Abstract

We study a Mach-Zehnder nonlinear fiber interferometer for the generation of amplitude-squeezed light. Numerical simulations of experiments with microstructure fiber are performed using linearization of the quantum nonlinear Shrödinger equation. We include in our model the effect of distributed linear losses in the fiber.

© 2002 Optical Society of America

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  1. R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. De Voe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1987).
    [CrossRef]
  2. M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett. 66, 153 (1991).
    [CrossRef] [PubMed]
  3. A. Sizmann and G. Leuchs, “The optical Kerr effect and quantum optics in fibers,” in Progress in Optics XXXIX, E. Wolf, ed. (Elsevier Scinece B.V.,1999).
    [CrossRef]
  4. Ch. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable Einstein-Podolsky-Rosen entanglement via the Kerr nonlinearity in an optical fibre,” Phys. Rev. Lett. 86, 4267 (2001).
    [CrossRef] [PubMed]
  5. A. Furasawa, J.L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science282, 706 (1998); S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A612302 (2000).
    [CrossRef]
  6. S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-number squeezed solitons from an asymmetric fiber-optic Sagnac interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
    [CrossRef]
  7. S. Spälter, M. Burk, U Ströner, A. Sizmann, and G. Leuchs, “Propagation of quantum properties of sub-picosecond solitons in a fiber,” Opt. Express 2, 77 (1998).
    [CrossRef]
  8. D. Krylov and K. Bergman, “Amplitude-squeezed solitons from an asymmetric fiber interferometer,” Opt. Lett. 23, 1390 (1998).
    [CrossRef]
  9. D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. 24, 948 (1999)
    [CrossRef]
  10. M. Fiorentino, J. E. Sharping, P. Kumar, D. Levandovsky, and M. Vasilyev, “Soliton squeezing in a Mach-Zehnder fiber interferometer,” Phys. Rev. A 64, 031801(R) (2001).
    [CrossRef]
  11. M. Fiorentino, J.E. Sharping, P. Kumar, A. Porzio, and R. Windeler, “Soliton squeezing in microstructure fiber,” submitted to Opt.Lett.
  12. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25 (2000).
    [CrossRef]
  13. X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggelton, S. G. Kosinsky, and R. S. Windeler, “Solitonself-phase shift in a short tapered air-silica microstructure fiber,” Opt. Lett. 26, 358 (2001).
    [CrossRef]
  14. J. E. Sharping, M. Fiorentino, and P. Kumar, “Four wave mixing in microstructure fibers,” Opt. Lett. 26, 1048 (2001).
    [CrossRef]
  15. F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth, and P. St. J. Russel, “Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber,” Opt. Lett. 26, 1558 (2001).
    [CrossRef]
  16. H. A. Haus and Y. Lai, “Quantum theory of soliton squeezing: a linearized approach,” J. Opt. Soc. Am. B 7, 386 (1990).
    [CrossRef]
  17. D. J. Kaup, “Perturbation theory for solitons in optical fibres,” Phys. Rev. A 42, 5689 (1990).
    [CrossRef] [PubMed]
  18. D. Levandovsky, M. Vasilyev, and P. Kumar, “Soliton squeezing in a highly transmissive loop mirror,” Opt. Lett. 24, 89 (1999).
    [CrossRef]
  19. C. R. Doerr, M. Shirasaki, and F. I. Khatri, “Simulation of pulsed squeezing in optical fiber with chromatic dispersion,” J. Opt. Soc. Am. B, 11, 142 (1994).
    [CrossRef]
  20. M. Shirasaki and H. A. Haus, “Squeezing of pulses in a nonlinear interferometer,” J. Opt. Soc. Am. B 7, 30 (1990)
    [CrossRef]
  21. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego,1995).
  22. C. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817 (1982).
    [CrossRef]
  23. W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, New York,1973).
  24. P. Kumar and J. Shapiro, “Squeezed-state generation via forward degenerate four-wave mixing,” Phys. Rev. A 30, 1568 (1984).
    [CrossRef]
  25. J. H. Shapiro and L. Boivin, “Raman-noise limit on squeezing in continuous-wave four-wave mixing,” Opt. Lett. 20, 925 (1990).
    [CrossRef]
  26. M. J. Werner, “Quantum soliton generation using an interferometer,” Phys. Rev. Lett. 81, 4132 (1998).
    [CrossRef]
  27. K. Bergman, H. A. Haus, E. P. Ippen, and M. Shirasaki, “Squeezing in a fiber interferometer with a gigahertz pump,” Opt. Lett. 19, 290 (1994).
    [CrossRef] [PubMed]

