Transcript PowerPoint Presentation - PERFORMANCE OF RESONANT BAR

SIGRA6 - Villa Mondragone 11 Sept.2002
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BREAKING THE BANDWIDTH BARRIER
IN RESONANT G.W. DETECTORS
or
Recipes for a broadband and sensitive antenna
MASSIMO BASSAN
Università di Roma “Tor Vergata” and INFN - Sezione Roma2
For the ROG Collaboration
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ABSTRACT
• BAR DETECTORS: A TUTORIAL AND SOME
TECHNICAL TERMS
– Crucial components that make an antenna work
– Sensitivity: h, Sh(f), Teff ,Df and all that
– A historical perspective
• BANDWIDTH: WHERE WE STAND and what we can expect
– Status of the existing detectors
– The two antennas of the ROG group
– Present sensitivity : is it meaningful ?
• WHAT TO DO NEXT: or
– Is there a future for bars in the “age of interferometers” ?
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ROG
A collaboration of:
INFN, Univ. Roma1, Univ. Roma2
and CNR
EXPLORER
(CERN)
2300 kg Al antenna
Resonances at 888,919 Hz
Cooled to 2.6 K
Readout:
Capacitive resonant transducer with
d.c. SQUID amplifier
Operational since 1990
Upgrade 1999
New run since 2000
Cosmic Ray telescope starting 2002
NAUTILUS
(LNF)
2300 kg Al antenna
Resonances at 906, 922 Hz
Cooled to 0.14 K
Readout:
Capacitive resonant transducer with
d.c. SQUID amplifier
Operational since1995
New run since 1998
Cosmic Ray Telescope
Veto for events due to EAS or hadrons
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A DICTIONARY OF ANTENNA TERMS
Thermal noise
SF = MkTwr/Q
Vp
Amplifier noise
Vn; In Tn=√Vn2In2 /k
Rp
Cd
Antenna
M
The mechanical
oscillator
Mass M
Speed of sound vs
Temperature T
Quality factor Q
Res. frequency fr
L0
Li
The transducer
The amplifier
Efficiency 
Noise temperature Tn
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NOISE TEMPERATURE, WAVE AMPLITUDE AND
SPECTRAL SENSITIVITY
wideband noise
DEmin  kB Tef f  2T
Df
therm al noise
A low effective temperature
makes the sensitivity higher and
the bandwidth larger
Bandwidth
4f T
Df 
Q Teff
strain sensitivity
Minimum detectable
energy change
ho 
1
g
Sh (fo )
L

2
2 Df
2v s  g
k BTeff
M
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BANDWIDTH IN A RESONANT DETECTOR
•Why are we sensitive only around resonance ?
•Why can we be sensitive in a region Df >>f/Q ?
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SENSITIVITY AND BANDWIDTH:
A Quick History Of Our Mistakes
• Pre-history (‘60s), naive approach: focus is on burst detection,
bandwidth is not an issue
– Sample as fast as you can (i.e. Df  ) to beat slowly varying thermal
noise:
DE min  kB T
Dt


can be made small at will : Obviously wrong !

• Gibbons & Hawking (PRD 1971): sampling time limited by
detector noise
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• Giffard (PRD 1976) introduces “back action” (the amplifier shakes
the antenna).
•First rigorous, although unpractical, derivation of minimum detectable energy:

1 
DE min  kB T  kB Tamp wDt 


wDt 

Dt

In Z
Vn
coupling
-more inbut
a moment
back
action:coefficient
amplif. noise,
Dt

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Pallottino Pizzella 1981
DE min  2kB Tamp
 2T

1  QT  1

amp

2
2 requirements for best sensitivity:
•T/Q << Tamp/
=>
Thermal noise negligible wrt Amplifier
•  >>1
=>
Amplifier noise dominated by back action
As of today, the challenge of meeting these 2 conditions is still open
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•1984 : we begin “talking bandwidth”
sensitivity implies and
requires bandwidth.
There is no trade off : is
there a free lunch after all ?
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So, to increase sensitivity and bandwidth, we need
a large 
What is this “energy coupling coefficient” ?
It is the figure of merit of the antenna transduction system:


