Abstract

We analyze a simple model that demonstrates the feasibility of using optical squeezed states to enhance the detection sensitivity limits of frequency-modulation laser-absorption spectroscopy. The model shows that the most significant noise reduction would result by squeezing the weak frequency-modulated sidebands rather than the strong carrier and that losses in the optical detector could be made to set the limiting noise floor. By using currently available detectors, an order-of-magnitude improvement in the quantum-limited sensitivity of frequency-modulation spectroscopy may be possible.

© 1987 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, J. F. Valley, Phys. Rev. Lett. 55, 2409 (1985); R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986); L. A.Wu Wu, H. F. Wu, H. J. Kimble, J. L. Hall, in Digest of International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), paper TuKK2; M. W. Maeda, P. Kumar, J. H. Shapiro, Opt. Lett. 12, 161 (1987).
    [CrossRef] [PubMed]
  2. D. F. Walls, Nature 306, 141 (1983).
    [CrossRef]
  3. C. M. Caves, Phys. Rev. D 23, 1693 (1981); R. S. Bondurant, J. H. Shapiro, Phys. Rev. D 30, 2548 (1984); B. Yurke, S. L. McCall, J. R. Klauder, Phys. Rev. A 33, 4033 (1986).
    [CrossRef] [PubMed]
  4. G. C. Bjorklund, Opt. Lett. 5, 15 (1980).
    [CrossRef] [PubMed]
  5. G. C. Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, Appl. Phys. B 32, 145 (1983).
    [CrossRef]
  6. E. A. Whittaker, M. Gehrtz, G. C. Bjorklund, J. Opt. Soc. Am. B 2, 1320 (1985).
    [CrossRef]
  7. M. D. Levenson, W. E. Moernor, D. E. Horne, Opt. Lett. 8, 108 (1983); M. Gehrtz, G. C. Bjorklund, E. A. Whittaker, J. Opt. Soc. Am. B 2, 1510 (1985); N. C. Wong, J. L. Hall, J. Opt. Soc. Am. B 2, 1527 (1985).
    [CrossRef] [PubMed]
  8. H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980); J. H. Shapiro, H. P. Yuen, J. A. Machado Mata, IEEE Trans. Inf. Theory IT-25, 179 (1979).
    [CrossRef]
  9. H. P. Yuen, V. W. S. Chan, Opt. Lett. 8, 177 (1983).
    [CrossRef] [PubMed]
  10. B. Yurke, Phys. Rev. A 32, 300, 311 (1985).
    [CrossRef] [PubMed]
  11. C. M. Caves, B. L. Schumaker, Phys. Rev. A 31, 3068 (1985); B. L. Schumaker, C. M. Caves, Phys. Rev. A 13, 3093 (1985).
    [CrossRef] [PubMed]

1985 (4)

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, J. F. Valley, Phys. Rev. Lett. 55, 2409 (1985); R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986); L. A.Wu Wu, H. F. Wu, H. J. Kimble, J. L. Hall, in Digest of International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), paper TuKK2; M. W. Maeda, P. Kumar, J. H. Shapiro, Opt. Lett. 12, 161 (1987).
[CrossRef] [PubMed]

E. A. Whittaker, M. Gehrtz, G. C. Bjorklund, J. Opt. Soc. Am. B 2, 1320 (1985).
[CrossRef]

B. Yurke, Phys. Rev. A 32, 300, 311 (1985).
[CrossRef] [PubMed]

C. M. Caves, B. L. Schumaker, Phys. Rev. A 31, 3068 (1985); B. L. Schumaker, C. M. Caves, Phys. Rev. A 13, 3093 (1985).
[CrossRef] [PubMed]

1983 (4)

1981 (1)

C. M. Caves, Phys. Rev. D 23, 1693 (1981); R. S. Bondurant, J. H. Shapiro, Phys. Rev. D 30, 2548 (1984); B. Yurke, S. L. McCall, J. R. Klauder, Phys. Rev. A 33, 4033 (1986).
[CrossRef] [PubMed]

1980 (2)

G. C. Bjorklund, Opt. Lett. 5, 15 (1980).
[CrossRef] [PubMed]

H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980); J. H. Shapiro, H. P. Yuen, J. A. Machado Mata, IEEE Trans. Inf. Theory IT-25, 179 (1979).
[CrossRef]

Bjorklund, G. C.