2001 (5)

Ch. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable Einstein-Podolsky-Rosen entanglement via the Kerr nonlinearity in an optical fibre,” Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

M. Fiorentino, J. E. Sharping, P. Kumar, D. Levandovsky, and M. Vasilyev, “Soliton squeezing in a Mach-Zehnder fiber interferometer,” Phys. Rev. A 64, 031801(R) (2001).
[CrossRef]

X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggelton, S. G. Kosinsky, and R. S. Windeler, “Solitonself-phase shift in a short tapered air-silica microstructure fiber,” Opt. Lett. 26, 358 (2001).
[CrossRef]

J. E. Sharping, M. Fiorentino, and P. Kumar, “Four wave mixing in microstructure fibers,” Opt. Lett. 26, 1048 (2001).
[CrossRef]

F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth, and P. St. J. Russel, “Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber,” Opt. Lett. 26, 1558 (2001).
[CrossRef]

2000 (1)

1999 (2)

1998 (4)

M. J. Werner, “Quantum soliton generation using an interferometer,” Phys. Rev. Lett. 81, 4132 (1998).
[CrossRef]

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-number squeezed solitons from an asymmetric fiber-optic Sagnac interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

S. Spälter, M. Burk, U Ströner, A. Sizmann, and G. Leuchs, “Propagation of quantum properties of sub-picosecond solitons in a fiber,” Opt. Express 2, 77 (1998).
[CrossRef]

D. Krylov and K. Bergman, “Amplitude-squeezed solitons from an asymmetric fiber interferometer,” Opt. Lett. 23, 1390 (1998).
[CrossRef]

1994 (2)

C. R. Doerr, M. Shirasaki, and F. I. Khatri, “Simulation of pulsed squeezing in optical fiber with chromatic dispersion,” J. Opt. Soc. Am. B, 11, 142 (1994).
[CrossRef]

K. Bergman, H. A. Haus, E. P. Ippen, and M. Shirasaki, “Squeezing in a fiber interferometer with a gigahertz pump,” Opt. Lett. 19, 290 (1994).
[CrossRef] [PubMed]

1991 (1)

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

1990 (4)

1987 (1)

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. De Voe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1987).
[CrossRef]

1984 (1)

P. Kumar and J. Shapiro, “Squeezed-state generation via forward degenerate four-wave mixing,” Phys. Rev. A 30, 1568 (1984).
[CrossRef]

1982 (1)

C. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817 (1982).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego,1995).

Arriaga, J.

F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth, and P. St. J. Russel, “Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber,” Opt. Lett. 26, 1558 (2001).
[CrossRef]

Bergman, K.

Boivin, L.

Braunstein, S. L.

A. Furasawa, J.L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science282, 706 (1998); S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A612302 (2000).
[CrossRef]

A. Furasawa, J.L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science282, 706 (1998); S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A612302 (2000).
[CrossRef]

Burk, M.

Caves, C.

C. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D 26, 1817 (1982).
[CrossRef]

Chandalia, J. K.

De Voe, R. G.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. De Voe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1987).
[CrossRef]

Doerr, C. R.

C. R. Doerr, M. Shirasaki, and F. I. Khatri, “Simulation of pulsed squeezing in optical fiber with chromatic dispersion,” J. Opt. Soc. Am. B, 11, 142 (1994).
[CrossRef]

Eggelton, B. J.

Ficker, J.

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-number squeezed solitons from an asymmetric fiber-optic Sagnac interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Fiorentino, M.

M. Fiorentino, J. E. Sharping, P. Kumar, D. Levandovsky, and M. Vasilyev, “Soliton squeezing in a Mach-Zehnder fiber interferometer,” Phys. Rev. A 64, 031801(R) (2001).
[CrossRef]

J. E. Sharping, M. Fiorentino, and P. Kumar, “Four wave mixing in microstructure fibers,” Opt. Lett. 26, 1048 (2001).
[CrossRef]

M. Fiorentino, J.E. Sharping, P. Kumar, A. Porzio, and R. Windeler, “Soliton squeezing in microstructure fiber,” submitted to Opt.Lett.

Fuchs, C. A.

A. Furasawa, J.L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science282, 706 (1998); S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A612302 (2000).
[CrossRef]

Furasawa, A.

A. Furasawa, J.L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science282, 706 (1998); S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A612302 (2000).
[CrossRef]

Haus, H. A.

Ippen, E. P.

Kaup, D. J.

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

Khatri, F. I.

