Abstract

We have studied the interferometric sensitivity for gravitational wave detection explicitly including the photodetector efficiency. We show that the sensitivity is very strongly affected by non-ideal pho-todetector efficiency when we inject a squeezed signal, as compared to the ordinary vacuum case. Quantum limits and resonance are also discussed for short time detections.

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References

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  1. C. M. Caves, Phys. Rev. Lett. 45, 75 (1980).
    [CrossRef]
  2. W. A. Edelstein, J. Hough, J. R. Pugh and W. Martin, J. Phys. E 11, 710 (1978).
    [CrossRef]
  3. C. M. Caves, Phys. Rev. D 23, 1693 (1981).
    [CrossRef]
  4. R. S. Bondurant and J. H. Shapiro, Phys. Rev. D 30, 2548 (1984).
    [CrossRef]
  5. A. F. Pace, M. J. Collett, D. F. Walls, Phys. Rev. A 47, 3173 (1993).
    [CrossRef] [PubMed]
  6. D. F Walls , Quantum Optics (Springer, Berlin, 1994).
  7. M. J. Collett, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984).
    [CrossRef]
  8. P. L. Kelley, W. H. Kleiner, Phys. Rev. 136, 316 (1964).
    [CrossRef]
  9. Kip S. Thorne, Rev. Mod. Phys. 52 285 (1980).
    [CrossRef]
  10. M. Ozawa in Squeezed and non classical States, edited by P. Tombesi and E. R. Pike (Plenum Press, N. Y., 1989).

Other (10)

C. M. Caves, Phys. Rev. Lett. 45, 75 (1980).
[CrossRef]

W. A. Edelstein, J. Hough, J. R. Pugh and W. Martin, J. Phys. E 11, 710 (1978).
[CrossRef]

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

R. S. Bondurant and J. H. Shapiro, Phys. Rev. D 30, 2548 (1984).
[CrossRef]

A. F. Pace, M. J. Collett, D. F. Walls, Phys. Rev. A 47, 3173 (1993).
[CrossRef] [PubMed]

D. F Walls , Quantum Optics (Springer, Berlin, 1994).

M. J. Collett, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984).
[CrossRef]

P. L. Kelley, W. H. Kleiner, Phys. Rev. 136, 316 (1964).
[CrossRef]

Kip S. Thorne, Rev. Mod. Phys. 52 285 (1980).
[CrossRef]

M. Ozawa in Squeezed and non classical States, edited by P. Tombesi and E. R. Pike (Plenum Press, N. Y., 1989).

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Figures (4)

Figure 1.
Figure 1.

Schematic representation of the optical detector for gravitational radiation.

Figure 2.
Figure 2.

Minimum detectable gravitational amplitude versus input power for the non-resonant case (curve a), and resonant case (curve b). Notice the comparison with the corresponding standard quantum limits (dashed line) r = 0, Ω = 20πseg-1 (non resonant case) ωg = 2000πseg-1.

Figure 3.
Figure 3.

Minimum detectable gravitational amplitude versus input power for r = 0, η = 1 (curve a), r = 0 , η = 0.9 (curve b) r = 4 , η = 1 (curve c) and r = 4,η = 0.9 (curve d). In all cases we took ϕ = 0.

Figure 4.
Figure 4.

Minimum detectable amplitude versus input power and mechanical frequency, near resonance. The upper surface corresponds to η = 0.9 and the lower one to η = 1. In both cases: r = 4, ϕ = 0.

Equations (48)