Caves, C. M.

C. M. Caves, B. L. Schumaker, Phys. Rev. A 31, 3068 (1985); B. L. Schumaker, C. M. Caves, Phys. Rev. A 13, 3093 (1985).
[CrossRef] [PubMed]

C. M. Caves, Phys. Rev. D 23, 1693 (1981); R. S. Bondurant, J. H. Shapiro, Phys. Rev. D 30, 2548 (1984); B. Yurke, S. L. McCall, J. R. Klauder, Phys. Rev. A 33, 4033 (1986).
[CrossRef] [PubMed]

Chan, V. W. S.

Gehrtz, M.

Hollberg, L. W.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, J. F. Valley, Phys. Rev. Lett. 55, 2409 (1985); R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986); L. A.Wu Wu, H. F. Wu, H. J. Kimble, J. L. Hall, in Digest of International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), paper TuKK2; M. W. Maeda, P. Kumar, J. H. Shapiro, Opt. Lett. 12, 161 (1987).
[CrossRef] [PubMed]

Horne, D. E.

Lenth, W.

G. C. Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

Levenson, M. D.

Mertz, J. C.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, J. F. Valley, Phys. Rev. Lett. 55, 2409 (1985); R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986); L. A.Wu Wu, H. F. Wu, H. J. Kimble, J. L. Hall, in Digest of International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), paper TuKK2; M. W. Maeda, P. Kumar, J. H. Shapiro, Opt. Lett. 12, 161 (1987).
[CrossRef] [PubMed]

Moernor, W. E.

Ortiz, C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

Schumaker, B. L.

C. M. Caves, B. L. Schumaker, Phys. Rev. A 31, 3068 (1985); B. L. Schumaker, C. M. Caves, Phys. Rev. A 13, 3093 (1985).
[CrossRef] [PubMed]

Shapiro, J. H.

H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980); J. H. Shapiro, H. P. Yuen, J. A. Machado Mata, IEEE Trans. Inf. Theory IT-25, 179 (1979).
[CrossRef]

Slusher, R. E.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, J. F. Valley, Phys. Rev. Lett. 55, 2409 (1985); R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986); L. A.Wu Wu, H. F. Wu, H. J. Kimble, J. L. Hall, in Digest of International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), paper TuKK2; M. W. Maeda, P. Kumar, J. H. Shapiro, Opt. Lett. 12, 161 (1987).
[CrossRef] [PubMed]

Valley, J. F.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, J. F. Valley, Phys. Rev. Lett. 55, 2409 (1985); R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986); L. A.Wu Wu, H. F. Wu, H. J. Kimble, J. L. Hall, in Digest of International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), paper TuKK2; M. W. Maeda, P. Kumar, J. H. Shapiro, Opt. Lett. 12, 161 (1987).
[CrossRef] [PubMed]

Walls, D. F.

D. F. Walls, Nature 306, 141 (1983).
[CrossRef]

Whittaker, E. A.

Yuen, H. P.

H. P. Yuen, V. W. S. Chan, Opt. Lett. 8, 177 (1983).
[CrossRef] [PubMed]

H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980); J. H. Shapiro, H. P. Yuen, J. A. Machado Mata, IEEE Trans. Inf. Theory IT-25, 179 (1979).
[CrossRef]

Yurke, B.

B. Yurke, Phys. Rev. A 32, 300, 311 (1985).
[CrossRef] [PubMed]

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, J. F. Valley, Phys. Rev. Lett. 55, 2409 (1985); R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986); L. A.Wu Wu, H. F. Wu, H. J. Kimble, J. L. Hall, in Digest of International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), paper TuKK2; M. W. Maeda, P. Kumar, J. H. Shapiro, Opt. Lett. 12, 161 (1987).
[CrossRef] [PubMed]

Appl. Phys. B (1)

G. C. Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

IEEE Trans. Inf. Theory (1)

H. P. Yuen, J. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980); J. H. Shapiro, H. P. Yuen, J. A. Machado Mata, IEEE Trans. Inf. Theory IT-25, 179 (1979).
[CrossRef]

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

Nature (1)

