Abstract

Pulsed squeezing in lossless optical fiber with Kerr nonlinearity and chromatic dispersion is numerically simulated by the use of the linearization approximation. The formalism developed here allows us to predict squeezing for an arbitrary initial complex pulse envelope in a fiber with nonlinearity and dispersion. The results show that squeezing is not necessarily reduced by large temporal and spectral distortions of the pulse caused by dispersion and can even be enhanced in certain cases.

© 1994 Optical Society of America

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References

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  1. 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]
  2. L.-A. Wu, M. Xiao, and H. J. Kimble, “Squeezed states of light from an optical parametric oscillator,” J. Opt. Soc. Am. B 4, 1465 (1987).
    [CrossRef]
  3. R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, and M. J. Potasek, “Pulsed squeezed light,” Phys. Rev. Lett. 59, 2566 (1987).
    [CrossRef] [PubMed]
  4. O. Aytür and P. Kumar, “Pulsed twin beams of light,” Phys. Rev. Lett. 65, 1551 (1990).
    [CrossRef] [PubMed]
  5. H. P. Yuen and J. H. Shapiro, “Generation and detection of two-photon coherent states in degenerate four-wave mixing,” Opt. Lett. 4, 334 (1979).
    [CrossRef] [PubMed]
  6. 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]
  7. M. D. Levenson, R. M. Shelby, M. Reid, and D. F. Walls, “Quantum nondemolition detection of optical quadrature amplitudes,” Phys. Rev. Lett. 57, 2473 (1986).
    [CrossRef] [PubMed]
  8. M. Kitagawa and Y. Yamamoto, “Number-phase minimum-uncertainty state with reduced number uncertainty in a Kerr nonlinear interferometer,” Phys. Rev. A 34, 3974 (1986).
    [CrossRef] [PubMed]
  9. S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor laser,” Phys. Rev. Lett. 58, 1000 (1987).
    [CrossRef] [PubMed]
  10. M. Shirasaki and H. A. Haus, “Squeezing of pulses in a nonlinear interferometer,” J. Opt. Soc. Am. B 7, 30 (1990).
    [CrossRef]
  11. K. Bergman and H. A. Haus, “Squeezing in fibers with optical pulses,” Opt. Lett. 16, 663 (1991).
    [CrossRef] [PubMed]
  12. M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett. 66, 153 (1991).
    [CrossRef] [PubMed]
  13. C. R. Doerr, I. Lyubomirsky, G. Lenz, J. Paye, H. A. Haus, and M. Shirasaki, “Optical squeezing with a short fiber,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper QFF-3.
  14. H. A. Haus and Y. Lai, “Quantum theory of soliton squeezing: a linearized approach,” J. Opt. Soc. Am. B 7, 386 (1990).
    [CrossRef]
  15. 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]
  16. P. D. Drummond and S. J. Carter, “Quantum-field theory of squeezing in solitons,” J. Opt. Soc. Am. B 4, 1565 (1987).
    [CrossRef]
  17. P. D. Drummond, S. J. Carter, and R. M. Shelby, “Time dependence of quantum fluctuations in solitons,” Opt. Lett. 14, 373 (1989).
    [CrossRef] [PubMed]
  18. R. M. Shelby, P. D. Drummond, and S. J. Carter, “Phase-noise scaling in quantum soliton propagation,” Phys. Rev. A 42, 2966 (1990).
    [CrossRef] [PubMed]
  19. F. Singer, M. J. Potasek, J. M. Fang, and M. C. Teich, “Femtosecond solitons in nonlinear optical fibers: classical and quantum effects,” Phys. Rev. A 46, 4192 (1992).
    [CrossRef] [PubMed]
  20. M. Shirasaki, “Quantum-noise reduction in a phase-sensitive interferometer using nonclassical light produced through Kerr media,” Opt. Lett. 16, 171 (1991).
    [PubMed]
  21. K. J. Blow, R. Loudon, and S. J. D. Phoenix, “Exact solution for quantum self-phase modulation,” J. Opt. Soc. Am. B 8, 1750 (1991).
    [CrossRef]
  22. M. J. Potasek and B. Yurke, “Squeezed-light generation in a medium governed by the nonlinear Schrodinger equation,” Phys. Rev. A 35, 3974 (1987).
    [CrossRef] [PubMed]
  23. L. G. Joneckis and J. H. Shapiro, “Quantum propagation in single-mode fiber,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper QFF-4.
  24. G. P. Agarwal, Nonlinear Fiber Optics (Academic, New York, 1989).
  25. Y. Lai, “Quantum theory of optical solitons,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1989).

