Transcript Dual Sphere Detectors - University of Maryland, College Park

Dual Sphere Detectors
by
Krishna Venkateswara
Contents
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Introduction
Review of noise sources in bar detectors
Spherical detectors
Dual sphere configuration
Sensitivity in SQL
Advantages/Drawbacks
Dual cylinders and sensitivity
Summary
Introduction
• Proposed by M. Cerdonio, L.
Conti et. al. in 2001
• Two nested spheres
• Fabry-Perot cavity as motion
sensor
Main advantages
• Wide bandwidth
• Spherical detector
Bar detectors with resonant
transducers
Noise energy=Thermal + Amplifier + Back-action
 2
a
s 
EN  k BTa
 k BTN 


Qa


2
 s

β = energy coupling factor
τ = integration time

2
S

S
S
 Ta

  , EN  2kB 
TN 
 Qa

 A large β is needed to reduce thermal noise.
Spherical Detectors
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A sphere has a spherical
symmetry and 5
degenerate quadrupole
modes.
Uniform cross-section to
GWs.
Can determine both source
direction (, ) and wave
polarization (h+, h).
Mount 6 radial transducers on truncated
icosahedral configuration.
 “Spherically symmetric” detection of the
sphere (Johnson & Merkowitz, 1993)
Dual sphere configuration
• Inner sphere has quadrupole mode at f
• Outer sphere at 2-3 times f
At frequencies in between, the two
spheres are driven out of phase by GW
Noise sources:
•Thermal noise
•Back-action noise
•Photon counting noise
Response of the surface of a sphere to GW
1 
2~
u ( )    bn An 2 (a) h ( ) Ln 2 ( )
2 n0
Noise spectral density for each sensor
S
[ th  ba ]
uu
2
2 ba 
2l  1
2l  1
2
2  2kT nl
2

Anl (a) Lnl ( ) 

Anl (a)  Pl (n  n j ) S FF 
4M
nl 4M
j
 Qnl

ba
S FF

4
c 2
2
2


1


h

F
P
l
2
1
 2 FLc 
1 


c


2
Total strain noise density
[ th  ba ]
[ th  ba ]
shot
Suu
(

)

S

S
, hollow
uu , solid
uu ( )
Shh   
2
2 ~
uhollow ( )  usolid ( ) h ( )
2
2


2
FL

1
m


shot
 33
c
Suu ( )  4  10 1  
  2

c
  F P Hz
 
Sensitivity at Standard Quantum Limit
(SQL)
Features
 R = 0.95 m, and a = 0.57 m
 Cross section proportional to ρvs5
 Molybdenum ρ = 10000 kg/m3 and vs= 6.2 km/s
Q ~ 20 million at T ≤ 4 K
Input light power of 7 W , Q/T ≥ 2·108 K-1
 Beryllium ρ = 1900 kg/m3 and vs= 13 km/s, Q ?
Input light power of 12 W , Q/T ≥ 2·108 K-1
 Sapphire ρ = 4000 kg/m3 and vs= 10 km/s
Q > 108 at T < 10 K
Advantages/Drawbacks
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Wideband
Spherical detector
High sensitivity (at
SQL)
Different frequency
band
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Complicated design
Sensor sensitivity
difficult to realize
Dual Cylinders
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Simpler design
Each mode contributes to noise while signal is
mainly from Quadrupole mode selective readout
Low thermal noise from high frequency modes
X d = x 1 – x2 + x 3 – x4
Readout and sensitivity
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a)
b)
Required displacement sensitivity ~ 3 * 10-23 m/√Hz
Demonstrated sensitivity ~ 5 * 10-20 m/√Hz using
Optomechanical sensor.
Capacitive sensor using SQUID amplifiers.
Summary
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Offers advantage of spherical detection and wide
bandwidth in an uncovered frequency band
Requires advanced suspension and complicated
construction
Dual cylinder design gives up isotropic sensitivity
but naturally supports ‘selective readout’ and
simpler design
Both require advances in optical transducers.
thank you!