Abstract

The continuous-time quantum theory of self-phase modulation (SPM) in lossless, dispersionless, single-mode fiber requires a nonzero response time, to capture the classical SPM limit properly, and an accompanying Raman noise, to ensure commutator preservation. The continuous-wave, four-wave mixing limit of this theory is shown to harbor a Raman-noise limit on fiber-based squeezed-state generation.

© 1995 Optical Society of America

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References

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  1. M. D. Levenson, R. M. Shelby, M. D. Reid, D. R. Walls, A. F. Aspect, Phys. Rev. A 32, 1550 (1985).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  3. K. J. Blow, R. Loudon, S. J. D. Phoenix, J. Opt. Soc. Am. B 8, 1750 (1991).
    [Crossref]
  4. K. J. Blow, R. Loudon, S. J. D. Phoenix, Phys. Rev. A 45, 8064 (1992).
    [Crossref] [PubMed]
  5. L. G. Joneckis, J. H. Shapiro, J. Opt. Soc. Am. B 10, 1102 (1993);erratum, L. G. Joneckis, J. H. Shapiro, J. Opt. Soc. Am. B 11,150 (1994).
    [Crossref] [PubMed]
  6. L. Boivin, F. X. Kärtner, H. A. Haus, Phys. Rev. Lett. 73, 240 (1994).
    [Crossref] [PubMed]
  7. D. J. Dougherty, F. X. Kärtner, H. A. Haus, E. P. Ippen, Opt. Lett. 20, 31 (1995).
    [Crossref] [PubMed]
  8. K. Bergman, H. A. Haus, Opt. Lett. 16,663 (1991).
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  9. M. Shirasaki, H. A. Haus, J. Opt. Soc. Am. B 7, 30 (1990).
    [Crossref]
  10. A. M. Fox, B. Huttner, J. F. Ryan, presented at Optical Society of America Annual Meeting, Dallas, Tex., October 2–7, 1994, paper WM6.

1995 (1)

1994 (1)

L. Boivin, F. X. Kärtner, H. A. Haus, Phys. Rev. Lett. 73, 240 (1994).
[Crossref] [PubMed]

1993 (1)

1992 (1)

K. J. Blow, R. Loudon, S. J. D. Phoenix, Phys. Rev. A 45, 8064 (1992).
[Crossref] [PubMed]

1991 (2)

1990 (1)

1986 (1)

M. Kitagawa, Y. Yamamoto, Phys. Rev. A 34, 3974 (1986).
[Crossref] [PubMed]

1985 (1)

M. D. Levenson, R. M. Shelby, M. D. Reid, D. R. Walls, A. F. Aspect, Phys. Rev. A 32, 1550 (1985).
[Crossref] [PubMed]

Aspect, A. F.

M. D. Levenson, R. M. Shelby, M. D. Reid, D. R. Walls, A. F. Aspect, Phys. Rev. A 32, 1550 (1985).
[Crossref] [PubMed]

Bergman, K.

Blow, K. J.

K. J. Blow, R. Loudon, S. J. D. Phoenix, Phys. Rev. A 45, 8064 (1992).
[Crossref] [PubMed]

K. J. Blow, R. Loudon, S. J. D. Phoenix, J. Opt. Soc. Am. B 8, 1750 (1991).
[Crossref]

Boivin, L.

L. Boivin, F. X. Kärtner, H. A. Haus, Phys. Rev. Lett. 73, 240 (1994).
[Crossref] [PubMed]

Dougherty, D. J.

Fox, A. M.

A. M. Fox, B. Huttner, J. F. Ryan, presented at Optical Society of America Annual Meeting, Dallas, Tex., October 2–7, 1994, paper WM6.

Haus, H. A.

Huttner, B.

A. M. Fox, B. Huttner, J. F. Ryan, presented at Optical Society of America Annual Meeting, Dallas, Tex., October 2–7, 1994, paper WM6.

Ippen, E. P.

Joneckis, L. G.

Kärtner, F. X.

Kitagawa, M.

M. Kitagawa, Y. Yamamoto, Phys. Rev. A 34, 3974 (1986).
[Crossref] [PubMed]

Levenson, M. D.

M. D. Levenson, R. M. Shelby, M. D. Reid, D. R. Walls, A. F. Aspect, Phys. Rev. A 32, 1550 (1985).
[Crossref] [PubMed]

Loudon, R.

K. J. Blow, R. Loudon, S. J. D. Phoenix, Phys. Rev. A 45, 8064 (1992).
[Crossref] [PubMed]

K. J. Blow, R. Loudon, S. J. D. Phoenix, J. Opt. Soc. Am. B 8, 1750 (1991).
[Crossref]

Phoenix, S. J. D.

K. J. Blow, R. Loudon, S. J. D. Phoenix, Phys. Rev. A 45, 8064 (1992).
[Crossref] [PubMed]

K. J. Blow, R. Loudon, S. J. D. Phoenix, J. Opt. Soc. Am. B 8, 1750 (1991).
[Crossref]

Reid, M. D.

M. D. Levenson, R. M. Shelby, M. D. Reid, D. R. Walls, A. F. Aspect, Phys. Rev. A 32, 1550 (1985).
[Crossref] [PubMed]

Ryan, J. F.

