Sapphire test-masses for measuring the standard quantum limit and achieving quantum non-demolition

M E Tobar, E N Ivanov, D K L Oi, B D Cuthbertson, D G Blair

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

In this paper rye show that the available technology is sufficient to measure the Standard Quantum Limit (SQL) of a low loss acoustic oscillator with a readout based on a microwave parametric transducer. The experiment makes use of the low electrical and acoustical losses in monocrystalline sapphire and new low-noise microwave technology. The crystal acts as an electrical vibration sensor and an acoustic oscillator in one monolithic structure. We analyze two new types of such structures: (1) The sapphire bar dielectric transducer and (2) the slotted sapphire dielectric transducer. We show that with a 40-60 dB double-cavity phase-noise suppression system the SQL may be measured using the sapphire bar. For the slotted structure, the phase noise requirements are less stringent because of its smaller resonant frequency and mass. We show that the SQL of this structure may be measured with a standard parametric readout. The principle of operation is demonstrated by some simple room-temperature experiments with all results verified using finite-element analysis.

Given that we call expect to measure the SQL with one of these schemes, we analyze the properties of a microwave displacement measurement system based upon a high-Q parametric transducer and a double-frequency oscillator. Such a readout system represents a practical implementation of a black action evasion (BAE) displacement sensor allowing the discrimination between the quadratures of the mechanical oscillator. We determine the set of conditions which allows the enhanced sensitivity with respect to the desired quadrature and suppressed sensitivity to the unwanted quadrature. We find that tuning of the BAE system at the particular quadrature of interest can be performed by varying the phase relationship between the microwave carriers available from the double-frequency oscillator. We establish the importance of having the frequency and the phase-control servos to maintain the optimal tuning of the micro-wave BAE readout system, as both the mechanical oscillator and the double-frequency pump oscillator are always subject to various sources of environmental interference.

LanguageEnglish
Pages153-166
Number of pages14
JournalApplied Physics B: Lasers and Optics
Volume64
Issue number2
DOIs
Publication statusPublished - Feb 1997

Fingerprint

sapphire
quadratures
oscillators
readout
transducers
mechanical oscillators
microwaves
tuning
servomotors
phase control
displacement measurement
acoustics
sensitivity
sensors
low noise
discrimination
resonant frequencies
Q factors
retarding
pumps

Keywords

  • gravitational wave detector
  • action evading measurement
  • harmonic oscillators
  • transducer
  • antenna

Cite this

Tobar, M E ; Ivanov, E N ; Oi, D K L ; Cuthbertson, B D ; Blair, D G . / Sapphire test-masses for measuring the standard quantum limit and achieving quantum non-demolition. In: Applied Physics B: Lasers and Optics. 1997 ; Vol. 64, No. 2. pp. 153-166.
@article{b6419f824e2f4dbcac92d29b218c6bdf,
title = "Sapphire test-masses for measuring the standard quantum limit and achieving quantum non-demolition",
abstract = "In this paper rye show that the available technology is sufficient to measure the Standard Quantum Limit (SQL) of a low loss acoustic oscillator with a readout based on a microwave parametric transducer. The experiment makes use of the low electrical and acoustical losses in monocrystalline sapphire and new low-noise microwave technology. The crystal acts as an electrical vibration sensor and an acoustic oscillator in one monolithic structure. We analyze two new types of such structures: (1) The sapphire bar dielectric transducer and (2) the slotted sapphire dielectric transducer. We show that with a 40-60 dB double-cavity phase-noise suppression system the SQL may be measured using the sapphire bar. For the slotted structure, the phase noise requirements are less stringent because of its smaller resonant frequency and mass. We show that the SQL of this structure may be measured with a standard parametric readout. The principle of operation is demonstrated by some simple room-temperature experiments with all results verified using finite-element analysis.Given that we call expect to measure the SQL with one of these schemes, we analyze the properties of a microwave displacement measurement system based upon a high-Q parametric transducer and a double-frequency oscillator. Such a readout system represents a practical implementation of a black action evasion (BAE) displacement sensor allowing the discrimination between the quadratures of the mechanical oscillator. We determine the set of conditions which allows the enhanced sensitivity with respect to the desired quadrature and suppressed sensitivity to the unwanted quadrature. We find that tuning of the BAE system at the particular quadrature of interest can be performed by varying the phase relationship between the microwave carriers available from the double-frequency oscillator. We establish the importance of having the frequency and the phase-control servos to maintain the optimal tuning of the micro-wave BAE readout system, as both the mechanical oscillator and the double-frequency pump oscillator are always subject to various sources of environmental interference.",
keywords = "gravitational wave detector, action evading measurement, harmonic oscillators, transducer, antenna",
author = "Tobar, {M E} and Ivanov, {E N} and Oi, {D K L} and Cuthbertson, {B D} and Blair, {D G}",
year = "1997",
month = "2",
doi = "10.1007/s003400050160",
language = "English",
volume = "64",
pages = "153--166",
journal = "Applied Physics B: Lasers and Optics",
issn = "0946-2171",
number = "2",

}

Sapphire test-masses for measuring the standard quantum limit and achieving quantum non-demolition. / Tobar, M E ; Ivanov, E N ; Oi, D K L ; Cuthbertson, B D ; Blair, D G .

