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Performances of a super conductive parabridge transducer for liquidhelium temperature applications
ICEC 15 Proceedings
P e r f o r m a n c e s o f a s u p e r c o n d u c t i v e p a r a b r i d g e t r a n s d u c e r for liquid
helium temperature applications. C.Cinquegrana 1 E.Majorana 3 N.Pergola 2, P.Puppo 1,2, P.Rapagnani 1,2, F.Ricci 1,2 1 Dipartimento di Fisica Universith di Roma "La Sapienza" 2 I.N.F.N. Sezione di Roma, P.le A. Moro g, 00185 Rome, Italy 3 Dipartimento di Fisica Universith di Siena
Abstract In order to measure very low vibration amplitudes at low temperatures a parametric transducer has been developed. The transducer is a differential capacitive device inserted in a super conducting bridge with low acoustic and electric dissipation. The central arm of the bridge is a super conducting coil made of niobium wire to give an electric resonance frequency of 125 kHz. In this configuration an electric quality factor of Qe = 6 . 103 and an overall balancing of 0.8 ppm has been obtained. We present the vibration measurements due to the thermal noise of the mechanical resonance of the transducer performed, at 4 K, in a displacement, range of 10-15 m.
Introduction Back Action Evading (BAE) [1] technique has been applied in the development of new parametric electromechanical transducers to improve their sensitivity. It consists essentially in detecting the motion of a mechanical oscillator by coupling dynamically one of the quadrature components of its displacement to one of the quadrature components of the charge at the output of a readout circuit at higher resonance frequency. A BAE detector is a phase sensitive device based on the measurement of one quadrature component of the mechanical oscillator, preventing it, at the same time, from the back action of the monitoring apparatus. Focusing on practical applications, a basic BAE scheme consists of two harmonic oscillators: the system, with angular frequency aJm, and the read-out electrical apparatus eve, coupled by an electrical field which must be: = y Eo {cos(
- LUm + COS(We
We have developed a theoretical model in order to predict the noise behaviour of our apparatus. According to the general theory of a BAE transducing scheme, only one component of the complex amplitude of the output voltage will present the response of the system to a mechanical excitation of the resonator. The other component will carry only the noise coming from the e.m. pumps and from the amplifier. The analysis is presented in detail in [2]. Here we recall that in the spectral density SV= of one of the o u t p u t components of the transducer, two terms of different spectral behaviour are present: a white noise due to the voltage noise of the amplifier, and a resonant term,
Cryogenics 1994 Vo134 ICEC Supplement
443
ICEC 15 Proceedings
which has the bandwidth of the electrical resonance, due to the pump noise reduced by the balance factor qz2 of the bridge, and to the current noise of the amplifier. On the quadrature component SVy, a narrow band term, which has the bandwidth of the mechanical resonance, is added to SV~. The main contribution to this term is due to the Brownian motion of the mechanical resonator, to which a residual effect of the p u m p noise onto the system, weighted by ~/~, is added.
/'\\
n~
Push-Pull Tra u=cer
X
~y z .~: . x > h
High
Wide Range - Variable Capacitance V
¢g N~ ~ "%~ f 1.
Input Transformer
Resoulo tin
V.rtahC..ci,...
Amp.
L. . . . J Superconducting Cull
Fixed Capacitances
F i g . l : Schematic diagram of the Back Action Evasion transducer circuit The experimental
set-up
The overall scheme of our apparatus is shown in fig. 1. The main b o d y of the transducer is made of A1 alloy 5056 which shows a steep increase of the Q value at low temperatures. It is a differential device having a push-pull geometry. Its main mechanical resonance is the first flexural mode of a disk fixed at the inner radius and free at the outer radius. This vibrating b o d y is the central plate of the push-puU capacitor, having a 0.17 m diameter and 0.065 m thickness and a mass of 0.380 kg.. The other electrodes are two rings of equal sizes, within the mechanical tolerances, one rigidly fastened with eight bolts on the base and the other one on the lid of the transducer. Before a thermal cycle at liquid helium temperature the two capacitances of the assembled transducer had both the value C = (1780 4- 1)pF and from these d a t a we deduce a value of the two gaps of d = (92.4 4- .1)#m and an upper limit for their relative difference Pd < 10 -3.