A. M. Fox, B. Huttner, J. F. Ryan, presented at Optical Society of America Annual Meeting, Dallas, Tex., October 2–7, 1994, paper WM6.

Shapiro, J. H.

Shelby, R. M.

M. D. Levenson, R. M. Shelby, M. D. Reid, D. R. Walls, A. F. Aspect, Phys. Rev. A 32, 1550 (1985).
[Crossref] [PubMed]

Shirasaki, M.

Walls, D. R.

M. D. Levenson, R. M. Shelby, M. D. Reid, D. R. Walls, A. F. Aspect, Phys. Rev. A 32, 1550 (1985).
[Crossref] [PubMed]

Yamamoto, Y.

M. Kitagawa, Y. Yamamoto, Phys. Rev. A 34, 3974 (1986).
[Crossref] [PubMed]

J. Opt. Soc. Am. B (3)

Opt. Lett. (2)

Phys. Rev. A (3)

K. J. Blow, R. Loudon, S. J. D. Phoenix, Phys. Rev. A 45, 8064 (1992).
[Crossref] [PubMed]

M. D. Levenson, R. M. Shelby, M. D. Reid, D. R. Walls, A. F. Aspect, Phys. Rev. A 32, 1550 (1985).
[Crossref] [PubMed]

M. Kitagawa, Y. Yamamoto, Phys. Rev. A 34, 3974 (1986).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

L. Boivin, F. X. Kärtner, H. A. Haus, Phys. Rev. Lett. 73, 240 (1994).
[Crossref] [PubMed]

Other (1)

A. M. Fox, B. Huttner, J. F. Ryan, presented at Optical Society of America Annual Meeting, Dallas, Tex., October 2–7, 1994, paper WM6.

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Figures (1)

Fig. 1
Fig. 1

Zero-frequency homodyne noise level of the minimum-noise quadrature, Smin(0), versus classical nonlinear phase shift ΦNL: 0 dB is the coherent-state (shot-noise) level; η = 0 is the ideal, instantaneous-interaction cw FWM result; η = 0.12 is the Raman-noise limit on squeezing, from Eq. (13), implied by the low-frequency Raman gain (Ref. 7).

Equations (17)

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E ^ OUT ( t ) = exp [ i Θ ^ ( t ) ] × exp [ i L d τ h ( t τ ) E ^ IN ( τ ) E ^ IN ( τ ) ] E ^ IN ( t ) ,
H ( ω ) d t h ( t ) exp ( i ω t ) ,
[ E ^ OUT ( t ) , E ^ OUT ( t ) ] = [ E ^ IN ( t ) , E ^ IN ( t ) ] = δ ( t t ) ,
[ Θ ^ ( t ) , Θ ^ ( t ) ] = ( i L / π ) d ω H i ( ω ) sin [ ω ( t t ) ] ,
Θ ^ ( t ) Θ ^ ( t ) + Θ ^ ( t ) Θ ^ ( t ) = ( L / π ) d ω H i ( ω ) × coth ( ω / 2 k T ) cos [ ω ( t t ) ] .
E ^ OUT = exp [ Θ ^ 2 / 2 ] exp { d τ [ exp [ i L h ( t τ ) ] 1 ] × | E IN | 2 } E IN ,
Θ ^ 2 = ( L / 2 π ) d ω H i ( ω ) coth ( ω / 2 k T ) .
E OUT E ^ OUT = exp ( i κ L | E IN | 2 ) E IN ,
Δ E ^ OUT ( t ) = exp ( i κ L | E IN | 2 ) [ i Θ ^ ( t ) E IN + Δ E ^ IN ( t ) + i L d τ h ( t τ ) | E IN | 2 Δ E ^ IN ( τ ) + i L d τ h ( t τ ) E IN 2 Δ E ^ IN ( τ ) ]
S min ( 0 ) = min θ [ S θ ( 0 ) ] = 1 + 2 S OUT ( n ) ( 0 ) 2 | S OUT ( p ) ( 0 ) | .
S OUT ( n ) ( 0 ) d τ Δ E ^ OUT ( t + τ ) Δ E ^ OUT ( t ) ,
S OUT ( p ) ( 0 ) d τ Δ E ^ OUT ( t + τ ) Δ E ^ OUT ( t )
S min ( 0 ) = 1 + 2 Φ NL [ Φ NL + 2 k T H i ( 0 ) / κ ] 2 Φ NL { 1 + [ Φ NL + 2 k T H i ( 0 ) / κ ] 2 } 1 / 2 .
z E ( z , t ) = i d τ h ( t τ ) | E ( z , τ ) | 2 E ( z , t ) .
d d z E P ( z ) = i κ | E P ( z ) | 2 E P ( z ) + i κ | E S ( z ) | 2 E P ( z ) H i ( Δ ω ) | E S ( z ) | 2 E P ( z ) ,
d d z E S ( z ) = i κ | E S ( z ) | 2 E S ( z ) + i κ | E P ( z ) | 2 E S ( z ) + H i ( Δ ω ) | E P ( z ) | 2 E S ( z ) ,
d d z I S ( z ) = 2 H i ( Δ ω ) A I P ( z ) ω P I S ( z ) ,

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