Abstract

A pulse-excited Sagnac fiber interferometer can perform squeezing. If this squeezed radiation is injected into a second Sagnac interferometer that is functioning as a fiber gyro that is itself nonlinear, additional unfavorable squeezing occurs in the gyro. By proper phase adjustment of the injected squeezed radiation it is possible to minimize this effect as long as the Sagnac interferometer that is performing the squeezing has a sufficiently large nonlinearity.

© 1991 Optical Society of America

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References

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  1. K. Bergman and H. A. Haus, “Squeezing in fibers with optical pulses,” Opt. Lett. 16, 663 (1991).
    [CrossRef] [PubMed]
  2. R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1986).
    [CrossRef] [PubMed]
  3. R. M. Shelby, M. D. Levenson, D. F. Walls, A. Aspect, and G. J. Milburn, “Generation of squeezed states of light with a fiber-optic ring interferometer,” Phys. Rev. A 33, 4008 (1986).
    [CrossRef] [PubMed]
  4. R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244 (1985).
    [CrossRef]
  5. M. Shirasaki and H. A. Haus, “Squeezing of pulses in a nonlinear interferometer,” J. Opt. Soc. Am. B 7, 30 (1990).
    [CrossRef]
  6. M. Shirasaki and H. A. Haus, “Noise reduction in quantum nondemolition measurement with a nonlinear Mach–Zehnder interferometer using squeezed vacuum,” J. Opt. Soc. Am. B 8, 681 (1991).
    [CrossRef]
  7. H. A. Haus, K. Watanabe, and Y. Yamamoto, “Quantum-nondemolition measurement of optical solitons,” J. Opt. Soc. Am. B 6, 1138 (1989).
    [CrossRef]

1991 (2)

1990 (1)

1989 (1)

1986 (2)

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

R. M. Shelby, M. D. Levenson, D. F. Walls, A. Aspect, and G. J. Milburn, “Generation of squeezed states of light with a fiber-optic ring interferometer,” Phys. Rev. A 33, 4008 (1986).
[CrossRef] [PubMed]

1985 (1)

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Aspect, A.

R. M. Shelby, M. D. Levenson, D. F. Walls, A. Aspect, and G. J. Milburn, “Generation of squeezed states of light with a fiber-optic ring interferometer,” Phys. Rev. A 33, 4008 (1986).
[CrossRef] [PubMed]

Bayer, P. W.

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Bergman, K.

DeVoe, R. G.

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

Haus, H. A.

Levenson, M. D.

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

R. M. Shelby, M. D. Levenson, D. F. Walls, A. Aspect, and G. J. Milburn, “Generation of squeezed states of light with a fiber-optic ring interferometer,” Phys. Rev. A 33, 4008 (1986).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Milburn, G. J.

R. M. Shelby, M. D. Levenson, D. F. Walls, A. Aspect, and G. J. Milburn, “Generation of squeezed states of light with a fiber-optic ring interferometer,” Phys. Rev. A 33, 4008 (1986).
[CrossRef] [PubMed]

Perlmutter, S. H.

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

Shelby, R. M.

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

R. M. Shelby, M. D. Levenson, D. F. Walls, A. Aspect, and G. J. Milburn, “Generation of squeezed states of light with a fiber-optic ring interferometer,” Phys. Rev. A 33, 4008 (1986).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Shirasaki, M.

Walls, D. F.

R. M. Shelby, M. D. Levenson, D. F. Walls, A. Aspect, and G. J. Milburn, “Generation of squeezed states of light with a fiber-optic ring interferometer,” Phys. Rev. A 33, 4008 (1986).
[CrossRef] [PubMed]

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

Watanabe, K.

Yamamoto, Y.

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

Opt. Lett. (1)

Phys. Rev. A (1)

R. M. Shelby, M. D. Levenson, D. F. Walls, A. Aspect, and G. J. Milburn, “Generation of squeezed states of light with a fiber-optic ring interferometer,” Phys. Rev. A 33, 4008 (1986).
[CrossRef] [PubMed]

Phys. Rev. B (1)

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Phys. Rev. Lett. (1)

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

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Figures (8)

Fig. 1
Fig. 1

Fiber ring squeezer.

Fig. 2
Fig. 2

Equivalent Mach–Zehnder squeezer.

Fig. 3
Fig. 3

Squeezer followed by a gyro.

Fig. 4
Fig. 4

Squeezer followed by a nonlinear gyro, with squeezed vacuum preparation at input to gyro.

Fig. 5
Fig. 5

Schematic of the homodyne detection.