In: Applied Physics B: Lasers and Optics, Vol. 64, No. 2, 02.1997, p. 153-166.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Sapphire test-masses for measuring the standard quantum limit and achieving quantum non-demolition

AU - Tobar, M E

AU - Ivanov, E N

AU - Oi, D K L

AU - Cuthbertson, B D

AU - Blair, D G

PY - 1997/2

Y1 - 1997/2

N2 - In this paper rye show that the available technology is sufficient to measure the Standard Quantum Limit (SQL) of a low loss acoustic oscillator with a readout based on a microwave parametric transducer. The experiment makes use of the low electrical and acoustical losses in monocrystalline sapphire and new low-noise microwave technology. The crystal acts as an electrical vibration sensor and an acoustic oscillator in one monolithic structure. We analyze two new types of such structures: (1) The sapphire bar dielectric transducer and (2) the slotted sapphire dielectric transducer. We show that with a 40-60 dB double-cavity phase-noise suppression system the SQL may be measured using the sapphire bar. For the slotted structure, the phase noise requirements are less stringent because of its smaller resonant frequency and mass. We show that the SQL of this structure may be measured with a standard parametric readout. The principle of operation is demonstrated by some simple room-temperature experiments with all results verified using finite-element analysis.Given that we call expect to measure the SQL with one of these schemes, we analyze the properties of a microwave displacement measurement system based upon a high-Q parametric transducer and a double-frequency oscillator. Such a readout system represents a practical implementation of a black action evasion (BAE) displacement sensor allowing the discrimination between the quadratures of the mechanical oscillator. We determine the set of conditions which allows the enhanced sensitivity with respect to the desired quadrature and suppressed sensitivity to the unwanted quadrature. We find that tuning of the BAE system at the particular quadrature of interest can be performed by varying the phase relationship between the microwave carriers available from the double-frequency oscillator. We establish the importance of having the frequency and the phase-control servos to maintain the optimal tuning of the micro-wave BAE readout system, as both the mechanical oscillator and the double-frequency pump oscillator are always subject to various sources of environmental interference.

AB - In this paper rye show that the available technology is sufficient to measure the Standard Quantum Limit (SQL) of a low loss acoustic oscillator with a readout based on a microwave parametric transducer. The experiment makes use of the low electrical and acoustical losses in monocrystalline sapphire and new low-noise microwave technology. The crystal acts as an electrical vibration sensor and an acoustic oscillator in one monolithic structure. We analyze two new types of such structures: (1) The sapphire bar dielectric transducer and (2) the slotted sapphire dielectric transducer. We show that with a 40-60 dB double-cavity phase-noise suppression system the SQL may be measured using the sapphire bar. For the slotted structure, the phase noise requirements are less stringent because of its smaller resonant frequency and mass. We show that the SQL of this structure may be measured with a standard parametric readout. The principle of operation is demonstrated by some simple room-temperature experiments with all results verified using finite-element analysis.Given that we call expect to measure the SQL with one of these schemes, we analyze the properties of a microwave displacement measurement system based upon a high-Q parametric transducer and a double-frequency oscillator. Such a readout system represents a practical implementation of a black action evasion (BAE) displacement sensor allowing the discrimination between the quadratures of the mechanical oscillator. We determine the set of conditions which allows the enhanced sensitivity with respect to the desired quadrature and suppressed sensitivity to the unwanted quadrature. We find that tuning of the BAE system at the particular quadrature of interest can be performed by varying the phase relationship between the microwave carriers available from the double-frequency oscillator. We establish the importance of having the frequency and the phase-control servos to maintain the optimal tuning of the micro-wave BAE readout system, as both the mechanical oscillator and the double-frequency pump oscillator are always subject to various sources of environmental interference.

KW - gravitational wave detector

KW - action evading measurement

KW - harmonic oscillators

KW - transducer

KW - antenna

U2 - 10.1007/s003400050160

DO - 10.1007/s003400050160

M3 - Article

VL - 64

SP - 153

EP - 166

JO - Applied Physics B: Lasers and Optics

T2 - Applied Physics B: Lasers and Optics

JF - Applied Physics B: Lasers and Optics

SN - 0946-2171

IS - 2

ER -