Mw 3 Z
2
transduction constant (V/m)
circuit impedance
resonator mass
Need large M to capture g.w. (M<=>cross section)
Need small M to efficiently couple to the amplifier
=> light mass resonant transducer (Paik ‘74)
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TWO MODE DETECTOR :
• A resonant transducer with a mass m=µM allows us to gain a factor
µ-1 in .
• => make a tiny transducer mass : Stanford 1980, m=20 g, µ~10-5
Badly penalized by thermal noise in the small resonator ! 2
kT
 x th 
mw 2
(In modern terms, transducer motion noise grows intolerably outside Df )
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TWO MODE DETECTOR (2)
• Indeed, the bandwidth is
limited by transfer time
between the oscillators (beat
frequency) to Df = fbeat = f õ
• An optimum does exist for
m: the value for which
fbeat= Df single mode
• This limited the useful
bandwidth to ~ 1 Hz
• Is there a way out ?
Beats in Explorer -Aug 2002
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MULTIMODE DETECTORS ?
• Iterate many (N) times the “light mass oscillator” trick
• Then µ= Mj/Mj+1 can grow up to ~10% (µ = Df / f )
• and final mass (m = MN ~ 0.1 g) makes  very large
Would it work ?
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MULTIMODE DETECTORS (2)
Hidden catch : N modes bring N kBT noise in the
detection bandwidth !
Multimode detectors have not been pursued in recent years
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So, we are back to the problem: how to increase 
in order to improve sensitivity and bandwidth
Let’s give another look at our “energy coupling coefficient” :


Mw 3 Z
2
resonator mass
transduction constant (V/m)
circuit impedance
Only surviving “handle” is .
It depends on the density of e.m. field stored in the transducer
What is the best transducer for the job ? (touchy question!)
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TRANSDUCERS
• A transducer (Trx) works converting a mechanical
signal in an electric one, by modulating a stored e.m.
field, that can be
– Electrostatic
=> Capacitive devices
– Magnetic (usually superconductive) => Inductive Trx
– a.c. electromagnetic (r.f through optical) => Parametric Trx
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A fair (?) comparison of transducers
Parametric Trx
• Best in principle (>1 )
• but beware of pump noise (both amplitude and phase)
Inductive Trx
• Direct coupling to a Squid amplifier
• High field density
Capacitive trx
•
•
•
Large active surface, small gap
Test @RT, no diff. contractions
a.c. coupling cuts off slow (and large !) antenna motion
It is ≈ a tie. We chose Capacitive
because it is convenient.
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TRANSDUCERS (3)
• A careful analysis of two mode antennas w/ passive transducers
[Bassan, Pizzella 1997] shows that
2 n Mk B T 1/4
DE  4


    
2  k B T 1/4
Df 


 n M 
• To a good approx. it works also for our 3mode antennas.
• By writing it out in terms of parameters, we find:

– gap
We need a small gap device, that holds high field
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THE SIMPLEST DEVICE: PARALLEL PLATE,
D.C. BIASED CAPACITOR
•
•
•
•
e.d.m. machining to carve the rosette
Diamond tool machining for flatness tolerance < 5 µm
Hand lapping for final finishing
Painstaking attention to dust and parallelism in assembling
Main credit to dr. Yu F.Minenkov for developing these techniques
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ROME GROUP TRANSDUCERS
Teflon insulators
Resonating disk
170
mm
• “OLD” MUSHROOM SHAPED
Antenna
Gap 10 m
Gap
50 m
Teflon insulators
Diam. 140 mm
• “NEW” ROSETTE SHAPED
Pb washers
Resonating
disk
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PRECISION MACHINING:
The rosette capacitive transducer; gap=9m
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THE LATEST CHALLENGE: A TRANSDUCER
FOR MINIGRAIL
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Quantum at work
dc-SQUID
Ib
Io
Io
L
Lin
• Flux quantization + Josephson effect
(2 JJ) in a superconducting loop of
inductance L
• Requires nanofabrication processes
• Yields the world most sensitive
magnetometer ( fA, µFo/rt(Hz) )
• Now available commercial devices of
good performance.
Resistors
Josephson
junction
V
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SIGRAV 15
Experimental flux noise spectral density
10-5
Fn (F0 Hz)
T=4.2 K