1992 (1)

F. Singer, M. J. Potasek, J. M. Fang, and M. C. Teich, “Femtosecond solitons in nonlinear optical fibers: classical and quantum effects,” Phys. Rev. A 46, 4192 (1992).
[CrossRef] [PubMed]

1991 (4)

1990 (4)

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

O. Aytür and P. Kumar, “Pulsed twin beams of light,” Phys. Rev. Lett. 65, 1551 (1990).
[CrossRef] [PubMed]

M. Shirasaki and H. A. Haus, “Squeezing of pulses in a nonlinear interferometer,” J. Opt. Soc. Am. B 7, 30 (1990).
[CrossRef]

R. M. Shelby, P. D. Drummond, and S. J. Carter, “Phase-noise scaling in quantum soliton propagation,” Phys. Rev. A 42, 2966 (1990).
[CrossRef] [PubMed]

1989 (1)

1987 (6)

L.-A. Wu, M. Xiao, and H. J. Kimble, “Squeezed states of light from an optical parametric oscillator,” J. Opt. Soc. Am. B 4, 1465 (1987).
[CrossRef]

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

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor laser,” Phys. Rev. Lett. 58, 1000 (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]

M. J. Potasek and B. Yurke, “Squeezed-light generation in a medium governed by the nonlinear Schrodinger equation,” Phys. Rev. A 35, 3974 (1987).
[CrossRef] [PubMed]

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]

M. D. Levenson, R. M. Shelby, M. Reid, and D. F. Walls, “Quantum nondemolition detection of optical quadrature amplitudes,” Phys. Rev. Lett. 57, 2473 (1986).
[CrossRef] [PubMed]

M. Kitagawa and Y. Yamamoto, “Number-phase minimum-uncertainty state with reduced number uncertainty in a Kerr nonlinear interferometer,” Phys. Rev. A 34, 3974 (1986).
[CrossRef] [PubMed]

1985 (1)

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]

1979 (1)

Agarwal, G. P.

G. P. Agarwal, Nonlinear Fiber Optics (Academic, New York, 1989).

Aytür, O.

O. Aytür and P. Kumar, “Pulsed twin beams of light,” Phys. Rev. Lett. 65, 1551 (1990).
[CrossRef] [PubMed]

Bergman, K.

Blow, K. J.

Carter, S. J.

R. M. Shelby, P. D. Drummond, and S. J. Carter, “Phase-noise scaling in quantum soliton propagation,” Phys. Rev. A 42, 2966 (1990).
[CrossRef] [PubMed]

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

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]

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]

Doerr, C. R.

C. R. Doerr, I. Lyubomirsky, G. Lenz, J. Paye, H. A. Haus, and M. Shirasaki, “Optical squeezing with a short fiber,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper QFF-3.

Drummond, P. D.

R. M. Shelby, P. D. Drummond, and S. J. Carter, “Phase-noise scaling in quantum soliton propagation,” Phys. Rev. A 42, 2966 (1990).
[CrossRef] [PubMed]

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

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]

Fang, J. M.

F. Singer, M. J. Potasek, J. M. Fang, and M. C. Teich, “Femtosecond solitons in nonlinear optical fibers: classical and quantum effects,” Phys. Rev. A 46, 4192 (1992).
[CrossRef] [PubMed]

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]

Haus, H. A.