444 Cryogenics 1994Vol 34 ICECSupplement
ICEC 15 Proceedings
The two capacitance of the transducer are inserted in a bridge, in order to minimize the effect of the noise of variable electrical field generators (usually called e.m. p u m p s ) . The central arm of the bridge is a readout coil which, together with the bridge capacitances, constitutes the electrical oscillator at frequency v~ coupled to the mechanical resonator. All connections and the central coil are made of superconducting niobium wire. To improve the bridge balance we use a primary variable capacitance driven by an electrical motor and a high resolution variable capacitance driven by a piezoelectric stack. In view of low temperature operation, the construction and the assembling procedures of these variable capacitances are rather complex and they had required careful design and extensive testings. The wide range variable capacitor is composed of two coaxial cylinders butterfly shaped made of Stainless Steel AISI 304L and assembled with a vacuum gap of 100 #m. This value requires a high machining precision, because the entire structure is supported only along the axis. The inner cylinder is rotated by a d.c. electrical motor through a high gain gear to improve the resolution of the capacitance. Both the electrical motor and the driving gear have been carefully modified to operate at 4 K with good reliability. The high resolution variable capacitance is a parallel plate capacitor, having one armature driven by a piezoelectric ceramic stack. A piezoelectric ceramic gives a very sensitive way to vary the gap of the capacitance, however, its efficiency decreases from room to liquid helium temperature. This imposes a constraint on the maximum value of the gap allowed in order to have a variation range of the order of 1 pF. The whole system is in a vacuum chamber cooled to liquid helium temperature. [3]. The circuit is biased in the BAE configuration using two commercial frequency synthesizers HP 3326A tuned to frequencies u~ - u,~ and u~ + vm. The output of the pick up coil is sent to a commercial low noise amplifier PAR 113. The two quadrature components of the signal from the transducer at frequency v~ are demodulated by means of a lock-in amplifier with integration time to = O. 1 s and sampled by computer with the same sampling time. Results and conclusion We tested the mechanical behaviour of the push-pull transducer at 4 K measuring its main electromechanical characteristcs before inserting it in the detection scheme. In particular we measured the frequency of the first flexural mode of the disk Um= 927.9 Hz and the mechanical quality factor Q ~_ 3.106. The BAE system worked successfully,
Cryogenics 1994 Vo134 ICEC Supplement 445
ICEC 15 Proceedings
showing a satisfactory geometrical balance and a good stability of the electrical and geometrical parameters during the thermal cycles between room and liquid helium temperatures. The bridge readout circuit was biased at Eo " 5-104 V / m and balanced down to 0.8 ppm (correspondig to a AC _~ 10-15 F). An electrical quality factor Q~ _ 6 • 103 was measured at the electrical resonance frequency of ~c = 125 kHz. The test on the noise behaviour of the system shows a good quantitative agreement with the theoretical model. In the lego plot of fig. 2 the distribution of two quadrature components of the transducer output noise is shown. We notice that the distribution along one axis is larger than along the other, because only one component of the system is mechanically sensitive.
•
"
.4"
// ~,,s / . s.~," .~,.+ j
8 ! ~'F / / t " j ~.t .I" f"
5 3-
:
t
f. .1"
/"
~
..... 271
" ' / / " ~
' -
.2g~ _ o .
......... ]
P
• _0.4 41. $
Fig.2: Lego plot of the spectrum of the Y phase. By performing the Fourier spectra of the two components of the t~ransducer output, we notice that the spectrum of the Y component (see fig. 3) shows a narrow peak not present on the X component. As the BAE theory predicts, in absence of external excitation, this peak is clue only to the thermal noise of the mechanical harmonic oscillator. In the data plotted in fig. 3, this peak corresponds to a vibration amplitude <
Xthcv >--~ 2 10-15
m
in good agreement with the root meansquare value of the thermal fluctuation amplitude.
446 Cryogenics 1994Vol 34 ICEC Supplement
ICEC 15 Proceedings
According to the general analysis of a BAE system, used as a detector of impulsive interactions, the sensitivity of this kind of transducer depends on several parameters. It can be shown [4] that, using as current amplifier a dc Squid, the quantum limit can be acheived by increasing the strenght of the pump field at the level of 3.106 V/m, by lowering the temperature of the system in the mK range and by using FCXO quartz oscillators and/or notch filters at the input of the bridge circuit. SVy
[ v2~z]
1
0.7525
0.505
[ 0.2575
0.01 0.005
0.01
0.015
[Hz]
0.02
0.025
0.03
Fig.3: Plot of the spectrum of the Y phase. The dotted line is the theoretical prevision.