10-6
=28 h
10-7
10-8 -2
10
T= 0.9 K
 = 5.5 h
10-1
100
101
102
103
104
frequency (Hz)
Carelli et al. 98
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CORRECT APPROACH TO SENSITIVITY:
• All our noise sources are white, but some appear
colored due to filtering of the resonators
• If the detector parameters are well known, compute the
transfer functions and sum the noise voltages at the
antenna output, or better still the noise displacements
at the input (where a g.w. has white spectrum)
• Compute the SNR(f) = const/ Sh(f).
• Plot Sh(f) to observe the bandwidth.
• Sh(f) provides info on sensitivity to all kinds of source
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10
15
10
10
10
5
10
0
red -> antenna
880
green -> t rx
blue ->b. a.
10
Noise Flux Spectra (Fi 2o/Hz)
Noise Force Spectra (N 2/Hz)
NOISE PLOTS FOR NAUTILUS 1998+
900
920
940
Frequency (Hz)
960
-5
10
-10
10
-15
10
-20
red -> antenna; green -> trx; blue ->b.a.
880
900
920
940
Frequency (Hz)
960
0.2
10
SNR
Total Noise (V/rt(Hz))
0.25
-5
0.15
0.1
0.05
0
900
910
920
930
Frequency (Hz)
940
900
910
920
Frequency (Hz)
930
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SIGRAV 15
Sh(f) per Nautilus 1998+
10
Nautilus 98
-18
gw spectral amplitude (h/rt(Hz))
10 -19
10
-20
10 -21
10
8.1e-22
-22
880
890
900
910
920
Frequency (Hz)
930
940
950
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The sensitivity of a detector is usually given in terms of
the 15
SIGRAV
noise spectral density referred to the input of the antenna
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The peak sensitivity
depends on T/MQ
The bandwidth depends
mainly on the
transducer and amplifier
Calibration peak
To increase the overall sensitivity a larger bandwidth is required.
This can be obtained decreasing the amplifier noise contribution
and/or by increasing the transducer coupling
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The readout chain has
been changed in 1999.
After a tune-up period,
EXPLORER has been on
the air since May 2000
WIDENING THE BAND
IN EXPLORER
EXPLORER 1999
The noise temperature is
very stable, at values < 5
mK for 84% of the
time.
Bandwidth: the detector
has a sensitivity better
than 10-20 Hz-1/2 on a
band larger than 40 Hz
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SIGRAV 15
10
15
10
10
10
10
red -> antenna
green -> t rx
blue ->b. a.
10
Noise Flux Spectra (Fi 2o/Hz)
Noise Force Spectra (N 2/Hz)
NOISE PLOTS FOR EXPLORER 2000+
5
0
10
880
900
920
940
Frequency (Hz)
960
-2
red -> antenna; green -> trx; blue ->b.a.
0
10
-5
10
-10
10
-15
10
-20
880
900
920
940
Frequency (Hz)
960
900
920
940
Frequency (Hz)
960
0.07
10
0.05
-3
SNR
Total Noise (V/rt(Hz))
0.06
10 -4
0.04
0.03
0.02
0.01
10
-5
880
900
920
940
Frequency (Hz)
960
0
880
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SIGRAV 15
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EXPLORER PERFORMANCES
-18
GW spectral amplitude (h/rt(Hz))
10
July 2001
h = 5 · 10-19
Calibration
peak
-19
December 2001
10
h = 2 · 10-19
-20
10
-21
10
880
890
900
910
frequency (Hz)
920
930
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10
-- - Ex plor er2001;
-19
c on Trx F E2 e
SQU I D QD - Param et ri Modif ic at i
gw spectral amplitude (h/rt(Hz))
0 .4 m ili o ns
5 m i lio n s
10
-20
10
-21
880
≈ 40 Hz
890
900
920
910
F requency ( H z)
930
940
950
• Which situation is to be preferred ?
• However, the blue line has a larger bandwidth , if we use the
current definition !
• While waiting for a better definition, we define as useful
bandwidth the region where Sh(f) <10-40/Hz
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SIGRAV 15
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THE ROLE OF WIDE-BAND NOISE:
NAUTILUS 2002 ?
Tuned to 935 HZ,
the frequency of the
pulsar in SN1987A
10-22 /Hz
6 10-23/√Hz
This is not science fiction:
A SQUID with 0.1 µ Fo/Hz
Carelli et al. Appl. Phys. Lett. 72,115 (1998)
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EXPLORER & NAUTILUS 1997
Crosscorrelation of stochastic g.w. background with two resonant
detectors
Astr. Astroph 351,1999- Phys. Lett. B, 385, 1996
12 hours of data
Bandwidth =0.1 Hz
Wgw < 6*10
A correlation between Nautilus and Auriga
(or Virgo) will lower this limit to Wgw =1
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THE FUTURE (in the age of interferometers)
• There is still ample room for improvements in sensitivity
• LIGO preliminary data shows IFOs might take longer to operate
than expected : bars are still the only sentinels
• A coincident detection by two totally different instruments will
be a stronger evidence
• Cross correlation IFO-Bar for stoch. bkgnd will be crucial
(D <2
• New, upcoming multimode resonators will exploit the
technology with a sensitivity boost + omnidirectionality
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TARGET SENSITIVITY OF EXPLORER
EXPLORER can reach a sensitivity of Teff=170 µK h = 1 · 10 -19
Sh (1/Hz)
10-19
• New transducer double
gap
C=20 nF
Q = 2 · 106
10-20
10-21
10-22850
• New transformer low
dissipation
Qe= 105
4 · 10-22
900
950
1000
frequency (Hz)
1050
• New SQUID
Fn= 0.5  F0/√Hz
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WHAT CAN WE OBSERVE WITH THESE
ANTENNAS ?
PLEASE STAY TUNED FOR NEXT TALK
(AFTER COFFEE)
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