K. Bergman and H. A. Haus, “Squeezing in fibers with optical pulses,” Opt. Lett. 16, 663 (1991).
[CrossRef] [PubMed]

M. Shirasaki and H. A. Haus, “Squeezing of pulses in a nonlinear interferometer,” J. Opt. Soc. Am. B 7, 30 (1990).
[CrossRef]

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

C. R. Doerr, I. Lyubomirsky, G. Lenz, J. Paye, H. A. Haus, and M. Shirasaki, “Optical squeezing with a short fiber,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper QFF-3.

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]

Itaya, Y.

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor laser,” Phys. Rev. Lett. 58, 1000 (1987).
[CrossRef] [PubMed]

Joneckis, L. G.

L. G. Joneckis and J. H. Shapiro, “Quantum propagation in single-mode fiber,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper QFF-4.

Kimble, H. J.

Kitagawa, M.

M. Kitagawa and Y. Yamamoto, “Number-phase minimum-uncertainty state with reduced number uncertainty in a Kerr nonlinear interferometer,” Phys. Rev. A 34, 3974 (1986).
[CrossRef] [PubMed]

Kumar, P.

O. Aytür and P. Kumar, “Pulsed twin beams of light,” Phys. Rev. Lett. 65, 1551 (1990).
[CrossRef] [PubMed]

Lai, Y.

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, “Quantum theory of optical solitons,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1989).

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]

Lenz, G.

C. R. Doerr, I. Lyubomirsky, G. Lenz, J. Paye, H. A. Haus, and M. Shirasaki, “Optical squeezing with a short fiber,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper QFF-3.

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]

M. D. Levenson, R. M. Shelby, M. Reid, and D. F. Walls, “Quantum nondemolition detection of optical quadrature amplitudes,” Phys. Rev. Lett. 57, 2473 (1986).
[CrossRef] [PubMed]

Loudon, R.

Lyubomirsky, I.

C. R. Doerr, I. Lyubomirsky, G. Lenz, J. Paye, H. A. Haus, and M. Shirasaki, “Optical squeezing with a short fiber,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper QFF-3.

Machida, S.

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor laser,” Phys. Rev. Lett. 58, 1000 (1987).
[CrossRef] [PubMed]

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]

Paye, J.

C. R. Doerr, I. Lyubomirsky, G. Lenz, J. Paye, H. A. Haus, and M. Shirasaki, “Optical squeezing with a short fiber,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper QFF-3.

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]

Phoenix, S. J. D.

Potasek, M. J.

F. Singer, M. J. Potasek, J. M. Fang, and M. C. Teich, “Femtosecond solitons in nonlinear optical fibers: classical and quantum effects,” Phys. Rev. A 46, 4192 (1992).
[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]

M. J. Potasek and B. Yurke, “Squeezed-light generation in a medium governed by the nonlinear Schrodinger equation,” Phys. Rev. A 35, 3974 (1987).
[CrossRef] [PubMed]

Reid, M.

M. D. Levenson, R. M. Shelby, M. Reid, and D. F. Walls, “Quantum nondemolition detection of optical quadrature amplitudes,” Phys. Rev. Lett. 57, 2473 (1986).
[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]

Shapiro, J. H.

H. P. Yuen and J. H. Shapiro, “Generation and detection of two-photon coherent states in degenerate four-wave mixing,” Opt. Lett. 4, 334 (1979).
[CrossRef] [PubMed]

L. G. Joneckis and J. H. Shapiro, “Quantum propagation in single-mode fiber,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper QFF-4.

Shelby, R. M.

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

R. M. Shelby, P. D. Drummond, and S. J. Carter, “Phase-noise scaling in quantum soliton propagation,” Phys. Rev. A 42, 2966 (1990).
[CrossRef] [PubMed]

P. D. Drummond, S. J. Carter, 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]

M. D. Levenson, R. M. Shelby, M. Reid, and D. F. Walls, “Quantum nondemolition detection of optical quadrature amplitudes,” Phys. Rev. Lett. 57, 2473 (1986).
[CrossRef] [PubMed]

Shirasaki, M.

