A Cryogenic Silicon Interferometer for
Gravitational-wave Detection
R. X. Adhikari
1,
∗
, K. Arai
1
, A. F. Brooks
1
, C. Wipf
1
, O. Aguiar
2
,
P. Altin
3
, B. Barr
4
, L. Barsotti
5
, R. Bassiri
6
, A. Bell
4
,
G. Billingsley
1
, R. Birney
7
, D. Blair
8
, E. Bonilla
6
, J. Briggs
4
,
D. D. Brown
9
, R. Byer
6
, H. Cao
9
, M. Constancio
2
, S. Cooper
10
,
T. Corbitt
11
, D. Coyne
1
, A. Cumming
4
, E. Daw
12
, R. DeRosa
13
,
G. Eddolls
4
, J. Eichholz
3
, M. Evans
5
, M. Fejer
6
, E. C. Ferreira
2
,
A. Freise
10
, V. V. Frolov
13
, S. Gras
5
, A. Green
14
, H. Grote
15
,
E. Gustafson
1
, E. D. Hall
5
, G. Hammond
4
, J. Harms
16
, G. Harry
17
,
K. Haughian
4
, D. Heinert
18
, M. Heintze
13
, F. Hellman
19
,
J. Hennig
20
, M. Hennig
20
, S. Hild
21
, J. Hough
4
, W. Johnson
11
,
B. Kamai
1
, D. Kapasi
3
, K. Komori
5
, D. Koptsov
22
, M. Korobko
23
,
W. Z. Korth
1
, K. Kuns
5
, B. Lantz
6
, S. Leavey
20
,
F. Magana-Sandoval
14
, G. Mansell
5
, A. Markosyan
6
,
A. Markowitz
1
, I. Martin
4
, R. Martin
24
, D. Martynov
10
,
D. E. McClelland
3
, G. McGhee
4
, T. McRae
3
, J. Mills
15
,
V. Mitrofanov
22
, M. Molina-Ruiz
19
, C. Mow-Lowry
10
, J. Munch
9
,
P. Murray
4
, S. Ng
9
, M. A. Okada
2
, D. J. Ottaway
9
, L. Prokhorov
10
,
V. Quetschke
25
, S. Reid
26
, D. Reitze
1
, J. Richardson
1
, R. Robie
1
,
I. Romero-Shaw
27
, R. Route
6
, S. Rowan
4
, R. Schnabel
23
,
M. Schneewind
20
, F. Seifert
28
, D. Shaddock
3
, B. Shapiro
6
,
D. Shoemaker
5
, A. S. Silva
2
, B. Slagmolen
3
, J. Smith
29
, N. Smith
1
,
J. Steinlechner
21
, K. Strain
4
, D. Taira
2
, S. Tait
4
, D. Tanner
14
,
Z. Tornasi
4
, C. Torrie
1
, M. Van Veggel
4
, J. Vanheijningen
8
,
P. Veitch
9
, A. Wade
3
, G. Wallace
26
, R. Ward
3
, R. Weiss
5
,
P. Wessels
20
, B. Willke
20
, H. Yamamoto
1
, M. J. Yap
3
, and C Zhao
8
1
LIGO, California Institute of Technology, Pasadena, CA 91125, USA
2
Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São
Paulo, Brazil
3
OzGrav, ANU Centre for Gravitational Astrophysics, Research Schools of Physics, and
Astronomy and Astrophysics, The Australian National University, Canberra, 2601,
Australia
4
SUPA, University of Glasgow, Glasgow G12 8QQ, UK
5
LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
6
Stanford University, Stanford, CA 94305, USA
7
SUPA, University of the West of Scotland, Paisley Scotland PA1 2BE, UK
8
OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia
9
OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia
arXiv:2001.11173v2 [astro-ph.IM] 10 Jun 2020
A Cryogenic Silicon Interferometer for Gravitational-wave Detection
2
10
University of Birmingham, Birmingham B15 2TT, UK
11
Louisiana State University, Baton Rouge, LA 70803, USA
12
The University of Sheffield, Sheffield S10 2TN, UK
13
LIGO Livingston Observatory, Livingston, LA 70754, USA
14
University of Florida, Gainesville, FL 32611, USA
15
Cardiff University, Cardiff CF24 3AA, UK
16
Gran Sasso Science Institute (GSSI), I-67100 L’Aquila, Italy
17
American University, Washington, D.C. 20016, USA
18
Institut für Festkörperphysik, Friedrich-Schiller-Universität Jena, D-07743 Jena,
Germany
19
University of California, Berkeley, CA 94720, USA
20
Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167
Hannover, Germany
21
Maastricht University, Duboisdomein 30, Maastrich Limburg 6200MD, Netherlands
22
Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
23
Universität Hamburg, D-22761 Hamburg, Germany
24
Montclair State University, Montclair, NJ 07043, USA
25
The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA
26
SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom
27
OzGrav, School of Physics and Astronomy, Monash University, Clayton 3800,
Victoria, Australia
28
National Institute of Standards and Technology (NIST), 100 Bureau Drive Stop 8171,
Gaithersburg, MD 20899, USA
29
California State University Fullerton, Fullerton, CA 92831, USA
∗
Corresponding author:
rana@caltech.edu
Abstract.
