An optical readout configuration
for advanced massive GW
detectors
Francesco Marin, Livia Conti, Maurizio De Rosa
Dipartimento di Fisica, Università di Firenze,LENS and INFN, Sezione
di Firenze
Via Sansone, 1, I-50019 Sesto Fiorentino (FI), Italy
e-mail: [email protected]
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Optical readout of
displacement
• Standard detection technique in interferometers
• Proposed in the 80’s for bar detectors1
• Recently applied to a room temperature detector2
[1] J.-P. Richard, J. Appl. Phys. 64, 2202 (1988)
[2] L. Conti et al., J. Appl. Phys. 93, 3589 (2003)
Room temperature Weber bar
with optical readout
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Room temperature Weber bar
with optical readout
transducer
cavity
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-18
10
optical fiber
beam-splitter
Phase
mod.
Power
stab.
Frequency
locking
FM sidebands
technique
reference
cavity
FM sidebands
technique
pzt actuator
-19
10
Data
acquisition
Low frequency
locking
temperature
control
√Shh (1/√Hz)
Nd:YAG
laser
-20
10
820
840
860
880
900
Frequency (Hz)
920
940
Room temperature Weber bar
with optical readout
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Work in progress:
•
Cleaner vacuum system
•
New mechanical suspension
•
Higher Finesse transducer cavity
•
Cooling (at least 77K)
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Brownian noise and radiation pressure (back-action) are
the usual sensitivity limiting sources in a few-modes
model, together with the displacement detection sensitivity
(displacement noise)
In a real, massive system: several modes, with their
thermal noise and back-action.
Small interrogation region means large
fluctuations
One must average over high order modes:
needs large interrogation region
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We must consider ‘local’ effects:
• Thermal noise
- photothermal
- thermodynamic
- Brownian
Depends on material parameters
At cryo-T:
- best material is sapphire
- predominant Brownian
• Radiation pressure
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Brownian noise:
SBr(!) =
4 kB T
!
Im (!)]
Radiation pressure effect:
0 12
2C
2 B
@
Srp(!) = j(!)j A
c
Scav
intracavity radiation noise spectral power:
Scav
=2
0 12
F
@ C
A Pin
h B
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Gaussian spot on a half-infinite mirror:
Im (!)] ' j(!)j
2
1
−
σ
|χsingle| = 1/2
π w Y
1
Single-spot noise:
k T 1 1 ; 2
!w Y
4 B
single
Br ( ) =
1=2
S
!
S
single
rp
0
BB
@
12
F CC
A
2(1
;
)
= 3=2c Y w 2 h Pin
2
Main figures
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Sapphire (1 K):
Young modulus
Y = 4·1011 Pa
Poisson coefficient σ = 0.25
Loss angle
φ = 3·109
Cavity Finesse:
F = 106
Displacement sensitivity
with 1 W:
7·10-45 m2/Hz
with 10 W:
7·10-46 m2/Hz
Target
(Ex.: dual sphere *)
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• Best stiffness: for laser power = 7 W
• Thermal noise negligible for Q/T > 2·108
Sxx = 10-45 m2/Hz
… but
With a waist of w = 1 mm:
SBr = 5·10-44 m2/Hz
Srp = 8·10-41 m2/Hz
We need a waist of
w > 20 cm !!!!
* M. Cerdonio et al., Phys. Rev. Lett. 87, 031101 (2001)
Possible solutions?
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Concave – Convex cavity :
(-R2) = R1 + r
Stable if d > r
If (d – r) << d << R1, R2 :
Ex. :
R = 10 m
r = 10 mm
d – r = 0.1 mm
λ = 1.064 µm
Delay line :
w
2
λR
≅
π
d
d−r
W = 5.8 mm
Low equivalent Finesse
Plano-concave
Cavity:
w
2
λ
≅
Rd
π
Folded Fabry-Perot (FFP)
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M3
M4
M1
θ
M1
M3
θ
M2
M2
(a)
(b)
F. Marin, L. Conti, M. De Rosa: “A folded FabryPerot cavity for optical sensing in gravitational
wave detectors”, Phys. Lett. A 309, 15 (2003)
Folded Fabry-Perot (FFP)
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M3
M4
M1
D
M2
Signal:
∝N
Brownian noise: ∝ √N
Radiation pressure: ∝ N·F (constant)
Displacement noise: ∝ 1/F ∝ N
Linewidth (→ bandwidth): ∝ 1/(N·F) (constant)
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For non-correlated spot fluctuations
Brownian noise effect:
S
2
2L
SBr
single
SBr
D2
= (2L)2 = 2
1
N
Radiation pressure effect:
2L
single
S
S
Sν
1
rp
rp
=
=
ν 2 (2L)2
4D2 N 2
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Taking into account correlations
N = single ;1
N nX
X
n=2 q=1
N +2
1 0
1
0
2
2
j
rn ; rq j C j
rn ; rq j C
B
B
exp @;
2 A I0 @
2 A
2w
2w
N Nakagawa et al., Phys. Rev. D 65, 082002 (2002)
Brownian noise effect:
FFP (! )
SBr
=
4
kB T
(4N + 4N
!
0
single)
+2
Radiation pressure effect:
FFP
Srp
=
0 12
@2A
c
Scav
2N
2
+ 2N + 2single
0
Correlation effect
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N
100
400
χN / χu
100
1
}
25
400
100
25
10
2-dim. array
} 1-dim. array
0
1
2
3
4
5
d/w
6
7
8
9
10
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-36
10
Pin = 1 W
-37
10
D = 6 mm
R = - 10 m
d =4w
-38
-1
(Hz )
10
a
-39
10
Sν / ν
2
b
-40
10
c
d
e
-41
10
-42
10
0
20
40
60
80
N
a: radiation pressure effect (no correlations)
b: radiation pressure effect (full)
c: Brownian noise @ 1.3 kHz (no correlations)
d: Brownian noise @ 1.3 kHz (full)
e: Shot-noise limited displacement sensitivity
100
-35
10
-36
10
-37
-1
10
-38
10
-39
10
-40
10
-41
10
-42
Sν / ν
(Hz )
10
2
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Pin = 7 W
b
a
c
0
D = 6 mm
R = - 10 m
d =4w
d
50
e
100
150
200
250
300
350
N
a: radiation pressure effect (no correlations)
b: radiation pressure effect (full)
c: Brownian noise @ 1.3 kHz (no correlations)
d: Brownian noise @ 1.3 kHz (full)
e: Shot-noise limited displacement sensitivity
Power density:
≈ 10 kW/mm2
Conclusions
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The FFP allows to closely approach with the
present technology the quantum-limited
sensitivity and best stiffness calculated for
the main modes of a high sensitivity, wide
bandwidth dual detector
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