Abstract

The signal-to-noise ratio for heterodyne laser radar with a coherent target-return beam and a squeezed local-oscillator beam is lower than that obtained using a coherent local oscillator, regardless of the method employed to combine the beams at the detector.

© 2007 Optical Society of America

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References

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  1. D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994).
  2. C. M. Caves, Phys. Rev. D 23, 1693 (1981).
    [CrossRef]
  3. R. H. Kingston, Optical Sources, Detectors and Systems: Fundamentals and Applications (Academic, 1995).
  4. Y.-Q. Li, D. Guzun, and M. Xiao, Phys. Rev. Lett. 82, 5225 (1999).
    [CrossRef]
  5. T. C. Ralph, Phys. Rev. Lett. 85, 677 (2000).
    [CrossRef] [PubMed]
  6. G. Hernandez, Fabry-Perot Interferometers (Cambridge, 1986).
  7. H. P. Yuen and V. W. S. Chan, Opt. Lett. 8, 177 (1983).
    [CrossRef] [PubMed]
  8. V. Annovazzi-Lodi, S. Donati, and S. Merlo, Opt. Quantum Electron. 24, 258 (1992).
    [CrossRef]
  9. Y.-Q. Li, P. Lynam, M. Xiao, and P. J. Edwards, Phys. Rev. Lett. 78, 3105 (1997).
    [CrossRef]
  10. C. W. Helstrom, Quantum Detection and Estimation Theory (Academic, 1976).
  11. K. Gottfreid and T.-M. Yan, Quantum Mechanics: Fundamentals, 2nd ed. (Springer, 2003).
  12. R. J. Glauber, in Quantum Optics and Electronics, C.DeWitt, A.Blandin, and C.Cohen-Tannoudji, eds. (Gordon and Breach, 1965).
  13. C. G. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge, 2005).
  14. H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer, 2000).

2000 (1)

T. C. Ralph, Phys. Rev. Lett. 85, 677 (2000).
[CrossRef] [PubMed]

1999 (1)

Y.-Q. Li, D. Guzun, and M. Xiao, Phys. Rev. Lett. 82, 5225 (1999).
[CrossRef]

1997 (1)

Y.-Q. Li, P. Lynam, M. Xiao, and P. J. Edwards, Phys. Rev. Lett. 78, 3105 (1997).
[CrossRef]

1992 (1)

V. Annovazzi-Lodi, S. Donati, and S. Merlo, Opt. Quantum Electron. 24, 258 (1992).
[CrossRef]

1983 (1)

1981 (1)

C. M. Caves, Phys. Rev. D 23, 1693 (1981).
[CrossRef]

Annovazzi-Lodi, V.

V. Annovazzi-Lodi, S. Donati, and S. Merlo, Opt. Quantum Electron. 24, 258 (1992).
[CrossRef]

Caves, C. M.

C. M. Caves, Phys. Rev. D 23, 1693 (1981).
[CrossRef]

Chan, V. W. S.

Donati, S.

V. Annovazzi-Lodi, S. Donati, and S. Merlo, Opt. Quantum Electron. 24, 258 (1992).
[CrossRef]

Edwards, P. J.

Y.-Q. Li, P. Lynam, M. Xiao, and P. J. Edwards, Phys. Rev. Lett. 78, 3105 (1997).
[CrossRef]

Gerry, C. G.

C. G. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge, 2005).

Glauber, R. J.

R. J. Glauber, in Quantum Optics and Electronics, C.DeWitt, A.Blandin, and C.Cohen-Tannoudji, eds. (Gordon and Breach, 1965).

Gottfreid, K.

K. Gottfreid and T.-M. Yan, Quantum Mechanics: Fundamentals, 2nd ed. (Springer, 2003).

Guzun, D.

Y.-Q. Li, D. Guzun, and M. Xiao, Phys. Rev. Lett. 82, 5225 (1999).
[CrossRef]

Haus, H. A.