References [1] C. M. Caves, K. S. Thorne, R.W.P. Drever, V.D. Sandberg, M. Zimmerman, Rev. Mod. Phys., 52, 341 (1980). [2] C. Cinquegrana, E. Majorana, P. Rapagnani, F. Ricci, Phys.Rev. D
4s, 247s (1993). [3] E. Majorana, P. Rapagnani, F. Ricci, Meas. Sci. Technol., 3, 501, (1991)
[4] C. Cinquegrana, E. Majorana, N. Pergola, P. Puppo, P. Rapagnani, F. l~cci, Internal Report n. 1032 24/3/94, Physics Department ,"La Sapienza" University, Rome, Italy
Cryogenics 1994 Vol 34 ICEC Supplement
447
P e r f o r m a n c e s o f a s u p e r c o n d u c t i v e p a r a b r i d g e t r a n s d u c e r for liquid
helium temperature applications. C.Cinquegrana 1 E.Majorana 3 N.Pergola 2, P.Puppo 1,2, P.Rapagnani 1,2, F.Ricci 1,2 1 Dipartimento di Fisica Universith di Roma "La Sapienza" 2 I.N.F.N. Sezione di Roma, P.le A. Moro g, 00185 Rome, Italy 3 Dipartimento di Fisica Universith di Siena
Abstract In order to measure very low vibration amplitudes at low temperatures a parametric transducer has been developed. The transducer is a differential capacitive device inserted in a super conducting bridge with low acoustic and electric dissipation. The central arm of the bridge is a super conducting coil made of niobium wire to give an electric resonance frequency of 125 kHz. In this configuration an electric quality factor of Qe = 6 . 103 and an overall balancing of 0.8 ppm has been obtained. We present the vibration measurements due to the thermal noise of the mechanical resonance of the transducer performed, at 4 K, in a displacement, range of 10-15 m.
Introduction Back Action Evading (BAE) [1] technique has been applied in the development of new parametric electromechanical transducers to improve their sensitivity. It consists essentially in detecting the motion of a mechanical oscillator by coupling dynamically one of the quadrature components of its displacement to one of the quadrature components of the charge at the output of a readout circuit at higher resonance frequency. A BAE detector is a phase sensitive device based on the measurement of one quadrature component of the mechanical oscillator, preventing it, at the same time, from the back action of the monitoring apparatus. Focusing on practical applications, a basic BAE scheme consists of two harmonic oscillators: the system, with angular frequency aJm, and the read-out electrical apparatus eve, coupled by an electrical field which must be: = y Eo {cos(
- LUm + COS(We
We have developed a theoretical model in order to predict the noise behaviour of our apparatus. According to the general theory of a BAE transducing scheme, only one component of the complex amplitude of the output voltage will present the response of the system to a mechanical excitation of the resonator. The other component will carry only the noise coming from the e.m. pumps and from the amplifier. The analysis is presented in detail in [2]. Here we recall that in the spectral density SV= of one of the o u t p u t components of the transducer, two terms of different spectral behaviour are present: a white noise due to the voltage noise of the amplifier, and a resonant term,
Cryogenics 1994 Vo134 ICEC Supplement
443
ICEC 15 Proceedings
which has the bandwidth of the electrical resonance, due to the pump noise reduced by the balance factor qz2 of the bridge, and to the current noise of the amplifier. On the quadrature component SVy, a narrow band term, which has the bandwidth of the mechanical resonance, is added to SV~. The main contribution to this term is due to the Brownian motion of the mechanical resonator, to which a residual effect of the p u m p noise onto the system, weighted by ~/~, is added.
/'\\
n~
Push-Pull Tra u=cer
X
~y z .~: . x > h
High
Wide Range - Variable Capacitance V
¢g N~ ~ "%~ f 1.
Input Transformer
Resoulo tin
V.rtahC..ci,...
Amp.
L. . . . J Superconducting Cull
Fixed Capacitances
F i g . l : Schematic diagram of the Back Action Evasion transducer circuit The experimental
set-up
The overall scheme of our apparatus is shown in fig. 1. The main b o d y of the transducer is made of A1 alloy 5056 which shows a steep increase of the Q value at low temperatures. It is a differential device having a push-pull geometry. Its main mechanical resonance is the first flexural mode of a disk fixed at the inner radius and free at the outer radius. This vibrating b o d y is the central plate of the push-puU capacitor, having a 0.17 m diameter and 0.065 m thickness and a mass of 0.380 kg.. The other electrodes are two rings of equal sizes, within the mechanical tolerances, one rigidly fastened with eight bolts on the base and the other one on the lid of the transducer. Before a thermal cycle at liquid helium temperature the two capacitances of the assembled transducer had both the value C = (1780 4- 1)pF and from these d a t a we deduce a value of the two gaps of d = (92.4 4- .1)#m and an upper limit for their relative difference Pd < 10 -3.
