).
[CrossRef] [PubMed]

Moores, J. D.

Orozco, L. A.

M. G. Raizen, L. A. Orozco, M. Xiao, T. L. Boyd, and H. J. Kimble, “Squeezed state generation by normal modes of a coupled system,” Phys. Rev. Lett. 59, 198 (1987).
[CrossRef] [PubMed]

Perlmutter, S. H.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broadband parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

Potasek, M. J.

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, “Pulsed squeezed light,” Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

Raizen, M. G.

M. G. Raizen, L. A. Orozco, M. Xiao, T. L. Boyd, and H. J. Kimble, “Squeezed state generation by normal modes of a coupled system,” Phys. Rev. Lett. 59, 198 (1987).
[CrossRef] [PubMed]

Reid, M. D.

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, “Squeezing of quantum solitons,” Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

Rosenbluh, M.

M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett. 66, 153 (1991).
[CrossRef] [PubMed]

Sandberg, V. D.

C. M. Caves, K. S. Thorne, K. W. P. Drever, V. D. Sandberg, and M. Zimmermann, “On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I,” Rev. Mod. Phys. 52, 341 (1980).
[CrossRef]

Shabat, A.

V. Zakharov and A. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62 (1972).

Shapiro, J. H.

Shelby, R. M.

M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett. 66, 153 (1991).
[CrossRef] [PubMed]

S. J. Carter, P. D. Drummond, and R. M. Shelby, “Time dependence of quantum fluctuations in solitons,” Opt. Lett. 14, 373 (1989).
[CrossRef] [PubMed]

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, “Squeezing of quantum solitons,” Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broadband parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

Slusher, R. E.

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, “Pulsed squeezed light,” Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409 (1985).
[CrossRef] [PubMed]

Stoler, D.

D. Stoler, “Photon antibunching and possible ways to observe it,” Phys. Rev. Lett. 33, 1397 (1974).
[CrossRef]

Takahashi, H.

H. Takahashi, Adv. Commun. Syst. 1, 227 (1965).

Thorne, K. S.

C. M. Caves, K. S. Thorne, K. W. P. Drever, V. D. Sandberg, and M. Zimmermann, “On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I,” Rev. Mod. Phys. 52, 341 (1980).
[CrossRef]

Valley, J. F.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409 (1985).
[CrossRef] [PubMed]

Walls, D. F.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broadband parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

Weiner, A. M.

Wu, H.

L. W. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

Wu, L. W.

L. W. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

Xiao, M.

M. G. Raizen, L. A. Orozco, M. Xiao, T. L. Boyd, and H. J. Kimble, “Squeezed state generation by normal modes of a coupled system,” Phys. Rev. Lett. 59, 198 (1987).
[CrossRef] [PubMed]

Yamamoto, Y.

S. Machida, Y. Yamamoto, and Y. Itaya, “Ultrabroadband amplitude squeezing in a semiconductor laser,” Phys. Rev. Lett. 60, 792 (1988).
[CrossRef] [PubMed]

Yuen, H. P.

H. P. Yuen, “Two-photon coherent states of the radiation field,” Phys. Rev. A 13, 2226 (1976).
[CrossRef]

Yurke, B.

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, “Pulsed squeezed light,” Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409 (1985).
[CrossRef] [PubMed]

B. Yurke, “Wideband photon counting and homodyne detection,” Phys. Rev. A 32, 311 (1985).
[CrossRef] [PubMed]

Zakharov, V.

V. Zakharov and A. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62 (1972).

Zimmermann, M.

C. M. Caves, K. S. Thorne, K. W. P. Drever, V. D. Sandberg, and M. Zimmermann, “On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I,” Rev. Mod. Phys. 52, 341 (1980).
[CrossRef]

Adv. Commun. Syst. (1)

H. Takahashi, Adv. Commun. Syst. 1, 227 (1965).

J. Opt. Soc. Am. B (5)

Opt. Lett. (8)

Phys. Rev. A (5)

H. P. Yuen, “Two-photon coherent states of the radiation field,” Phys. Rev. A 13, 2226 (1976).
[CrossRef]

Y. Lai and H. A. Haus, “Quantum theory of self-induced transparency solitons: a linearization approach,” Phys. Rev. A 42, 2925 (1990).
[CrossRef] [PubMed]