M. Shirasaki, “Quantum-noise reduction in a phase-sensitive interferometer using nonclassical light produced through Kerr media,” Opt. Lett. 16, 171 (1991).
[PubMed]

M. Shirasaki and H. A. Haus, “Squeezing of pulses in a nonlinear interferometer,” J. Opt. Soc. Am. B 7, 30 (1990).
[CrossRef]

C. R. Doerr, I. Lyubomirsky, G. Lenz, J. Paye, H. A. Haus, and M. Shirasaki, “Optical squeezing with a short fiber,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper QFF-3.

Singer, F.

F. Singer, M. J. Potasek, J. M. Fang, and M. C. Teich, “Femtosecond solitons in nonlinear optical fibers: classical and quantum effects,” Phys. Rev. A 46, 4192 (1992).
[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]

Teich, M. C.

F. Singer, M. J. Potasek, J. M. Fang, and M. C. Teich, “Femtosecond solitons in nonlinear optical fibers: classical and quantum effects,” Phys. Rev. A 46, 4192 (1992).
[CrossRef] [PubMed]

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]

M. D. Levenson, R. M. Shelby, M. Reid, and D. F. Walls, “Quantum nondemolition detection of optical quadrature amplitudes,” Phys. Rev. Lett. 57, 2473 (1986).
[CrossRef] [PubMed]

Wu, L.-A.

Xiao, M.

Yamamoto, Y.

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor laser,” Phys. Rev. Lett. 58, 1000 (1987).
[CrossRef] [PubMed]

M. Kitagawa and Y. Yamamoto, “Number-phase minimum-uncertainty state with reduced number uncertainty in a Kerr nonlinear interferometer,” Phys. Rev. A 34, 3974 (1986).
[CrossRef] [PubMed]

Yuen, H. P.

Yurke, B.

M. J. Potasek and B. Yurke, “Squeezed-light generation in a medium governed by the nonlinear Schrodinger equation,” Phys. Rev. A 35, 3974 (1987).
[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]

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]

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

Opt. Lett. (4)

Phys. Rev. A (4)

R. M. Shelby, P. D. Drummond, and S. J. Carter, “Phase-noise scaling in quantum soliton propagation,” Phys. Rev. A 42, 2966 (1990).
[CrossRef] [PubMed]

F. Singer, M. J. Potasek, J. M. Fang, and M. C. Teich, “Femtosecond solitons in nonlinear optical fibers: classical and quantum effects,” Phys. Rev. A 46, 4192 (1992).
[CrossRef] [PubMed]

M. Kitagawa and Y. Yamamoto, “Number-phase minimum-uncertainty state with reduced number uncertainty in a Kerr nonlinear interferometer,” Phys. Rev. A 34, 3974 (1986).
[CrossRef] [PubMed]

M. J. Potasek and B. Yurke, “Squeezed-light generation in a medium governed by the nonlinear Schrodinger equation,” Phys. Rev. A 35, 3974 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett. (8)

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]

S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of amplitude squeezing in a constant-current-driven semiconductor laser,” Phys. Rev. Lett. 58, 1000 (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]

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]

M. D. Levenson, R. M. Shelby, M. Reid, and D. F. Walls, “Quantum nondemolition detection of optical quadrature amplitudes,” Phys. Rev. Lett. 57, 2473 (1986).
[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]

O. Aytür and P. Kumar, “Pulsed twin beams of light,” Phys. Rev. Lett. 65, 1551 (1990).
[CrossRef] [PubMed]

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

Other (4)

C. R. Doerr, I. Lyubomirsky, G. Lenz, J. Paye, H. A. Haus, and M. Shirasaki, “Optical squeezing with a short fiber,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper QFF-3.

L. G. Joneckis and J. H. Shapiro, “Quantum propagation in single-mode fiber,” in Quantum Electronics and Laser Science Conference, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper QFF-4.

G. P. Agarwal, Nonlinear Fiber Optics (Academic, New York, 1989).

Y. Lai, “Quantum theory of optical solitons,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1989).

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Figures (6)

Fig. 1
Fig. 1

Squeezing schematic consisting of a fiber nonlinear interferometer and a balanced homodyne detector.