C. R. Doerr, M. Shirasaki, and F. I. Khatri, “Simulation of pulsed squeezing in optical fiber with chromatic dispersion,” J. Opt. Soc. Am. B, 11, 142 (1994).
[CrossRef]

Kimble, H. J.

A. Furasawa, J.L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science282, 706 (1998); S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A612302 (2000).
[CrossRef]

A. Furasawa, J.L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science282, 706 (1998); S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A612302 (2000).
[CrossRef]

Knight, J. C.

F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth, and P. St. J. Russel, “Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber,” Opt. Lett. 26, 1558 (2001).
[CrossRef]

Knox, W. H.

König, F.

Ch. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable Einstein-Podolsky-Rosen entanglement via the Kerr nonlinearity in an optical fibre,” Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-number squeezed solitons from an asymmetric fiber-optic Sagnac interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Korolkova, N.

Ch. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable Einstein-Podolsky-Rosen entanglement via the Kerr nonlinearity in an optical fibre,” Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Kosinsky, S. G.

Krylov, D.

Kumar, P.

M. Fiorentino, J. E. Sharping, P. Kumar, D. Levandovsky, and M. Vasilyev, “Soliton squeezing in a Mach-Zehnder fiber interferometer,” Phys. Rev. A 64, 031801(R) (2001).
[CrossRef]

J. E. Sharping, M. Fiorentino, and P. Kumar, “Four wave mixing in microstructure fibers,” Opt. Lett. 26, 1048 (2001).
[CrossRef]

D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. 24, 948 (1999)
[CrossRef]

D. Levandovsky, M. Vasilyev, and P. Kumar, “Soliton squeezing in a highly transmissive loop mirror,” Opt. Lett. 24, 89 (1999).
[CrossRef]

P. Kumar and J. Shapiro, “Squeezed-state generation via forward degenerate four-wave mixing,” Phys. Rev. A 30, 1568 (1984).
[CrossRef]

M. Fiorentino, J.E. Sharping, P. Kumar, A. Porzio, and R. Windeler, “Soliton squeezing in microstructure fiber,” submitted to Opt.Lett.

Lai, Y.

Lam, P. K.

Ch. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable Einstein-Podolsky-Rosen entanglement via the Kerr nonlinearity in an optical fibre,” Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Leuchs, G.

Ch. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable Einstein-Podolsky-Rosen entanglement via the Kerr nonlinearity in an optical fibre,” Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-number squeezed solitons from an asymmetric fiber-optic Sagnac interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

S. Spälter, M. Burk, U Ströner, A. Sizmann, and G. Leuchs, “Propagation of quantum properties of sub-picosecond solitons in a fiber,” Opt. Express 2, 77 (1998).
[CrossRef]

A. Sizmann and G. Leuchs, “The optical Kerr effect and quantum optics in fibers,” in Progress in Optics XXXIX, E. Wolf, ed. (Elsevier Scinece B.V.,1999).
[CrossRef]

Levandovsky, D.

Levenson, M. D.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. De Voe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1987).
[CrossRef]

Liu, X.

Louisell, W. H.

W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, New York,1973).

Moores, M. D.

F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth, and P. St. J. Russel, “Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber,” Opt. Lett. 26, 1558 (2001).
[CrossRef]

Omenetto, F. G.

F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth, and P. St. J. Russel, “Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber,” Opt. Lett. 26, 1558 (2001).
[CrossRef]

Perlmutter, S. H.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. De Voe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1987).
[CrossRef]

Polzik, E. S.

A. Furasawa, J.L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science282, 706 (1998); S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A612302 (2000).
[CrossRef]

Porzio, A.

M. Fiorentino, J.E. Sharping, P. Kumar, A. Porzio, and R. Windeler, “Soliton squeezing in microstructure fiber,” submitted to Opt.Lett.

Ranka, J. K.

Rosenbluh, M.

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

Russel, P. St. J.

F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth, and P. St. J. Russel, “Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber,” Opt. Lett. 26, 1558 (2001).
[CrossRef]

Schmitt, S.

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-number squeezed solitons from an asymmetric fiber-optic Sagnac interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Shapiro, J.

P. Kumar and J. Shapiro, “Squeezed-state generation via forward degenerate four-wave mixing,” Phys. Rev. A 30, 1568 (1984).
[CrossRef]

Shapiro, J. H.

Sharping, J. E.

