100 h SQUID AMPLIFIERS FOR THE ULTRACRYOGENIC GRAVITATIONAL WAVE - - PDF document

25/3/03 Moriond Workshop 1

100 h SQUID AMPLIFIERS FOR THE ULTRACRYOGENIC GRAVITATIONAL WAVE DETECTORS

Paolo Falferi, Michele Bonaldi, Andrea Vinante, Renato Mezzena, Giovanni Andrea Prodi, Stefano Vitale, and Massimo Cerdonio Istituto di Fotonica e Nanotecnologie, CNR-ITC and INFN, Trento, Italy Dipartimento di Fisica, Università di Padova and INFN, Padova, Italy Dipartimento di Fisica, Università di Trento and INFN, Trento, Italy

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Resonant Detector Sensitivity

Important Factors

• Temperature and Q of bar and transducer
• Amplifier noise
• Matching network

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Two tuned modes (bar and transducer) Tbar=100 mK Q+, Q- = 3×106

820 840 860 880 900 920 940 960 980 1E-22 1E-21 1E-20

Shh

1/2 (Hz

• 1/2)

Frequency (Hz)

Effect of the Amplifier Sensitivity Tn=15 µK ——> ε=350 h Tn=0.35 µK ——> ε=8 h Low noise SQUIDs are needed

!

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Bar SQUID Amplifier Matching Transformer Capacitive Resonant Transducer Decoupling Capacitor Cryogenic Switch Transducer Charging Line L LS

Schematic electromechanical circuit

• f the g. w. detector AURIGA

Besides bar and transducer there is a third electrical mode.

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Equivalent Electrical Scheme

• f the AURIGA Detector

Li LBAR CBAR LTR CTR C L LS From the point of view of the SQUID the detector is constituted by 3 coupled electrical resonators 1) Bar 2) Transducer 3) resonator given by the transducer capacitance C and the inductance L of the matching transformer primary coil

The tuning of the third mode is convenient if 1) its Q is high (∼106) 2) its noise is thermal

!

High Q resonators with thermal noise are needed

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Common characteristics

• SQUID Tn= 15 µK
• Tbar=100 mK
• Q+, Q- = 3×106

820 840 860 880 900 920 940 960 980 1E-22 1E-21 1E-20

Shh

1/2 (Hz

• 1/2)

Frequency (Hz)

Effect of the Tuning of the Third Mode 2 tuned modes 3 tuned modes, Qel=400000

!

A full SQUID noise characterization is needed

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Summary The reasons for the development of a low noise SQUID able to operate strongly coupled to a high Q LC resonator are

• In a noise matched g.w. detector the minimum

detectable energy is determined by the SQUID Tn

• The tuning of the third electrical mode is

convenient only if its Q is very high

• The LC resonator is a good simulator of the

detector

• With the high Q LC resonator we can give a

full noise characterization of the SQUID amplifier

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Mi Li

Hz A RM TL k S

i SQ B i 2 25 2 2

10 16

−

≈ ≅

3 2 2 37 2 2

10 11 Hz V R T k M S

B i v

ω ω

−

≈ ≅ R T k L i S

B SQ iv

ω 12 ≅ Expected noise

Vn In Li

SQUID current amplifier noise model

VOUT IIN

The SQUID Amplifier SQUID operated in flux locked loop Typical values

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{ }

B v i B iv v i n

k S S k S S S T 2 2 Im2 ≤ − = ω ε

n BT

k =

Noise Temperature True Energy Resolution Energy Resolution from additive noise

(incomplete expression)

2

2 2 1 '

i i i i

M S L S L

φ

ε = =

25/3/03 Moriond Workshop 10 Feedback Line SQUID Sensor Vout SQUID Amplifier Matching Network Iin

Advantages

• the noise contribution of the electronics at

TAMB can be made negligible

• the effect of EM interference is reduced
• the noise is, in principle, thermal

Two-stage SQUID amplifier

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M S L S L 2 2 '

Φ

= = ε Energy Resolution from additive noise

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Vth Vn In r C rc L Lp Li M

( ) ( )

                +         =

2 2 2

2

eq t v i eq B R i a

• ut

L L M S Q L T k G MT Q Q ω ω σ

Back Action Noise Measurement

Resonator thermal noise SQUID back action noise

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Characteristics of the resonators

• Resonance frequency = 200 Hz-20 kHz
• Q = (2 - 0.5)×106
• L = 20 mH - 7 H
• C = 1 - 600 nF

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Two-stage SQUID Resonance Frequency = 1670 Hz Quality Factor = 1.1 × 106 L = 0.55 H C = 19 nF

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Two-stage SQUID Noise Temperature

11 kHz 1670 Hz

1 2 3 4 5 40 80 120 160 200 SQUID Noise Temperature (µΚ) Temperature (K)

• Intercept different from zero in the 1/f

noise region

• Slope in agreement with the theory

within a factor two

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TEST FACILITY at Legnaro Labs

Ultracryogenic site for the development of transduction systems

90 cm

Low loss matching stage and SQUID amplifier Mechanical suspensions Resonant capacitive transducer

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TRANSDUCER

• Q=1.1 × 106
• thermal noise at 4.2 K
• El. Field 8 × 106 V/m

TRANSDUCER + MATCHING STAGE + SQUID

• The system is stable
• Few spurious peaks in the spectrum

ELECTRICAL MODE

• Q=450000
• thermal noise at 2 - 4.2 K

TWO-STAGE SQUID

• Additive and back action noise as expected
• Sufficient dynamic range

800 900 1000 1100 10

• 13

10

• 11

1x10

• 9

1x10

• 7

SQUID Output V

2/Hz

Frequency (Hz)