Fig. 2
Fig. 2

(a) Antisqueezing and (b) squeezing versus second-order dispersion. The input pulse is a 200-fs sech that is a soliton at β2 = −20 ps2/km. The solid curve is for l = 0.64 m, the dashed curve is for l = 1.28 m, the dotted curve is for l = 1.92 m, and the dashed-dotted curve is for l = 2.56 m. These lengths correspond to nonlinear phase shifts for the soliton of 0.5, 1.0, 1.5, and 2.0 rad, respectively.

Fig. 3
Fig. 3

Pulse shapes at the output after traveling l = 2.56 m with various amounts of second-order dispersion. Parameters are the same as in Fig. 2. The coordinates are intensity versus time, and all pulses have the same scale.

Fig. 4
Fig. 4

(a) Antisqueezing and (b) squeezing versus second-order dispersion with third-order dispersion included (β3 = 0.1 ps3/km). All other parameters are the same as in Fig. 2.

Fig. 5
Fig. 5

Pulse shape at the output after traveling l = 2.56 m with β2 = −1 ps2/km and β3 = 0.1 ps3/km. Parameters are the same as in Fig. 4. The coordinates are intensity versus time with the same scale as in Fig. 3.

Fig. 6
Fig. 6

(a) Antisqueezing and (b) squeezing versus second-order dispersion with third-order dispersion included (β3 = 0.1 ps3/km). The input pulse is a sech as in Figs. 2 and 5, except the pulse intensity FWHM is 100 fs. All other parameters are the same.

Equations (36)