J. E. Sharping, M. Fiorentino, and P. Kumar, “Four wave mixing in microstructure fibers,” Opt. Lett. 26, 1048 (2001).
[CrossRef]

M. Fiorentino, J. E. Sharping, P. Kumar, D. Levandovsky, and M. Vasilyev, “Soliton squeezing in a Mach-Zehnder fiber interferometer,” Phys. Rev. A 64, 031801(R) (2001).
[CrossRef]

Sharping, J.E.

M. Fiorentino, J.E. Sharping, P. Kumar, A. Porzio, and R. Windeler, “Soliton squeezing in microstructure fiber,” submitted to Opt.Lett.

Shelby, R. M.

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

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. De Voe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1987).
[CrossRef]

Shirasaki, M.

Silberhorn, Ch.

Ch. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable Einstein-Podolsky-Rosen entanglement via the Kerr nonlinearity in an optical fibre,” Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Sizmann, A.

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-number squeezed solitons from an asymmetric fiber-optic Sagnac interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

S. Spälter, M. Burk, U Ströner, A. Sizmann, and G. Leuchs, “Propagation of quantum properties of sub-picosecond solitons in a fiber,” Opt. Express 2, 77 (1998).
[CrossRef]

A. Sizmann and G. Leuchs, “The optical Kerr effect and quantum optics in fibers,” in Progress in Optics XXXIX, E. Wolf, ed. (Elsevier Scinece B.V.,1999).
[CrossRef]

Sorensen, J.L.

A. Furasawa, J.L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science282, 706 (1998); S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A612302 (2000).
[CrossRef]

Spälter, S.

Stentz, A. J.

Ströner, U

Taylor, A. J.

F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth, and P. St. J. Russel, “Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber,” Opt. Lett. 26, 1558 (2001).
[CrossRef]

Vasilyev, M.

Wadsworth, W. J.

F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth, and P. St. J. Russel, “Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber,” Opt. Lett. 26, 1558 (2001).
[CrossRef]

Walls, D. F.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. De Voe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1987).
[CrossRef]

Weiß, O.

Ch. Silberhorn, P. K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable Einstein-Podolsky-Rosen entanglement via the Kerr nonlinearity in an optical fibre,” Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Werner, M. J.

M. J. Werner, “Quantum soliton generation using an interferometer,” Phys. Rev. Lett. 81, 4132 (1998).
[CrossRef]

Windeler, R.

M. Fiorentino, J.E. Sharping, P. Kumar, A. Porzio, and R. Windeler, “Soliton squeezing in microstructure fiber,” submitted to Opt.Lett.

Windeler, R. S.

Wolff, M.

S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-number squeezed solitons from an asymmetric fiber-optic Sagnac interferometer,” Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Xu, C.

J. Opt. Soc. Am. B (2)

J. Opt. Soc. Am. B, (1)

C. R. Doerr, M. Shirasaki, and F. I. Khatri, “Simulation of pulsed squeezing in optical fiber with chromatic dispersion,” J. Opt. Soc. Am. B, 11, 142 (1994).
[CrossRef]

Opt. Express (1)

Opt. Lett. (9)

D. Krylov and K. Bergman, “Amplitude-squeezed solitons from an asymmetric fiber interferometer,” Opt. Lett. 23, 1390 (1998).
[CrossRef]

D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. 24, 948 (1999)
[CrossRef]

D. Levandovsky, M. Vasilyev, and P. Kumar, “Soliton squeezing in a highly transmissive loop mirror,” Opt. Lett. 24, 89 (1999).
[CrossRef]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25 (2000).
[CrossRef]

X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggelton, S. G. Kosinsky, and R. S. Windeler, “Solitonself-phase shift in a short tapered air-silica microstructure fiber,” Opt. Lett. 26, 358 (2001).
[CrossRef]

J. E. Sharping, M. Fiorentino, and P. Kumar, “Four wave mixing in microstructure fibers,” Opt. Lett. 26, 1048 (2001).
[CrossRef]

F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth, and P. St. J. Russel, “Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber,” Opt. Lett. 26, 1558 (2001).
[CrossRef]

J. H. Shapiro and L. Boivin, “Raman-noise limit on squeezing in continuous-wave four-wave mixing,” Opt. Lett. 20, 925 (1990).
[CrossRef]

K. Bergman, H. A. Haus, E. P. Ippen, and M. Shirasaki, “Squeezing in a fiber interferometer with a gigahertz pump,” Opt. Lett. 19, 290 (1994).
[CrossRef] [PubMed]

Phys. Rev. A (3)

P. Kumar and J. Shapiro, “Squeezed-state generation via forward degenerate four-wave mixing,” Phys. Rev. A 30, 1568 (1984).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Schematic model of the nonlinear fiber Mach-Zehnder interferometer. BS, beamsplitter; SA, spectrum analyzer.

