sigra6 - villa mondragone 11 sept.2002 breaking the bandwidth barrier in resonant g.w. detectors in...
TRANSCRIPT
QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.SIGRA6 - Villa Mondragone 11 Sept.2002
BREAKING THE BANDWIDTH BARRIERBREAKING THE BANDWIDTH BARRIER
IN RESONANT G.W. DETECTORSIN RESONANT G.W. DETECTORS
MASSIMO BASSAN Università di Roma “Tor Vergata” and INFN - Sezione Roma2 For the ROG Collaboration
or
Recipes for a broadband and sensitive antenna
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
ABSTRACT
• BAR DETECTORS: A TUTORIAL AND SOME TECHNICAL TERMS– Crucial components that make an antenna work– Sensitivity: h, Sh(f), Teff ,f 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” ?
PREEMPTIED
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
ROGA collaboration of:
INFN, Univ. Roma1, Univ. Roma2 and CNR
EXPLORER(CERN)
2300 kg Al antennaResonances at 888,919 HzCooled to 2.6 K
Readout: Capacitive resonant transducer with d.c. SQUID amplifier
Operational since 1990Upgrade 1999New run since 2000
Cosmic Ray telescope starting 2002
NAUTILUS(LNF)
2300 kg Al antennaResonances at 906, 922 HzCooled to 0.14 K
Readout: Capacitive resonant transducer with d.c. SQUID amplifier
Operational since1995New run since 1998
Cosmic Ray Telescope Veto for events due to EAS or hadrons
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
A DICTIONARY OF ANTENNA TERMS A DICTIONARY OF ANTENNA TERMS
The mechanical oscillator
Mass MSpeed of sound vs
Temperature TQuality factor Q
Res. frequency fr
The transducer
Efficiency
The amplifier
Noise temperature Tn
Vp
Antenna
M
Cd
Rp
Vp
Antenna
M
Cd
Rp
L0 Li
Thermal noiseSF = MkTr/Q Amplifier noise
Vn; In Tn=√Vn2In
2 /k
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
Minimum detectable energy change
A low effective temperature makes the sensitivity higher and the bandwidth larger
ΔEmin ≡kBTeff =2Twideband noisethermal noise
Δf
Δf =4fQ
TTeff
Bandwidth
ho =1τg
Sh(fo)2πΔf
=L
2vs2τg
kBTeff
M
NOISE TEMPERATURE, WAVE AMPLITUDE AND SPECTRAL SENSITIVITY
strain sensitivity
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
BANDWIDTH IN A RESONANT DETECTOR•Why are we sensitive only around resonance ?
•Why can we be sensitive in a region f >>f/Q ?
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
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. to beat slowly varying thermal
noise:
can be made small at will : Obviously wrong !
• Gibbons & Hawking (PRD 1971): sampling time limited by
detector noise
€
f → ∞)
€
Emin = kBTΔt
τ
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
• Giffard (PRD 1976) introduces “back action” (the amplifier shakes
the antenna).
€
Emin = kBTΔt
τ+ kBTamp λβωΔt +
1
λβωΔt
⎛
⎝ ⎜
⎞
⎠ ⎟
•First rigorous, although unpractical, derivation of minimum detectable energy:
€
λ =InZ
Vn
coupling coefficient -more in a momentback action: amplif. noise, but t
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
Pallottino Pizzella 1981
€
Emin = 2kBTamp 1+ λ−2( )
2Tλ
βQTamp
+1 ⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
•T/ Q << Tamp/λ => Thermal noise negligible wrt Amplifier
• λ >>1 => Amplifier noise dominated by back action
As of today, the challenge of meeting these 2 conditions is still open
2 requirements for best sensitivity:
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
•1984 : we begin “talking bandwidth”
sensitivity implies and requires bandwidth.
There is no trade off : is there a free lunch after all ?
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
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:
€
=α 2
Mω3Z
transduction constant (V/m)
circuit impedanceresonator 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)
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
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 !
(In modern terms, transducer motion noise grows intolerably outside f )
€
< x th2 >=
kT
mω2
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
TWO MODE DETECTOR (2)
• Indeed, the bandwidth is limited by transfer time between the oscillators (beat frequency) to f = fbeat = f √µ
• An optimum does exist for m: the value for which
fbeat= f single mode
• This limited the useful bandwidth to ~ 1 Hz
• Is there a way out ?Beats in Explorer -Aug 2002
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
MULTIMODE DETECTORS ?
• Iterate many (N) times the “light mass oscillator” trick
• Then µ= Mj/Mj+1 can grow up to ~10% (µ = f / f )
• and final mass (m = MN ~ 0.1 g) makes very large
Would it work ?
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
MULTIMODE DETECTORS (2)
Hidden catch : N modes bring N kBT noise in the detection bandwidth !
Multimode detectors have not been pursued in recent years
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
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” :
€
=α 2
Mω3Z
transduction constant (V/m)
circuit impedanceresonator mass
Only surviving “handle” is α.
It depends on the density of e.m. field stored in the transducer
What is the best transducer for the job ? (touchy question!)
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
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
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
A fair (?) comparison of transducersParametric 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 motionIt is ≈ a tie. We chose Capacitive
because it is convenient.
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
TRANSDUCERS (3)
• A careful analysis of two mode antennas w/ passive transducers [Bassan, Pizzella 1997] shows that
• To a good approx. it works also for our 3mode antennas.