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A ˆ / z = i κ A ˆ A ˆ A ˆ + i F 1 { [ β ( ω ) β 0 ] F ( A ˆ ) } ,
F [ A ˆ ( t ) ] A ˜ ˆ ( ω ) 1 2 π d t A ˆ ( t ) exp ( i ω t ) ,
F 1 [ A ˜ ˆ ( ω ) ] A ˆ ( t ) d ω A ˜ ˆ ( ω ) exp ( i ω t ) .
β ( ω ) = β 0 + ( ω ω 0 ) β 1 + 1 2 ( ω ω 0 ) 2 β 2 + 1 6 ( ω ω 0 ) 3 β 3 + ,
β n = ( d n β d ω n ) ω = ω 0 .
A ˆ = A + b ˆ ,
b ˆ z = 2 i κ | A | 2 b ˆ + i κ A 2 b ˆ + i F 1 { [ β ( ω ) β 0 ] F ( b ˆ ) } .
b ˆ j ( n + 1 ) = [ 1 + 2 i κ Δ z | A j ( n ) | 2 ] b ˆ j ( n ) + i κ Δ z [ A j ( n ) ] 2 b ˆ j ( n ) + i Δ z D F 1 { [ β ( 2 π q / M Δ t + ω 0 ) β 0 ] × D F [ b ˆ j ( n ) ] } ,
D F ( b ˆ j ) b ˜ ˆ q 1 M j = 0 M 1 b ˆ j exp ( i 2 π j q M ) ,
D F 1 ( b ˜ ˆ q ) b ˆ j q = 0 M 1 b ˜ ˆ q exp ( i 2 π j q M ) .
b ˆ z = 2 i κ | A | 2 b ˆ + i κ A 2 b ˆ 1 2 i β 2 2 b ˆ t 2 ,
b ˆ j ( n + 1 ) = [ 1 + 2 i κ Δ z | A j ( n ) | 2 ] b ˆ j ( n ) + i κ Δ z [ A j ( n ) ] 2 b ˆ j ( n ) 1 2 i β 2 Δ z b ˆ j 1 ( n ) 2 b ˆ j ( n ) + b ˆ j + 1 ( n ) ( Δ t ) 2 .
b ˆ j ( n ) = k [ μ j k ( n ) a ˆ k + ν j k ( n ) a ˆ k ] ,
[ a ˆ j , a ˆ k ] = δ j k ,
[ a ˆ j , a ˆ k ] = 0 ,
μ j k ( n + 1 ) = [ 1 + 2 i κ Δ z | A j ( n ) | 2 + i β 2 Δ z ( Δ t ) 2 ] μ j k ( n ) + i κ Δ z [ A j ( n ) ] 2 ν j k * ( n ) i β 2 Δ z 2 ( Δ t ) 2 [ μ j 1 , k ( n ) + μ j + 1 , k ( n ) ] ,
ν j k ( n + 1 ) = [ 1 + 2 i κ Δ z | A j ( n ) | 2 + i β 2 Δ z ( Δ t ) 2 ] ν j k ( n ) + i κ Δ z [ A j ( n ) ] 2 μ j k * ( n ) i β 2 Δ z 2 ( Δ t ) 2 [ ν j 1 , k ( n ) + ν j + 1 , k ( n ) ] .
μ j k ( 0 ) = δ j k ,
ν j k ( 0 ) = 0.
b ˜ ˆ q ( n ) = k [ μ ˜ q k ( n ) a ˆ k + ν ˜ q k ( n ) a ˆ k ] ,
μ j k ( n + 1 ) = [ 1 + 2 i κ Δ z | A j ( n ) | 2 ] μ j k ( n ) + i κ Δ z [ A j ( n ) ] 2 ν j k * ( n ) + i Δ z D F 1 { [ β ( 2 π q / M Δ t + ω 0 ) β 0 ] μ ˜ q k ( n ) } ,
ν j k ( n + 1 ) = [ 1 + 2 i κ Δ z | A j ( n ) | 2 ] ν j k ( n ) + i κ Δ z [ A j ( n ) ] 2 μ j k * ( n ) + i Δ z D F 1 { [ β ( 2 π q / M Δ t + ω 0 ) β 0 ] ν ˜ q k ( n ) } .
A L ( 0 ) = 1 ( 2 ) 1 / 2 C ( 0 ) ,
b ˆ L ( 0 ) = 1 ( 2 ) 1 / 2 [ c ˆ ( 0 ) + d ˆ ( 0 ) ] ,
A R ( 0 ) = 1 ( 2 ) 1 / 2 C ( 0 ) ,
b ˆ R ( 0 ) = 1 ( 2 ) 1 / 2 [ c ˆ ( 0 ) + d ˆ ( 0 ) ] .
b ˆ L ( N ) = 1 ( 2 ) 1 / 2 [ c ˆ ( N ) + d ˆ ( N ) ] ,
b ˆ R ( N ) = 1 ( 2 ) 1 / 2 [ c ˆ ( N ) + d ˆ ( N ) ] .
I ˆ j = C j * ( N ) exp ( i ϕ ) d ˆ j ( N ) + C j ( N ) exp ( i ϕ ) d ˆ j ( N ) .
I ˆ j = 1 ( 2 ) 1 / 2 C j * exp ( i ϕ ) × k [ μ j k ( a ˆ k L + a ˆ k R ) + ν j k ( a ˆ k L + a ˆ k R ) ] + 1 ( 2 ) 1 / 2 C j exp ( i ϕ ) × k [ μ j k * ( a ˆ k L + a ˆ k R ) + ν j k * ( a ˆ k L + a ˆ k R ) ] ,
Φ 0 | I ˜ ˆ 0 | 2 = 1 2 M 2 j l I ˆ l I l j + I ˆ l j I ˆ l .
R = Φ 0 | ( μ , ν ) Φ 0 | ( μ j k = δ j k , ν j k = 0 ) .
a ˆ j a ˆ k = δ j k ,
a ˆ j a ˆ k = a ˆ j a ˆ k = a ˆ j a ˆ k = 0 ,
R = j k l Re [ C l * C j * exp ( 2 i ϕ ) ( μ I k ν j k + μ j k ν l k ) + C l C j * ( μ l k * μ j k + ν l k * ν j k ) ] l | C l | 2 .
R max ( min ) = j k l { Re [ C l C j * ( μ l k * μ j k + ν l k * ν j k ) ] ± | C l * C j * ( μ l k ν j k + μ j k ν l k ) | } l | C l | 2 .

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