D. J. Kaup, “Perturbation theory for solitons in optical fibers,” Phys. Rev. A 42, 5689 (1990).
[CrossRef] [PubMed]

R. S. Bondurant, “Response of ideal photodetectors to photon flux and/or energy flux,” Phys. Rev. A 32, 2797 (1985).
[CrossRef] [PubMed]

B. Yurke, “Wideband photon counting and homodyne detection,” Phys. Rev. A 32, 311 (1985).
[CrossRef] [PubMed]

Phys. Rev. D (1)

J. N. Hollenhorst, “Quantum limits on resonant-mass gravitational-radiation detectors,” Phys. Rev. D 19, 1669 (1979).
[CrossRef]

Phys. Rev. Lett. (9)

D. Stoler, “Photon antibunching and possible ways to observe it,” Phys. Rev. Lett. 33, 1397 (1974).
[CrossRef]

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of squeezed states generated by four-wave mixing in an optical cavity,” Phys. Rev. Lett. 55, 2409 (1985).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broadband parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1986).
[CrossRef] [PubMed]

L. W. Wu, H. J. Kimble, J. L. Hall, and H. Wu, “Generation of squeezed states by parametric down conversion,” Phys. Rev. Lett. 57, 2520 (1986).
[CrossRef] [PubMed]

M. G. Raizen, L. A. Orozco, M. Xiao, T. L. Boyd, and H. J. Kimble, “Squeezed state generation by normal modes of a coupled system,” Phys. Rev. Lett. 59, 198 (1987).
[CrossRef] [PubMed]

M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett. 66, 153 (1991).
[CrossRef] [PubMed]

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, “Squeezing of quantum solitons,” Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

S. Machida, Y. Yamamoto, and Y. Itaya, “Ultrabroadband amplitude squeezing in a semiconductor laser,” Phys. Rev. Lett. 60, 792 (1988).
[CrossRef] [PubMed]

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, “Pulsed squeezed light,” Phys. Rev. Lett. 59, 2566 (1987).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

C. M. Caves, K. S. Thorne, K. W. P. Drever, V. D. Sandberg, and M. Zimmermann, “On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I,” Rev. Mod. Phys. 52, 341 (1980).
[CrossRef]

Sov. Phys. JETP (1)

V. Zakharov and A. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34, 62 (1972).

Other (2)

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

Y. Lai, “Noise analysis of soliton communication systems—a new approach,” IEEE J. Lightwave Technol. (to be published).

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Figures (7)

Fig. 1
Fig. 1

Pulse shapes of soliton excitations.

Fig. 2
Fig. 2

Balanced homodyne detection.

Fig. 3
Fig. 3

Squeezing ratio of solitons in optical fibers.

Fig. 4
Fig. 4

Fiber ring interferometer for squeezing generation.

Fig. 5
Fig. 5

Squeezing spectrum.

Fig. 6
Fig. 6

Fiber ring gyro with squeezed radiation injection.

Fig. 7
Fig. 7

Squeezing ratio of fiber ring gyros using solitons.

Equations (103)

