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 ϕ0,fi=1.6×105 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.

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
).
27.
The PZT thermal noise is calculated using Eq. (1) with the following parameters: Q = 70, ω0=2π×40 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
).
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