D. F. Walls, Nature 306, 141 (1983).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (2)

B. Yurke, Phys. Rev. A 32, 300, 311 (1985).
[CrossRef] [PubMed]

C. M. Caves, B. L. Schumaker, Phys. Rev. A 31, 3068 (1985); B. L. Schumaker, C. M. Caves, Phys. Rev. A 13, 3093 (1985).
[CrossRef] [PubMed]

Phys. Rev. D (1)

C. M. Caves, Phys. Rev. D 23, 1693 (1981); R. S. Bondurant, J. H. Shapiro, Phys. Rev. D 30, 2548 (1984); B. Yurke, S. L. McCall, J. R. Klauder, Phys. Rev. A 33, 4033 (1986).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, J. F. Valley, Phys. Rev. Lett. 55, 2409 (1985); R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, D. F. Walls, Phys. Rev. Lett. 57, 691 (1986); L. A.Wu Wu, H. F. Wu, H. J. Kimble, J. L. Hall, in Digest of International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), paper TuKK2; M. W. Maeda, P. Kumar, J. H. Shapiro, Opt. Lett. 12, 161 (1987).
[CrossRef] [PubMed]

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Figures (1)

Fig. 1
Fig. 1

Diagram of the model chosen to carry out the calculation described in the paper. See the text for a detailed description.

Equations (19)

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c ( ω ) = exp [ i ϕ ( ω ) ] b ( ω ) .
d ( ω ) = η ( ω ) 1 / 2 c ( ω ) + [ 1 - η ( ω ) ] 1 / 2 c N ( ω ) .
I in ( t ) = 1 2 π 0 d ω 0 d ω d ( ω ) d ( ω ) exp [ i ( ω - ω ) t ] .
b ( ω ) = α ( ω ) + a S ( ω ) ,
α ( ω ) = ( δ ( ω - ω 0 ) + M { δ [ ω - ( ω 0 + ω s ) ] - δ [ ω - ( ω 0 - ω s ) ] } ) .
a S ( ω ) = G ( ω ) a ( ω ) + M ( ω ) a ( 2 ω 0 - ω ) ,
c N ( ω ) ψ = 0 ,
a ( ω ) ψ = 0.
lim T 1 2 T - T T d t ψ I in ψ 2 = 1 2 π α 2 ( 1 + 2 M 2 ) + 1 2 π 0 d ω M ( ω ) 2 .
I F ( t ) = 1 2 π ω s - ( Δ ω / 2 ) ω s + ( Δ ω / 2 ) [ I ( ω ) exp ( - i ω t ) + h . c . ] ,
I ( ω ) = 1 2 π 0 d ω d ( ω ) d ( ω + ω ) .
ψ I F ( t ) ψ = M α 2 2 π ( [ η ( ω 0 ) η ( ω 0 + ω s ) ] 1 / 2 × exp { i [ ϕ ( ω 0 + ω s ) - ϕ ( ω 0 ) ] } exp ( - i ω s t ) + [ η ( ω 0 - ω s ) η ( ω 0 ) ] 1 / 2 exp { i [ ϕ ( ω 0 ) - ϕ ( ω 0 - ω s ) ] } × exp ( - i ω s t ) + c . c ) .
ϕ ( ω 0 ± ω s ) = ϕ 0 + ϕ ± ,             ϕ ( ω 0 ) = ϕ 0 ,
η ( ω 0 ) = η exp ( - δ 0 ) , η ( ω 0 ± ω s ) = η exp ( - δ 0 - δ ± ) .
P s = ω s 2 π 0 ( 2 π / ω s ) d t ψ I F ( t ) ψ 2 .
P s = [ M α 2 η exp ( - δ 0 ) 2 π ] 2 ( / 4 l δ 2 + ϕ 2 ) ,
P N = ψ [ I F ( t ) - I F ( t ) ] 2 ψ = 2 α 2 η exp ( - δ 0 ( 2 π ) 2 × ω s - ( Δ ω / 2 ) ω s + ( Δ ω / 2 ) d ω { η exp ( - δ 0 ) [ ( 2 G - 1 ) + 2 G 1 / 2 ( G - 1 ) 1 / 2 cos θ ] + 2 - η exp ( - δ 0 ) } .
P N = α 2 η exp ( - δ 0 ) Δ ω ( 2 π ) 2 × [ η exp ( - δ 0 ) ( 1 4 G ) + 1 - η exp ( - δ 0 ) ] .
A = 1 / [ 1 - η exp ( - δ 0 ) ] .

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