We present a direct measurement of the displacement noise spectrum of a macroscopic silicon flexure at room temperature. A cantilever attached to the 100 μm thick flexure holds a mirror which forms part of an optical cavity to enhance the displacement sensitivity to thermal noise. We predict the displacement noise spectrum using a simple model that assumes the dominant source of frequency-dependent loss is thermo-elastic damping and find good agreement with the experimental data. The measurement is consistent with a frequency-independent loss of combined with frequency-dependent thermo-elastic damping as the dominant losses. A crossover between the two that occurs well above the flexure resonant frequency allows a broadband measurement of the thermal noise of the silicon flexure. The flexure material, geometry, and measurement band are similar to those of planned future gravitational wave detectors.
References
1.
M.
Tse
, H.
Yu
, N.
Kijbunchoo
et al,“Quantum-enhanced advanced LIGO detectors in the era of gravitational-wave astronomy
,” Phys. Rev. Lett.
123
, 231107
(2019
).2.
LIGO Scientific Collaboration,
J.
Aasi
, B. P.
Abbott
, R.
Abbott
et al, “Advanced LIGO
,” Classical Quantum Gravity
32
, 074001
(2015
).3.
F.
Acernese
, M.
Agathos
, L.
Aiello
et al, “Increasing the astrophysical reach of the advanced virgo detector via the application of squeezed vacuum states of light
,” Phys. Rev. Lett.
123
, 231108
(2019
).4.
B. P.
Abbott
, R.
Abbott
, T. D.
Abbott
et al, “Observation of gravitational waves from a binary black hole merger
,” Phys. Rev. Lett.
116
, 061102
(2016
).5.
B. P.
Abbott
, R.
Abbott
, T. D.
Abbott
et al, “GW170817: Observation of gravitational waves from a binary neutron star inspiral
,” Phys. Rev. Lett.
119
, 161101
(2017
).6.
B. P.
Abbott
, R.
Abbott
, T. D.
Abbott
et al, “GWTC-1: A gravitational-wave transient catalog of compact binary mergers observed by LIGO and virgo during the first and second observing runs
,” Phys. Rev. X
9
, 031040
(2019
).7.
G. I.
González
and P. R.
Saulson
, “Brownian motion of a mass suspended by an anelastic wire
,” J. Acoust. Soc. Am.
96
, 207
(1994
).8.
D.
Reitze
, R. X.
Adhikari
, S.
Ballmer
et al, “Cosmic explorer: The U.S. contribution to gravitational-wave astronomy beyond LIGO
,” arXiv:1907.04833 (2019
).9.
M.
Punturo
, M.
Abernathy
, F.
Acernese
et al, “The Einstein Telescope: A third-generation gravitational wave observatory
,” Classical Quantum Gravity
27
, 19
(2010
).10.
The LIGO Scientific Collaboration, “
Instrument science white paper
,” LIGO Report No. T1900409 (The LIGO Scientific Collaboration
, 2019
).11.
S.
Rowan
, R. L.
Byer
, M. M.
Fejer
et al, “Test mass materials for a new generation of gravitational wave detectors,” Proc. SPIE
4856
, 292
–297
(2003
).12.
W.
Winkler
, K.
Danzmann
, A.
Ruediger
et al, “Heating by optical absorption and the performance of interferometric gravitational wave detectors
,” Phys. Rev. A
44
, 7022
–7036
(1991
).13.
R.
Nawrodt
, C.
Schwarz
, S.
Kroker
et al, “Investigation of mechanical losses of thin silicon flexures at low temperatures
,” Classical Quantum Gravity
30
, 115008
(2013
).14.
T. T.-H.
Nguyen
, C.
Mow-Lowry
, B. J. J.
Slagmolen
et al, “Frequency dependence of thermal noise in gram-scale cantilever flexures
,” Phys. Rev. D
92
(11
), 112004
(2015
).15.
M.
Kajima
, N.
Kusumi
, S.
Moriwaki
et al, “Wide-band measurement of mechanical thermal noise using a laser interferometer
,” Phys. Lett. A
263
, 21
(1999
).16.
K.
Yamamoto
, S.
Otsuka
, M.
Ando
et al, “Experimental study of thermal noise caused by an inhomogeneously distributed loss
,” Phys. Lett. A
280
, 289
(2001
).17.
P.
Paolino
and L.
Bellon
, “Frequency dependence of viscous and viscoelastic dissipation in coated microcantilevers from noise measurement
,” Nanotechnology
20
, 405705
(2009
).18.
T. T.-H.
Nguyen
, “Suspension thermal noise and opto-mechanics in gram-scale flexures
,” Ph.D. thesis (Australian National University
, 2015
).19.
See https://www.piezomechanik.com/ for Piezomechanik HPSt 1000/25-15/5.
20.
R. W. P.
Drever
, J. L.
Hall
, F. V.
Kowalski
et al, “Laser phase and frequency stabilisation using an optical resonator
,” Appl. Phys. B
31
, 97
(1983
).21.
E. D.
Black
, “An introduction to Pound–Drever–Hall laser frequency stabilization
,” Am. J. Phys.
69
, 79
(2001
).22.
J.
Winterflood
, “High performance vibration isolation for gravitational wave detection
,” Ph.D. thesis (University of Western Australia
2001
).23.
J.
Winterflood
, D. G.
Blair
, and B.
Slagmolen
, “High performance vibration isolation using springs in Euler column buckling mode
,” Phys. Lett. A
300
, 122
(2002
).24.
B. J. J.
Slagmolen
, “Direct Measurement of the spectral distribution of thermal noise
,” Ph.D. thesis (Australian National University
, 2005
).25.
See https://www.sigmaaldrich.com/AU/en/product/aldrich/z742916 for Liquinox.
26.
See https://www.masterbond.com/tds/ep30-2 for Masterbond.
27.
The PZT thermal noise is calculated using Eq. (1) with the following parameters: Q = 70, kHz, m = 11.5 g.
28.
P. R.
Saulson
, “Thermal noise in mechanical experiments
,” Phys. Rev. D
42
, 2437
(1990
).29.
R. F.
Greene
and H. B.
Callen
, “On a theorem of irreversible thermodynamics. II
,” Phys. Rev.
88
, 1387
(1952
).30.
M.
Cerdonio
, L.
Conti
, A.
Heidmann
et al, “Thermoelastic effects at low temperatures and quantum limits in displacement measurements
,” Phys. Rev. D
63
, 082003
(2001
).31.
I. W.
Martin
, R.
Bassiri1
, R.
Nawrodt
et al, “Effect of heat treatment on mechanical dissipation in Ta2O5 coatings
,” Class. Quantum Grav.
27
, 225020
(2010
).32.
P. A.
Altin
, T. T.-H.
Nguyen
, B. J. J.
Slagmolen
et al, “A robust single-beam optical trap for a gram-scale mechanical oscillator
,” Sci. Rep.
7
, 14546
(2017
).33.
H.
Yu
, L.
McCuller
, M.
Tse
et al, “Quantum correlations between light and the kilogram-mass mirrors of LIGO
,” Nature
583
, 43
–47
(2020
).34.
E. V.
Russell
, N. E.
Israeloff
, L. E.
Walther
et al, “Nanometer scale dielectric fluctuations at the glass transition
,” Phys. Rev. Lett.
81
, 1461
–1464
(1998
).35.
E.
Vidal Russell
and N. E.
Israeloff
, “Direct observation of molecular cooperativity near the glass transition
,” Nature
408
, 695
–698
(2000
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
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