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( x + 1 v g t ) A ( x , t ) = i 1 2 k 2 t 2 A ( x , t ) - i κ A * ( x , t ) A ( x , t ) A ( x , t ) .
τ = t - x / v g t 0             with             t 0 = Area ω k κ ,
z = x x 0             with             x 0 = 2 ( Area ω ) 2 k κ 2 ,
U = - sgn ( k ) A A 0             with             A 0 = ω Area ( κ k ) 1 / 2 ,
i z U ( z , τ ) = - 2 τ 2 U ( z , τ ) + 2 c U * ( z , τ ) U ( z , τ ) U ( z , τ ) ,
U 0 ( z , τ ) = ( n 0 c 1 / 2 / 2 ) exp [ i p 0 τ + i θ ( z ) ] × sech { ( n 0 c / 2 ) [ τ - T ( z ) ] } ,
θ ( z ) = θ 0 + ( n 0 2 c 2 / 4 ) z - p 0 2 z ,
T ( z ) = T 0 + 2 p 0 z .
[ U ^ ( z , τ ) , U ^ ( z , τ ) ] = δ ( τ - τ ) ,
[ U ^ ( z , τ ) , U ^ ( z , τ ) ] = [ U ^ ( z , τ ) , U ^ ( z , τ ) ] = 0.
i z U ^ ( z , τ ) = - 2 τ 2 U ^ ( z , τ ) + 2 c U ^ ( z , τ ) U ^ ( z , τ ) U ^ ( z , τ ) ,
H ^ = [ τ U ^ ( z , τ ) τ U ^ ( z , τ ) d τ + c U ^ ( z , τ ) U ^ ( z , τ ) U ^ ( z , τ ) U ^ ( z , τ ) d τ ] .
U ^ ( z , τ ) = [ U 0 ( 0 , τ ) + u ^ ( z , τ ) ] exp [ i ( n 0 2 c 2 / 4 ) z ]
z u ^ ( z , τ ) = i [ 2 τ 2 - n 0 2 c 2 4 + 4 c U 0 ( 0 , τ ) 2 ] u ^ ( z , τ ) + i 2 c U 0 ( 0 , τ ) 2 u ^ ( z , τ ) ,
[ u ^ ( z , τ ) , u ^ ( z , τ ) ] = δ ( τ - τ ) ,
[ u ^ ( z , τ ) , u ^ ( z , τ ) ] = [ u ^ ( z , τ ) , u ^ ( z , τ ) ] = 0.
z u ^ ( z , τ ) = P u ^ ( z , τ ) ,
u ^ = [ u ^ 1 u ^ 2 ] ,
P = [ 0 - P 1 P 2 0 ] ,
P 1 = 2 τ 2 - n 0 2 c 2 4 + 2 c U 0 ( 0 , τ ) 2 ,
P 2 = 2 τ 2 - n 0 2 c 2 4 + 6 c U 0 ( 0 , τ ) 2 ,
2 z 2 u ^ 1 ( z , τ ) = - P 1 P 2 u ^ 1 ( z , τ ) ,
2 z 2 u ^ 2 ( z , τ ) = - P 2 P 1 u ^ 2 ( z , τ ) .
f n ( τ ) U 0 ( 0 , τ ) n 0 = [ 1 n 0 - c 2 τ tanh ( n 0 c 2 τ ) ] U 0 ( 0 , τ ) ,
f θ ( τ ) 1 i U 0 ( 0 , τ ) θ 0 = U 0 ( 0 , τ ) ,
f p ( τ ) 1 i U 0 ( 0 , τ ) p 0 = τ U 0 ( 0 , τ ) ,
f T ( τ ) U 0 ( 0 , τ ) τ 0 = [ n 0 c 2 tanh ( n 0 c 2 τ ) ] U 0 ( 0 , τ ) .
P 1 f θ ( τ ) = 0 ,
P 2 f T ( τ ) = 0 ,
P 2 f n ( τ ) = ( n 0 c 2 / 2 ) f θ ( τ ) ,
P 1 f p ( τ ) = 2 f T ( τ ) .
P 2 = - [ P 1 P 2 0 0 P 2 P 1 ] ,
f n ( τ ) [ f n ( τ ) 0 ] ,
f θ ( τ ) [ 0 f θ ( τ ) ] ,
f p ( τ ) [ 0 f p ( τ ) ] ,
