SIGRA6 - Villa Mondragone 11 Sept.2002 BREAKING THE BANDWIDTH BARRIER IN RESONANT G.W. DETECTORS IN...

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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

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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 ,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


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


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


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


BANDWIDTH IN A RESONANT DETECTOR•Why are we sensitive only around resonance ?

•Why can we be sensitive in a region f >>f/Q ?


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


• 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


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:


•1984 : we begin “talking bandwidth”

sensitivity implies and requires bandwidth.

There is no trade off : is there a free lunch after all ?


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)


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


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


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 ?


MULTIMODE DETECTORS (2)

Hidden catch : N modes bring N kBT noise in the detection bandwidth !

Multimode detectors have not been pursued in recent years


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!)


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


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.


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


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


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


PRECISION MACHINING:PRECISION MACHINING:

The rosette capacitive transducer; gap=9m


THE LATEST CHALLENGE: A TRANSDUCER FOR MINIGRAIL


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


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


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


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


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


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


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


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+


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


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


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


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


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


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


WHAT CAN WE OBSERVE WITH THESE ANTENNAS ?

PLEASE STAY TUNED FOR NEXT TALK (AFTER COFFEE)

SIGRA6 - Villa Mondragone 11 Sept.2002 BREAKING THE BANDWIDTH BARRIER IN RESONANT G.W. DETECTORS IN...

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