Fig. 2.
Fig. 2.

(a) Schematic model of symmetric split-step Fourier propagation in a fiber. The fiber is divided in a large number of segments of length Δz. The dispersionis calculated at the midplane of each segment (here indicated with a dashed line). (b) Inclusion of loss is obtained by inserting beamsplitters of reflectivity Γ Δz between segments. The beamsplitters couple in modes νj(k) that are assumed to be in vacuum state.

Fig. 3.
Fig. 3.

Plot of QNR versus fiber transmittivity in case of distributed losses (continuous curve) and lumped losses (dashed curve). Propagation distance in the fiber is 4.3 soliton periods, T 1 = 0.1, the strong-pulse arm is injected with a fundamental soliton, and T 2 = 0.035.

Fig. 4.
Fig. 4.

A schematic of our experimental setup. The shaded area highlights the components that form the Mach-Zehnder polarization interferometer. OPO, optical-parametric oscillator; HWP, half-wave plate; QWP, quarter-wave plate; PBS, polarizing beamsplitter; M, mirror.

Fig. 5.
Fig. 5.

Plots of QNR corrected for detection losses in the PM-fiber (a) and MF (b) as a function of the energy of the strong pulse expressed in terms of squared soliton-number N 2. The experimental data (diamonds) are compared with numerical simulations (circles). (a) PM fiber, L = 4.3 soliton periods, T 1 = 0.1, T 2 = 0.032; (b) MF, L = 5.9 soliton periods, T 1 = 0.095, T 2 = 0.037, Γ = 0.01. The numerical simulation in (b) is limited to the maximum value of N 2 by the computational resources at our disposal.

Equations (20)

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U ̂ z = i U ̂ U ̂ U ̂ + i 2 2 U ̂ t 2 ,
U ̂ = U ¯ + u ̂ ,
U ¯ z = i U ¯ 2 U ¯ + i 2 2 U ¯ t 2 ,
u ̂ z = 2 i U ¯ 2 u ̂ + i U ¯ 2 u ̂ + i 2 2 u ̂ t 2 .
u ̂ ( z , t ) j = 1 M u ̂ j ( z ) M ,
u ̂ j ( z ) m = 1 M ( μ jm ( z ) u ̂ m ( 0 ) + ν jm * ( z ) u ̂ m ( 0 ) ) ,
μ jm z = 2 i U ¯ 2 μ jm + iU ¯ 2 ν jm i 2 FFT 1 [ ω 2 FFT [ μ jm ] ] ,
ν jm z = 2 i U ¯ 2 ν jm + iU ¯ 2 μ jm i 2 FFT 1 [ ω 2 FFT [ ν jm ] ] ,
U ¯ = R 2 U ¯ + T 2 U ¯ e ,
u ̂ = R 2 u ̂ + T 2 u ̂ e .
Φ 0 j , m = 1 M ( U ¯ j U ̂ j U ¯ 2 ) ( U ̂ m U ̂ m U ¯ 2 )
R 2 m = 1 M j = 1 M U ¯ j ( μ jm e i θ j + ν jm e i θ j ) 2
+ T 2 m = 1 M j = 1 M U ¯ j ( μ jm e i θ j + ν jm e i θ j ) 2 ,
QNR = Φ 0 ( μ , μ , ν , ν ) Φ 0 ( μ jm = μ jm = δ jm , ν jm = ν jm = 0 ) .
U ¯ z = ( i U ¯ 2 Γ ) U ¯ + i 2 2 U ¯ t 2 ,
u ̂ j ( z ) m = 1 M ( μ jm ( L ) ( z ) u ̂ m ( 0 ) + ν jm ( L ) * ( z ) u ̂ m ( 0 ) ) + Γ Δ z k = 1 P ( m = 1 M ( ξ jm ( k ) v ̂ m ( k ) + η jm ( k ) * v ̂ m ( k ) ) ) ,
Φ 0 R 2 m = 1 M j = 1 M U ¯ j ( μ jm e i θ j + ν jm e i θ j ) 2
+ R 2 ( Γ Δ z ) 2 k = 1 P m = 1 M j = 1 M U ¯ j ( ξ jm e i θ j + η jm e i θ j ) 2
+ T 2 m = 1 M j = 1 M U ¯ j ( μ jm e i θ j + ν jm e i θ j ) 2
+ T 2 ( Γ Δ z ) 2 k = 1 P m = 1 M j = 1 M U ¯ j ( ξ jm e i θ j + η jm e i θ j ) 2 ,

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