Abstract

Using analytic theory and numerical experiments, we show that a quantum nondemolition measurement of the photon number of optical solitons in a single-mode optical fiber can be made. We describe the soliton-collision interferometer with which we propose to make this measurement and discuss simulations of the performance of this interferometer.

© 1990 Optical Society of America

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References

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  1. H. A. Haus, K. Watanabe, Y. Yamamoto, J. Opt. Soc. Am. B 6, 1138 (1989).
    [CrossRef]
  2. N. Imoto, H. A. Haus, Y. Yamamoto, Phys. Rev. Lett. 32, 2287 (1985).
  3. N. Imoto, S. Watkins, Y. Sasaki, Opt. Commun. 61, 159 (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).
    [CrossRef]
  4. R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
    [CrossRef]
  5. Two colliding solitons are considered an N = 2 soliton in the Zakharov–Shabat inverse-scattering method. The usual hyperbolic-secant solitons are N = 1 solitons.
  6. M. J. LaGasse, D. Liu-Wong, J. G. Fujimoto, H. A. Haus, Opt. Lett. 14, 311 (1989).
    [CrossRef] [PubMed]
  7. S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, P. W. Smith, Opt. Lett. 13, 904 (1988).
    [CrossRef] [PubMed]
  8. J. A. Fleck, J. R. Morris, E. S. Bliss, IEEE J. Quantum Electron. QE-14, 353 (1978);D. Yevick, B. Hermansson, Opt. Commun. 47, 101 (1983);W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Heritage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
    [CrossRef]
  9. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

1989 (2)

1988 (1)

1987 (1)

N. Imoto, S. Watkins, Y. Sasaki, Opt. Commun. 61, 159 (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).
[CrossRef]

1985 (2)

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[CrossRef]

N. Imoto, H. A. Haus, Y. Yamamoto, Phys. Rev. Lett. 32, 2287 (1985).

1978 (1)

J. A. Fleck, J. R. Morris, E. S. Bliss, IEEE J. Quantum Electron. QE-14, 353 (1978);D. Yevick, B. Hermansson, Opt. Commun. 47, 101 (1983);W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Heritage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
[CrossRef]

1972 (1)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Bayer, P. W.

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Bliss, E. S.

J. A. Fleck, J. R. Morris, E. S. Bliss, IEEE J. Quantum Electron. QE-14, 353 (1978);D. Yevick, B. Hermansson, Opt. Commun. 47, 101 (1983);W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Heritage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
[CrossRef]

Fleck, J. A.

J. A. Fleck, J. R. Morris, E. S. Bliss, IEEE J. Quantum Electron. QE-14, 353 (1978);D. Yevick, B. Hermansson, Opt. Commun. 47, 101 (1983);W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Heritage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
[CrossRef]

Friberg, S. R.

Fujimoto, J. G.

Haus, H. A.

Imoto, N.

N. Imoto, S. Watkins, Y. Sasaki, Opt. Commun. 61, 159 (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).
[CrossRef]

N. Imoto, H. A. Haus, Y. Yamamoto, Phys. Rev. Lett. 32, 2287 (1985).

LaGasse, M. J.

Levenson, M. D.

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Liu-Wong, D.

Morris, J. R.

J. A. Fleck, J. R. Morris, E. S. Bliss, IEEE J. Quantum Electron. QE-14, 353 (1978);D. Yevick, B. Hermansson, Opt. Commun. 47, 101 (1983);W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Heritage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
[CrossRef]

Sasaki, Y.

N. Imoto, S. Watkins, Y. Sasaki, Opt. Commun. 61, 159 (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).
[CrossRef]

Sfez, B. G.

Shabat, A. B.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Shelby, R. M.

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Silberberg, Y.

Smith, P. W.

Watanabe, K.

Watkins, S.

N. Imoto, S. Watkins, Y. Sasaki, Opt. Commun. 61, 159 (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).
[CrossRef]

Weiner, A. M.

Yamamoto, Y.

H. A. Haus, K. Watanabe, Y. Yamamoto, J. Opt. Soc. Am. B 6, 1138 (1989).
[CrossRef]

N. Imoto, H. A. Haus, Y. Yamamoto, Phys. Rev. Lett. 32, 2287 (1985).

Zakharov, V. E.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

IEEE J. Quantum Electron. (1)

J. A. Fleck, J. R. Morris, E. S. Bliss, IEEE J. Quantum Electron. QE-14, 353 (1978);D. Yevick, B. Hermansson, Opt. Commun. 47, 101 (1983);W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Heritage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
[CrossRef]

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

Opt. Commun. (1)

N. Imoto, S. Watkins, Y. Sasaki, Opt. Commun. 61, 159 (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).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (1)

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Phys. Rev. Lett. (1)

N. Imoto, H. A. Haus, Y. Yamamoto, Phys. Rev. Lett. 32, 2287 (1985).

Sov. Phys. JETP (1)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Other (1)

Two colliding solitons are considered an N = 2 soliton in the Zakharov–Shabat inverse-scattering method. The usual hyperbolic-secant solitons are N = 1 solitons.

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Figures (4)

Fig. 1
Fig. 1

Soliton-collision interferometer. A signal soliton collides with a probe soliton, causing a phase shift. The probe and reference solitons interfere at the optical homodyne detector, giving the collision-induced probe phase shift and thus the photon number (energy) of the signal soliton. GVD, group-velocity dispersion; PD's, photodetectors.

Fig. 2
Fig. 2

Simulated soliton collisions. (a) The solitons are separated by νoff = 5.6Δν0m = 2.0) and produce small timing shifts, (b) νoff = 0.6Δν0m = 0.2), the spectra overlap, and the timing shift is large. Propagation lengths are (a) 1.5z0 and (b) 10z0; A = 1.0 for all solitons.

Fig. 3
Fig. 3

(a) Collision-induced phase shifts and (b) collision-induced timing shifts for the probe soliton as a function of signal amplitude As. The numerical results are given by the symbols, and the theoretical results are given by the solid curves.

Fig. 4
Fig. 4

Sensitivity to initial conditions. Two A = 1.0 solitons (νoff = 1.4Δν0, Δm= 0.5) are launched: (a) when separated by 1.7τ0, they do not fuse; (b) when separated by 1.1τ0, they fuse. The propagation length is 4.0z0

Equations (2)

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i u ( ζ , s ) ζ = u ( ζ , s ) 2 2 s 2 + | u ( ζ , s ) | 2 u ( ζ , s ) ,
u ( 0 , s ) = A p sech ( A p s ) + A s sech [ A s ( s s off ) ] × exp ( iπs Δ m ) .

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