H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer, 2000).

Helstrom, C. W.

C. W. Helstrom, Quantum Detection and Estimation Theory (Academic, 1976).

Hernandez, G.

G. Hernandez, Fabry-Perot Interferometers (Cambridge, 1986).

Kingston, R. H.

R. H. Kingston, Optical Sources, Detectors and Systems: Fundamentals and Applications (Academic, 1995).

Knight, P. L.

C. G. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge, 2005).

Li, Y.-Q.

Y.-Q. Li, D. Guzun, and M. Xiao, Phys. Rev. Lett. 82, 5225 (1999).
[CrossRef]

Y.-Q. Li, P. Lynam, M. Xiao, and P. J. Edwards, Phys. Rev. Lett. 78, 3105 (1997).
[CrossRef]

Lynam, P.

Y.-Q. Li, P. Lynam, M. Xiao, and P. J. Edwards, Phys. Rev. Lett. 78, 3105 (1997).
[CrossRef]

Merlo, S.

V. Annovazzi-Lodi, S. Donati, and S. Merlo, Opt. Quantum Electron. 24, 258 (1992).
[CrossRef]

Milburn, G. J.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994).

Ralph, T. C.

T. C. Ralph, Phys. Rev. Lett. 85, 677 (2000).
[CrossRef] [PubMed]

Walls, D. F.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994).

Xiao, M.

Y.-Q. Li, D. Guzun, and M. Xiao, Phys. Rev. Lett. 82, 5225 (1999).
[CrossRef]

Y.-Q. Li, P. Lynam, M. Xiao, and P. J. Edwards, Phys. Rev. Lett. 78, 3105 (1997).
[CrossRef]

Yan, T.-M.

K. Gottfreid and T.-M. Yan, Quantum Mechanics: Fundamentals, 2nd ed. (Springer, 2003).

Yuen, H. P.

Opt. Lett. (1)

Opt. Quantum Electron. (1)

V. Annovazzi-Lodi, S. Donati, and S. Merlo, Opt. Quantum Electron. 24, 258 (1992).
[CrossRef]

Phys. Rev. D (1)

C. M. Caves, Phys. Rev. D 23, 1693 (1981).
[CrossRef]

Phys. Rev. Lett. (3)

Y.-Q. Li, D. Guzun, and M. Xiao, Phys. Rev. Lett. 82, 5225 (1999).
[CrossRef]

T. C. Ralph, Phys. Rev. Lett. 85, 677 (2000).
[CrossRef] [PubMed]

Y.-Q. Li, P. Lynam, M. Xiao, and P. J. Edwards, Phys. Rev. Lett. 78, 3105 (1997).
[CrossRef]

Other (8)

C. W. Helstrom, Quantum Detection and Estimation Theory (Academic, 1976).

K. Gottfreid and T.-M. Yan, Quantum Mechanics: Fundamentals, 2nd ed. (Springer, 2003).

R. J. Glauber, in Quantum Optics and Electronics, C.DeWitt, A.Blandin, and C.Cohen-Tannoudji, eds. (Gordon and Breach, 1965).

C. G. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge, 2005).

H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer, 2000).

G. Hernandez, Fabry-Perot Interferometers (Cambridge, 1986).

R. H. Kingston, Optical Sources, Detectors and Systems: Fundamentals and Applications (Academic, 1995).

D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994).