Fig. 6
Fig. 6

Squeezing ratio using cw or rectangular pulses.

Fig. 7
Fig. 7

Squeezing ratio using Gaussian pulses.

Fig. 8
Fig. 8

Squeezing ratio using solitons.

Equations (37)

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[ c ^ , c ^ ] = 1.
f ^ L = [ f ^ L 1 f ^ L 2 ] ,
f g = [ f g 1 f g 2 ] ,
c ^ = [ c ^ 1 c ^ 2 ] ,
s + n ^ f L T f g Δ ϕ 2 + f L T c ^ ,
S = s 2 = ½ f L T f g 2 ( Δ ϕ ) 2 ,
N = n ^ 2 = f L T C ( c ^ ) f L .
C ( c ^ ) ½ c ^ c ^ T + ( c ^ c ^ T ) T
N c = ¼ f L T f L .
S L f L T f L ,
S g f g T f g ,
F f L T f g 2 S L S g .
R N N c = f L T C ( c ^ ) f L ¼ S L .
S = ½ F S L S g ( Δ ϕ ) 2 ,
N = ¼ S L R ,
S / N = 2 F S g R ( Δ ϕ ) 2 .
b ^ = μ 0 a ^ + ν 0 a ^ ,
μ 0 = 1 + i Φ s ,             ν 0 = i Φ s ,
Φ s = 2 π λ n 2 l I A eff .
b ^ = M 0 a ^ ,
M 0 = [ 1 0 2 Φ s 1 ] .
C ( b ^ ) = M 0 C ( a ^ ) M 0 T = 1 4 M 0 M 0 T = 1 4 [ 1 2 Φ s 2 Φ s 1 + 4 Φ s 2 ] .
det [ C ( b ^ ) - λ I ] = 0.
λ = ¼ [ 1 + 2 Φ s 2 ± 2 Φ s ( 1 + Φ s 2 ) 1 / 2 ] .
λ = ¼ ( μ 0 ± ν 0 ) 2 ,
μ 0 = ( 1 + Φ s 2 ) 1 / 2 ,             ν 0 = Φ s .
c ^ = M g R ( ϕ ) b ^ ,
f L = [ 0 1 ] .
N = [ 0 , 1 ] C ( c ^ ) [ 0 1 ] = [ 0 , 1 ] M g R ( ϕ ) C ( b ^ ) R T ( ϕ ) M g T [ 0 1 ] .
[ 0 , 1 ] M g = [ 2 Φ g , 1 ] = ( 1 + 4 Φ g 2 ) 1 / 2 [ 0 , 1 ] R ( - θ ) ,
sin θ = 2 Φ g ( 1 + 4 Φ g 2 ) 1 / 2 ,
cos θ = 1 ( 1 + 4 Φ g 2 ) 1 / 2 .
N = ( 1 + 4 Φ g 2 ) [ 0 , 1 ] R ( - θ ) R ( ϕ ) C ( b ^ ) R T ( ϕ ) R T ( - θ ) [ 0 1 ] .
R min ϕ { [ 0 , 1 ] M g R ( ϕ ) C ( b ^ ) R T ( ϕ ) M g T [ 0 1 ] } 1 4 = ( 1 + 4 Φ g 2 ) [ 1 + 2 Φ s 2 - 2 Φ s ( 1 + Φ s 2 ) 1 / 2 ] .
R min ϕ { [ 0 , f L ( t ) ] M g R ( ϕ ) C [ b ^ ( t ) ] R T ( ϕ ) M g T [ 0 f L ( t ) ] d t } 1 4 f L ( t ) 2 d t = min ϕ ( f L ( t ) 2 [ 1 + 4 Φ g 2 ( t ) ] { 1 + 2 Φ s 2 ( t ) + 2 Φ s ( t ) [ 1 + Φ s 2 ( t ) ] 1 / 2 cos [ 2 ϕ - 2 θ ( t ) - γ ( t ) ] } d t ) f L ( t ) 2 d t = f L ( t ) 2 [ 1 + 4 Φ g 2 ( t ) ] { 1 + 2 Φ s 2 ( t ) - 2 Φ s ( t ) [ 1 + Φ s 2 ( t ) ] 1 / 2 cos [ 2 θ ( 0 ) + γ ( 0 ) - 2 θ ( t ) - γ ( t ) ] } d t f L ( t ) 2 d t .
sin [ γ ( t ) ] = 1 [ 1 + Φ s 2 ( t ) ] 1 / 2 ,
cos [ γ ( t ) ] = Φ s ( t ) [ 1 + Φ s 2 ( t ) ] 1 / 2 .

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