444 Cryogenics 1994Vol 34 ICECSupplement
ICEC 15 Proceedings
The two capacitance of the transducer are inserted in a bridge, in order to minimize the effect of the noise of variable electrical field generators (usually called e.m. p u m p s ) . The central arm of the bridge is a readout coil which, together with the bridge capacitances, constitutes the electrical oscillator at frequency v~ coupled to the mechanical resonator. All connections and the central coil are made of superconducting niobium wire. To improve the bridge balance we use a primary variable capacitance driven by an electrical motor and a high resolution variable capacitance driven by a piezoelectric stack. In view of low temperature operation, the construction and the assembling procedures of these variable capacitances are rather complex and they had required careful design and extensive testings. The wide range variable capacitor is composed of two coaxial cylinders butterfly shaped made of Stainless Steel AISI 304L and assembled with a vacuum gap of 100 #m. This value requires a high machining precision, because the entire structure is supported only along the axis. The inner cylinder is rotated by a d.c. electrical motor through a high gain gear to improve the resolution of the capacitance. Both the electrical motor and the driving gear have been carefully modified to operate at 4 K with good reliability. The high resolution variable capacitance is a parallel plate capacitor, having one armature driven by a piezoelectric ceramic stack. A piezoelectric ceramic gives a very sensitive way to vary the gap of the capacitance, however, its efficiency decreases from room to liquid helium temperature. This imposes a constraint on the maximum value of the gap allowed in order to have a variation range of the order of 1 pF. The whole system is in a vacuum chamber cooled to liquid helium temperature. [3]. The circuit is biased in the BAE configuration using two commercial frequency synthesizers HP 3326A tuned to frequencies u~ - u,~ and u~ + vm. The output of the pick up coil is sent to a commercial low noise amplifier PAR 113. The two quadrature components of the signal from the transducer at frequency v~ are demodulated by means of a lock-in amplifier with integration time to = O. 1 s and sampled by computer with the same sampling time. Results and conclusion We tested the mechanical behaviour of the push-pull transducer at 4 K measuring its main electromechanical characteristcs before inserting it in the detection scheme. In particular we measured the frequency of the first flexural mode of the disk Um= 927.9 Hz and the mechanical quality factor Q ~_ 3.106. The BAE system worked successfully,
Cryogenics 1994 Vo134 ICEC Supplement 445
ICEC 15 Proceedings
showing a satisfactory geometrical balance and a good stability of the electrical and geometrical parameters during the thermal cycles between room and liquid helium temperatures. The bridge readout circuit was biased at Eo " 5-104 V / m and balanced down to 0.8 ppm (correspondig to a AC _~ 10-15 F). An electrical quality factor Q~ _ 6 • 103 was measured at the electrical resonance frequency of ~c = 125 kHz. The test on the noise behaviour of the system shows a good quantitative agreement with the theoretical model. In the lego plot of fig. 2 the distribution of two quadrature components of the transducer output noise is shown. We notice that the distribution along one axis is larger than along the other, because only one component of the system is mechanically sensitive.
•
"
.4"
// ~,,s / . s.~," .~,.+ j
8 ! ~'F / / t " j ~.t .I" f"
5 3-
:
t
f. .1"
/"
~
..... 271
" ' / / " ~
' -
.2g~ _ o .
......... ]
P
• _0.4 41. $
Fig.2: Lego plot of the spectrum of the Y phase. By performing the Fourier spectra of the two components of the t~ransducer output, we notice that the spectrum of the Y component (see fig. 3) shows a narrow peak not present on the X component. As the BAE theory predicts, in absence of external excitation, this peak is clue only to the thermal noise of the mechanical harmonic oscillator. In the data plotted in fig. 3, this peak corresponds to a vibration amplitude <
Xthcv >--~ 2 10-15
m
in good agreement with the root meansquare value of the thermal fluctuation amplitude.
446 Cryogenics 1994Vol 34 ICEC Supplement
ICEC 15 Proceedings
According to the general analysis of a BAE system, used as a detector of impulsive interactions, the sensitivity of this kind of transducer depends on several parameters. It can be shown [4] that, using as current amplifier a dc Squid, the quantum limit can be acheived by increasing the strenght of the pump field at the level of 3.106 V/m, by lowering the temperature of the system in the mK range and by using FCXO quartz oscillators and/or notch filters at the input of the bridge circuit. SVy
[ v2~z]
1
0.7525
0.505
[ 0.2575
0.01 0.005
0.01
0.015
[Hz]
0.02
0.025
0.03
Fig.3: Plot of the spectrum of the Y phase. The dotted line is the theoretical prevision.
References [1] C. M. Caves, K. S. Thorne, R.W.P. Drever, V.D. Sandberg, M. Zimmerman, Rev. Mod. Phys., 52, 341 (1980). [2] C. Cinquegrana, E. Majorana, P. Rapagnani, F. Ricci, Phys.Rev. D
4s, 247s (1993). [3] E. Majorana, P. Rapagnani, F. Ricci, Meas. Sci. Technol., 3, 501, (1991)
[4] C. Cinquegrana, E. Majorana, N. Pergola, P. Puppo, P. Rapagnani, F. l~cci, Internal Report n. 1032 24/3/94, Physics Department ,"La Sapienza" University, Rome, Italy
Cryogenics 1994 Vol 34 ICEC Supplement
447