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Equations (34)

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SNR = ( ψ 1 S ̂ ψ 1 ψ 0 S ̂ ψ 0 ) 2 Var 0 S ,
Var 0 S = ψ 0 S ̂ 2 ψ 0 ψ 0 S ̂ ψ 0 2 .
S ̂ = τ 1 0 τ d t cos ( ω H t + θ H ) I ̂ ( t ) ,
ω H = ω T ω LO .
I ̂ ( t ) = κ E ̂ ( ) ( t ) E ̂ ( + ) ( t ) ,
E ̂ ( + ) ( t ) = k i ( ω k 2 ϵ 0 V ) 1 2 a ̂ k exp ( i ω k t ) .
[ a ̂ k , a ̂ l ] = [ a ̂ k , a ̂ l ] = 0 , [ a ̂ k , a ̂ l ] = δ k l .
S ̂ = κ 4 ϵ 0 V l , k st ω l ω k = ω H ( ω l ω k ) 1 2 a ̂ l a ̂ k exp ( i ϵ ( ω l ω k ) θ H ) ,
ϵ ( x ) = sign of x .
ψ 0 = α , ξ k LO k k LO 0 k .
ψ 1 = β k T α , ξ k LO k k T , k LO 0 k .
a ̂ k 0 k = 0 k a ̂ k = 0 ,
β a ̂ k T β k T k T = β , β a ̂ k T β k T k T = β * ,
α , ξ a ̂ k LO α , ξ k LO k LO = α ,
α , ξ a ̂ k LO α , ξ k LO k LO = α * ,
ψ 0 S ̂ ψ 0 = 0 ,
ψ 1 S ̂ ψ 1 = κ 2 ϵ 0 V ( ω T ω LO ) 1 2 a β cos ( θ T θ LO + θ H ) ,
θ T = arg β , θ LO = arg α .
ψ 0 S ̂ 2 ψ 0 = ( κ 4 ϵ 0 V ) 2 k s.t. ω LO ω k = ω H l s.t. ω l ω LO = ω H ω LO ( ω k ω l ) 1 2 ψ 0 a ̂ k LO a ̂ k a ̂ l a ̂ k LO ψ 0 exp ( i [ ϵ ( ω LO ω k ) + ϵ ( ω l ω LO ) ] θ H ) .
ψ 0 S ̂ 2 ψ 0 = ( κ 4 ϵ 0 V ) 2 k s.t. ω LO ω k = ω H ω LO ω k n ¯ LO ,
n ¯ LO = α , ξ a ̂ k LO a ̂ k LO α , ξ k LO k LO .
Var 0 S = ( κ 4 ϵ 0 V ) 2 k s.t. ω LO ω k = ω H ω LO ω k n ¯ LO .
ω T ω LO ω .
ψ 1 S ̂ ψ 1 = κ ω 2 ϵ 0 V α β cos ( θ T θ LO + θ H ) ,
Var 0 S = 2 ( κ ω 4 ϵ 0 V ) 2 n ¯ LO .
SNR = 2 α 2 β 2 cos 2 ( θ T θ LO + θ H ) n ¯ LO = 2 ( 1 sinh 2 ( r ) n ¯ LO ) n ¯ T cos 2 ( θ T θ LO + θ H ) ,
β 2 = n ¯ k T = β a ̂ k T a ̂ k T β k T k T ,
n ¯ LO = α 2 + sinh 2 ( r ) .
S ̂ = τ 1 0 τ d t I ̂ ( t ) = κ ω k 2 ϵ 0 V a ̂ k a ̂ k
Var 0 S = ψ 0 S ̂ 2 ψ 0 ψ 0 S ̂ ψ 0 2 ,
Var 0 S = ( κ ω LO 2 ϵ V ) 2 var n LO ,
var n LO = [ α , ξ ( a ̂ k LO a ̂ k LO ) 2 α , ξ k LO k LO ( α , ξ a ̂ k LO a ̂ k LO α , ξ k LO k LO ) 2 ] .
S ̂ = κ 2 ϵ 0 V l , k ( ω l ω k ) 1 2 a ̂ l a ̂ k exp ( i ϵ ( ω l ω k ) θ H )
× 1 2 i τ { exp ( i θ H ) ω l ω k + ω H [ exp ( i ( ω l ω k + ω H ) τ ) 1 ] + exp ( i θ H ) ω l ω k ω H [ exp ( i ( ω l ω k ω H ) τ ) 1 ] } .

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