f T ( τ ) [ f T ( τ ) 0 ] ,
f ( τ ) g ( τ ) [ f 1 ( τ ) g 1 ( τ ) + f 2 ( τ ) g 2 ( τ ) ] d τ ,
f ( τ ) Pg ( τ ) = P A f ( τ ) g ( τ )
P A = [ 0 P 2 - P 1 0 ] .
( P A ) 2 = - [ P 2 P 1 0 0 P 1 P 2 ] .
S = [ 0 1 1 0 ] ,
f n ( τ ) S f θ ( τ ) = [ f θ ( τ ) 0 ] ,
f θ ( τ ) S f n ( τ ) = [ 0 f n ( τ ) ] ,
f p ( τ ) S f T ( τ ) = [ f T ( τ ) 0 ] ,
f T ( τ ) S f p ( τ ) = [ 0 f p ( τ ) ] ,
f k ( τ ) f l ( τ ) = 0             if k l ,
f n ( τ ) f n ( τ ) = f θ ( τ ) f θ ( τ ) = 1 / 2 ,
f p ( τ ) f p ( τ ) = f T ( τ ) f T ( τ ) = n 0 / 2.
u ^ ( z , τ ) = Δ n ^ ( z ) f n ( τ ) + Δ T ^ ( z ) f T ( τ ) + Δ θ ^ ( z ) f θ ( τ ) + Δ p ^ ( z ) f p ( τ ) + continuum ,
Δ n ^ ( z ) = f n ( τ ) u ^ ( z , τ ) f n ( τ ) f n ( τ ) = 2 f n ( τ ) u ^ ( z , τ ) ,
Δ θ ^ ( z ) = f θ ( τ ) u ^ ( z , τ ) f θ ( τ ) f θ ( τ ) = 2 f θ ( τ ) u ^ ( z , τ ) ,
Δ p ^ ( z ) = f p ( τ ) u ^ ( z , τ ) f p ( τ ) f p ( τ ) = 2 n 0 f p ( τ ) u ^ ( z , τ ) ,
Δ T ^ ( z ) = f T ( τ ) u ^ ( z , τ ) f T ( τ ) f T ( τ ) = 2 n 0 f T ( τ ) u ^ ( z , τ ) .
d d z Δ n ^ ( z ) = 0 ,
d d z Δ θ ^ ( z ) = n 0 c 2 2 Δ n ^ ( z ) ,
d d z Δ p ^ ( z ) = 0 ,
d d z Δ T ^ ( z ) = 2 Δ p ^ ( z ) .
Δ n ^ ( z ) = Δ n ^ ( 0 ) ,
Δ θ ^ ( z ) = Δ θ ^ ( 0 ) + ( n 0 c 2 / 2 ) z Δ n ^ ( 0 ) ,
Δ p ^ ( z ) = Δ p ^ ( 0 ) ,
Δ T ^ ( z ) = Δ T ^ ( 0 ) + 2 z Δ p ^ ( 0 ) .
[ Δ n ^ ( z ) , Δ θ ^ ( z ) ] = i ,
[ Δ T ^ ( z ) , n 0 Δ p ^ ( z ) ] = i ,
Δ n ^ 2 ( 0 ) = n 0 ,
Δ θ ^ 2 ( 0 ) = 1 3 ( 1 + π 2 12 ) 1 n 0 0.607 n 0 ,
Δ p ^ 2 ( 0 ) = n 0 c 2 12 ,
Δ T ^ 2 ( 0 ) = π 2 3 1 n 0 3 c 2 3.29 n 0 3 c 2 .
Δ n ^ 2 ( 0 ) Δ θ ^ 2 ( 0 ) 0.607 > 0.25 ,
n 0 2 Δ p ^ 2 ( 0 ) Δ T ^ 2 ( 0 ) 0.27 > 0.25.
Δ n ^ 2 ( z ) = n 0 ,
Δ θ ^ 2 ( z ) = 0.607 / n 0 + ( n 0 3 c 4 / 4 ) z 2 ,
Δ p ^ 2 ( z ) = n 0 c 2 / 12 ,
Δ T ^ 2 ( z ) = 3.29 / n 0 3 c 2 + ( n 0 c 2 / 3 ) z 2 .
M ^ ( z ) = H ( k ) [ u L ( τ ) u ^ ( z , τ ) + u L * ( τ ) u ^ ( z , τ ) ] exp ( i k τ ) d τ = H ( k ) { Re [ u L ( τ ) ] u ^ 1 ( z , τ ) + Im [ u L ( τ ) ] u ^ 2 ( z , τ ) } exp ( i k τ ) d τ ,
M ^ ( z ) = f L ( τ ) u ^ ( z , τ ) [ f L 1 ( τ ) u ^ 1 ( z , τ ) + f L 2 ( τ ) u ^ 2 ( z , τ ) ] d τ ,
