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.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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, and D. F. Walls, Phys. Rev. A 47, 3173 (1993).
    [Crossref] [PubMed]
  6. Walls D.F, Quantum Optics (Springer, Berlin, 1994).
  7. M. J. Collett and C. W. Gardiner, Phys. Rev. A 30, 1386 (1984).
    [Crossref]
  8. P. L. Kelley and W. H. Kleiner, Phys. Rev. 136, 316 (1964).
    [Crossref]
  9. Kip S Thorne, Rev. Mod. Phys. 52285 (1980).
    [Crossref]
  10. M. Ozawa in Squeezed and non classical States, edited by P. Tombesi and E. R. Pike (Plenum Press, N. Y., 1989)

1993 (1)

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

1984 (2)

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

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

1981 (1)

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

1980 (2)

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

Kip S Thorne, Rev. Mod. Phys. 52285 (1980).
[Crossref]

1978 (1)

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

1964 (1)

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

Bondurant, R. S.

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

Caves, C. M.

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

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

Collett, M. J.

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

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

D.F, Walls

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

Edelstein, W. A.

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

Gardiner, C. W.

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

Hough, J.

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

Kelley, P. L.

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

Kleiner, W. H.

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

Martin, W.

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

Ozawa, M.

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

Pace, A. F.

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

Pugh, J. R.

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

Shapiro, J. H.

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

Thorne, Kip S

Kip S Thorne, Rev. Mod. Phys. 52285 (1980).
[Crossref]

Walls, D. F.

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

J. Phys. E (1)

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

Phys. Rev. (1)

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

Phys. Rev. A (2)

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

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

Phys. Rev. D (2)

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

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

Phys. Rev. Lett. (1)

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

Rev. Mod. Phys. (1)

Kip S Thorne, Rev. Mod. Phys. 52285 (1980).
[Crossref]

Other (2)

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

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

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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)

Equations on this page are rendered with MathJax. Learn more.

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

Metrics