• By writing it out in terms of parameters, we find:– α gap€
E = 42φn
α φ
MkBT
τ
⎛
⎝ ⎜
⎞
⎠ ⎟
1/4
Δf =2α φ
φn
kBT
Mτ
⎛
⎝ ⎜
⎞
⎠ ⎟
1/4
We need a small gap device, that holds high field
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
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
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
ROME GROUP TRANSDUCERSROME GROUP TRANSDUCERS
• “OLD” MUSHROOM SHAPED
• “NEW” ROSETTE SHAPEDResonatingdisk Pb washers
Teflon insulators
Gap 10 m
Diam. 140 mm
170 mm
Resonating diskTeflon insulators
Antenna
Gap 50 m
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
PRECISION MACHINING:PRECISION MACHINING:
The rosette capacitive transducer; gap=9m
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
THE LATEST CHALLENGE: A TRANSDUCER FOR MINIGRAIL
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
dc-SQUID
• Flux quantization + Josephson effect (2 JJ) in a superconducting loop of inductance L
• Requires nanofabrication processes
• Yields the world most sensitive magnetometer ( fA, µo/rt(Hz) )
• Now available commercial devices of good performance.
Ib
Io Io
LV
Lin
Josephson junction
Resistors
Quantum at work
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
10-2 10-1 100 101 102 103 10410-8
10-7
10-6
10-5
= 5.5 h
=28 h
T= 0.9 K
T=4.2 K
frequency (Hz)
n (
0 H
z)
Carelli et al. 98
Experimental flux noise spectral density
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
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
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
NOISE PLOTS FOR NAUTILUS 1998+
880 900 920 940 960100
105
1010
1015
Frequency (Hz)
Noise Force Spectra (N
2/Hz)
red -> antenna green -> trx blue ->b.a.
880 900 920 940 96010 -20
10 -15
10 -10
10 -5
Frequency (Hz)
Noise Flux Spectra (Fi
o2/Hz)
red -> antenna; green -> trx; blue ->b.a.
900 910 920 930 940
10 -5
Frequency (Hz)
Total Noise (V/rt(Hz))
900 910 920 9300
0.05
0.1
0.15
0.2
0.25
Frequency (Hz)
SNR
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
Sh(f) per Nautilus 1998+
880 890 900 910 920 930 940 95010 -22
10 -21
10 -20
10 -19
10 -18
Frequency (Hz)
gw spectral amplitude (h/rt(Hz))
8.1e-22
Nautilus 98
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
Calibration peakThe bandwidth depends mainly on the
transducer and amplifier
The sensitivity of a detector is usually given in terms of the noise spectral density referred to the input of the antenna
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
The peak sensitivity depends on T/MQ
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
WIDENING THE BAND IN EXPLORERER
The readout chain has been changed in 1999. After a tune-up period, EXPLORER has been on the air since May 2000
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
EXPLORER 1999
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
880 900 920 940 960100
105
1010
1015
Frequency (Hz)
Noise Force Spectra (N
2/Hz)
red -> antenna green -> trx blue ->b.a.
880 900 920 940 96010 -20
10 -15
10 -10
10 -5
100
Frequency (Hz)
Noise Flux Spectra (Fi
o2/Hz)
red -> antenna; green -> trx; blue ->b.a.
880 900 920 940 96010 -5
10 -4
10 -3
10 -2
Frequency (Hz)
Total Noise (V/rt(Hz))
880 900 920 940 9600
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Frequency (Hz)
SNR
NOISE PLOTS FOR EXPLORER 2000+
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
July 2001
h = 5 · 10-19
880 890 900 910 920 93010
-21
10-20
10-19
10-18
frequency (Hz)
GW spectral amplitude (h/rt(Hz))
Calibration peak
December 2001
h = 2 · 10-19
EXPLORER PERFORMANCESEXPLORER PERFORMANCES
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
880 890 900 910 920 930 940 95010 -21
10 -20
10 -19
Frequency (Hz)
gw spectral amplitude (h/rt(Hz))
--- Explorer2001; con Trx FE2 e SQUID QD - Parametri Modificati
0.4 milions 5 milions
• 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
≈ 40 Hz
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
THE ROLE OF WIDE-BAND NOISE:
This is not science fiction:
A SQUID with 0.1 µ o/Hz
Carelli et al. Appl. Phys. Lett. 72,115 (1998)
10-22 /Hz
NAUTILUS 2002 ?
Tuned to 935 HZ, the frequency of the pulsar in SN1987A
6 10-23/√Hz
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
12 hours of data
Bandwidth =0.1 Hz
gw < 6*10
A correlation between Nautilus and Auriga(or Virgo) will lower this limit to gw =1
EXPLORER & NAUTILUS 1997
Crosscorrelation of stochastic g.w. background with two resonant detectors
Astr. Astroph 351,1999- Phys. Lett. B, 385, 1996
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
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 <λ
• New, upcoming multimode resonators will exploit the technology with a sensitivity boost + omnidirectionality
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
TARGET SENSITIVITY OF EXPLORERTARGET SENSITIVITY OF EXPLORER
EXPLORER can reach a sensitivity of Teff=170 µK h = 1 · 10 -19
• New transducer double gap
C=20 nF Q = 2 · 106
• New transformer low dissipation
Qe= 105
850 900 950 1000 105010-22
10-21
10-20
10-19
frequency (Hz)
Sh
(1/
Hz)
4 · 10-22
• New SQUID
n= 0.5 0/√Hz
SIGRAV 15 QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
WHAT CAN WE OBSERVE WITH THESE ANTENNAS ?
PLEASE STAY TUNED FOR NEXT TALK (AFTER COFFEE)