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H = ħ Δ a a + ħ Ω b b + ħ κ a a ( b + b )
+ ħ k S ( t ) ( b + b ) ,
κ = ω 0 L ħ 2 m Ω k = L ω g m 2 ħ Ω h g ,
a out + a in = γ a a ,
a = x + iy = a 0 + δ a + δ a ,
b = q + ip = b 0 + δ b + δ b ,
δ x out ( ω ) = 0
δ y out ( ω ) = γ a k μ Ω S ( ω ) ʌ a ( ʌ b 2 + Ω 2 ) .
ʌ a , b = γ a , b 2 +
δ X out ( ω ) = ( γ a ʌ a + 1 ) δ X in ( ω )
δ Y out = γ a μ 2 Ω ʌ a 2 ( ʌ b 2 + Ω 2 ) δ X in ( ω ) ( γ a ʌ a + 1 ) δ Y in ( ω )
ʌ a ʌ b μ γ a γ b ʌ a 2 ( ʌ b 2 + Ω 2 ) δ q in ( ω ) ʌ a Ω μ γ a γ b ʌ a 2 ( ʌ b 2 + Ω 2 ) δ P in ( ω ) .
Δ x ħ Δ t m .
( Δ x ) ext = F 0 2 m Δ t 2 ,
( Δ x ) ext = F 0 m γ Δ t ,
h g , min N R = 2 ω g 2 Δ t 2 1 L ħ Δ t m ,
h g , min R = γ ω g 2 Δ t 1 L ħ Δ t m ,
a in 1 = 1 2 ( c 1 + i c 2 ) , a in 2 = 1 2 ( c 1 i c 2 ) ,
d 1 = 1 2 ( a out 2 i a out 1 ) , d 2 = 1 2 ( a out 2 + i a out 1 ) .
< c 1 > = 2 α 0 and < c 2 > = 0 .
D ( t ) = d 1 ( t ) d 1 ( t ) d 2 ( t ) d 2 ( t )
S ( t ) = d 1 ( t ) d 1 ( t ) d 2 ( t ) d 2 ( t ) .
δD ( t ) = 2 α 0 ( δ y out 1 ( t ) δ y out 2 ( t ) ) = 4 α 0 δ y out 1 ( t ) ,
S ( t ) = S 0 = 2 ( α 0 ) 2 .
P ( n 1 , n 2 , Δ t ) = < : ( Ω 1 ) n 1 n 1 ! e Ω 1 ( Ω 2 ) n 2 n 2 ! e Ω 2 : >
Ω 1,2 = η t Δ t t d 1,2 ( t′ ) d 1,2 ( t′ ) dt ,
I ( t ) = G e Δ t ( N 1 N 2 ) ,
i ( t ) = G e Δ t : Ω 1 ( t ) Ω 2 ( t ) : .
i ( t ) = η G e : D ( t ) : = η G e δ D ( t ) .
Δ 2 i ( t ) = ( G e Δ t ) 2 { η 2 < : ( δ D ( t ) ) 2 : > Δ t 2 + η < : S ( t ) : > Δ t }
S pc tot ( ω ) = ( G e ) 2 π α 0 2 ( η 2 S rp ( ω ) + η ) ,
S rp ( ω ) = ( 16 κ 2 α 0 2 Ω ) 2 cosh ( 2 r ) + cos ( ϕ ) sinh ( 2 r ) ( γ a 4 + ω 2 ) 2 ( ( γ b 2 4 + Ω 2 ω 2 ) 2 + γ b 2 ω 2 )
+ 32 κ 2 α 0 2 Ω ( γ b 4 + Ω 2 ω 2 ) sin ( ϕ ) sinh ( 2 r ) ( γ a 4 + ω 2 ) 2 ( ( γ b 2 4 + Ω 2 ω 2 ) 2 + γ b 2 ω 2 )
+ 16 κ 2 α 0 2 γ b ( γ b 4 + Ω 2 ω 2 ) ( γ a 4 + ω 2 ) 2 ( ( γ b 2 4 + Ω 2 ω 2 ) 2 + γ b 2 ω 2 )
+ cosh ( 2 r ) cos ( ϕ ) sinh ( 2 r ) 1
i ( t ) = η G e α 0 2 16 κ k Ω ( γ a 2 4 + ω g 2 ) 1 / 2 ( ( γ b 2 4 + Ω 2 ω g 2 ) 2 + γ b 2 ω g 2 ) 1 / 2 .
Δ 2 i ( t ) = Δ ω d ω S pc tot ( ω ) .
Δ 2 i ( t ) = ( Ge ) 2 π α 0 2 ( η 2 ( α 0 4 ( cosh ( 2 r ) + cos ( θ ) sinh ( 2 r ) ) I 0
+ α 0 2 ( I 1 + sin ( θ ) sinh ( 2 r ) I 2 ) + ( cosh ( 2 r ) cos ( θ ) sinh ( 2 r ) ) 2 π Δ t )
+ ( η η 2 ) 2 π Δ t )
I 0 = ( 16 κ 2 Ω ) 2 1 ( γ a 2 4 + ω 2 ) 2 ( ( γ b 2 4 + Ω 2 ω 2 ) 2 + γ b 2 ω 2 )
I 1 = 16 κ 2 γ b γ b 2 4 + Ω 2 + ω 2 ( γ a 2 4 + ω 2 ) 2 ( ( γ b 2 4 + Ω 2 ω 2 ) 2 + γ b 2 ω 2 )
I 2 = 32 κ 2 Ω γ b 2 4 + Ω 2 + ω 2 ( γ a 2 4 + ω 2 ) 2 ( ( γ b 2 4 + Ω 2 ω 2 ) 2 + γ b 2 ω 2 ) .
SNR 2 = i 2 ( t ) Δ 2 i ( t ) = AP BP 2 + CP + D’
A = ( 16 ω 0 ω g 2 h g ) 2 Δ ħ ω 0 ( γ a 2 4 + ω g 2 ) ( ( γ b 2 4 + Ω 2 ω g 2 ) 2 + γ b 2 ω g 2 )
B = I 0 2 π ( ħ ω 0 ) 2 ( cosh ( 2 r ) + cos ( θ ) sinh ( 2 r ) ) η Δ t
C = 1 2 π ħ ω 0 ( I 1 + I 2 sin ( θ ) sinh ( 2 r ) ) η Δ t
D = ( cosh ( 2 r ) cos ( θ ) sinh ( 2 r ) 1 ) η + 1

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