f L ( τ ) [ Re [ u L ( τ ) ] exp ( i k τ ) Im [ u L ( τ ) ] exp ( i k τ ) ] .
f L f L d τ = 1
f L = 2 ( c n f n + c θ f θ ) ,
M ^ ( z ) = c n Δ n ^ ( z ) + c θ Δ θ ^ ( z ) = [ c n + ( 2 c θ / n 0 ) Φ ( z ) ] Δ n ^ ( 0 ) + c θ Δ θ ^ ( 0 ) ,
c n 2 Δ n ^ 2 ( 0 ) + c θ 2 Δ θ ^ 2 ( 0 ) = 1 / 4 ,
R ( z ) M ^ 2 ( z ) / M ^ 2 ( 0 ) = 4 [ c n + ( 2 c θ / n 0 ) Φ ] 2 Δ n ^ 2 ( 0 ) + 4 c θ 2 Δ θ ^ 2 ( 0 ) .
R opt ( z ) = 1 + 2 Φ 1 2 ( z ) - 2 Φ 1 ( z ) [ 1 + Φ 1 2 ( z ) ] 1 / 2 ,
Φ 1 ( z ) ( 1 / n 0 ) Φ ( z ) [ Δ n ^ 2 ( 0 ) / Δ θ ^ 2 ( 0 ) ] 1 / 2 .
u ^ ( z , τ ) = exp ( P z ) u ^ ( 0 , τ ) .
f L ( τ ) u ^ ( z , τ ) = f L ( τ ) exp ( P z ) u ^ ( 0 , τ ) = exp ( P A z ) f L ( τ ) u ^ ( 0 , τ ) F L ( z , τ ) u ^ ( 0 , τ ) ,
M ^ ( z ) M ^ ( z ) = 1 / 4 R ( z ) ,
R ( z ) = { F L 1 ( z , τ ) 2 + F L 2 ( z , τ ) 2 - 2 Im [ F L 1 * ( z , τ ) F L 2 ( z , τ ) ] } d τ .
f L = ( cos θ L ) [ f L 1 f L 2 ] + ( sin θ L ) [ - f L 2 f L 1 ] ,
R ( z ) = A ( z ) cos 2 θ L + 2 B ( z ) cos θ L sin θ L + C ( z ) sin 2 θ L ,
[ F 1 F 2 ] [ exp ( P A z ) ] [ f L 1 f L 2 ] ,
[ F 3 F 4 ] [ exp ( P A z ) ] [ - f L 2 f L 1 ] ,
A ( z ) = [ F 1 2 + F 2 2 - 2 Im ( F 1 * F 2 ) ] d z ,
B ( z ) = [ Re ( F 1 * F 3 ) + Re ( F 2 * F 4 ) - Im ( F 1 * F 4 + F 3 * F 2 ) ] d z ,
C ( z ) = [ F 3 2 + F 4 2 - 2 Im ( F 3 * F 4 ) ] d z .
R min ( z ) = A ( z ) + C ( z ) - { [ A ( z ) - C ( z ) ] 2 + 4 B 2 ( z ) } 1 / 2 2 .
S = F n s n L ( Δ ϕ ) 2 ,
F = f L f s 2 / f L f L f s f s .
N = ( n L / 4 ) R ,
S / N = ( 4 F n s / R ) ( Δ ϕ ) 2 .
u ^ ( z s + z g , τ ) = exp ( P z g ) R ( θ ) exp ( P z s ) u ^ ( 0 , τ ) .
R ( θ ) = [ cos θ sin θ - sin θ cos θ ] .
f L ( τ ) u ^ ( z s + z g , τ ) = f L ( τ ) exp ( P z g ) R ( θ ) exp ( P z s ) u ^ ( 0 , τ ) 0 = exp ( P A z s ) R ( - θ ) exp ( P A z g ) f L ( τ ) u ^ ( 0 , τ ) F L ( z s + z g , τ ) u ^ ( 0 , τ ) .
R = { F L 1 ( z s + z g , τ ) 2 + F L 2 ( z s + z g , τ ) 2 - 2 Im [ F L 1 * ( z s + z g , τ ) F L 2 ( z s + z g , τ ) ] } d τ .

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