The detection of gravitational waves from compact binary mergers by LIGO
has opened the era of gravitational wave astronomy, revealing a previously hidden side
of the cosmos. To maximize the reach of the existing LIGO observatory facilities, we
have designed a new instrument able to detect gravitational waves at distances 5 times
further away than possible with Advanced LIGO, or at greater than 100 times the event
rate. Observations with this new instrument will make possible dramatic steps toward
understanding the physics of the nearby universe, as well as observing the universe
out to cosmological distances by the detection of binary black hole coalescences. This
article presents the instrument design and a quantitative analysis of the anticipated
noise floor.
CONTENTS
3
Contents
1 Introduction
5
1.1 Justification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.2 Design overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.3 Article overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
2 Test Masses
11
2.1 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Size and composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Phase noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6 Thermal lensing and active wavefront control . . . . . . . . . . . . . . . . . 15
3 Optical Coatings
17
3.1 Basic optical requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Brownian noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.1 Amorphous Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.2 Crystalline coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Optical absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 Choice of Laser Wavelength
22
4.1 Quantum limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.1.1 Photodetector quantum efficiency . . . . . . . . . . . . . . . . . . . . . 22
4.2 Noise Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2.1 Coating thermal noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2.2 Optical scatter loss and noise . . . . . . . . . . . . . . . . . . . . . . . 23
4.2.3 Residual gas noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.3 Absorption and Impact on Cryogenics . . . . . . . . . . . . . . . . . . . . . . 24
4.3.1 Absorption in the HR coatings . . . . . . . . . . . . . . . . . . . . . . . 24
4.3.2 Absorption in the test mass substrate . . . . . . . . . . . . . . . . . . 24
4.3.3 Absorption in auxiliary fused silica components . . . . . . . . . . . . 24
4.4 Radiation Pressure Instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.4.1 Opto-Mechanical Angular Instability . . . . . . . . . . . . . . . . . . 25
4.4.2 Parametric Instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5 Quantum Noise
29
5.1 Squeezed vacuum generation for 2000 nm . . . . . . . . . . . . . . . . . . . . 29
5.2 Filter Cavities for Input Squeezing . . . . . . . . . . . . . . . . . . . . . . . . 30
5.3 Loss Control: General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.4 Loss Control: Quantum efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 32
CONTENTS
4
5.4.1 Extended InGaAs photodetectors . . . . . . . . . . . . . . . . . . . . . 32
5.4.2 HgCdTe (MCT) photodetectors . . . . . . . . . . . . . . . . . . . . . . 33
5.4.3 InAsSb photodetectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6 Suspensions
34
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
6.2 Suspension design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
6.3 Fabrication of a monolithic silicon final stage . . . . . . . . . . . . . . . . . . 35
6.3.1 Production of silicon ribbons . . . . . . . . . . . . . . . . . . . . . . . . 36
6.3.2 Hydroxide-catalysis bonding of the final stage . . . . . . . . . . . . . 36
6.3.3 Vertical suspension isolation . . . . . . . . . . . . . . . . . . . . . . . . 37
6.4 Suspension thermal noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
7 Laser Technology
39
7.1 Laser requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
7.1.1 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
7.1.2 Remaining requirements . . . . . . . . . . . . . . . . . . . . . . . . . . 40
7.2 Laser candidate technologies and examples . . . . . . . . . . . . . . . . . . . 40
7.2.1 Single-frequency, low-noise source . . . . . . . . . . . . . . . . . . . . 41
7.2.2 High power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
7.3 Summary of laser prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
8 Configurations
43
9 Conclusion
44
Appendices
45
A Cryogenics
45
A.1 Heat Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
A.1.1 Absorption of the laser beam . . . . . . . . . . . . . . . . . . . . . . . 45
A.1.2 Ambient environmental heating of the test mass . . . . . . . . . . . 46
A.2 Radiative cooling of the test mass . . . . . . . . . . . . . . . . . . . . . . . . . 47
A.2.1 Cold Shields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Introduction
5
1. Introduction
The first detection of gravitational waves (GW) from the object GW150914 [1] by the
Advanced LIGO (aLIGO) detectors inaugurated a new field of study: gravitational
wave astronomy. The subsequent detection of a binary neutron star merger [2] has
highlighted the possibilities of this new field.
GW detectors provide a probe of physics in a new regime. They offer the best
information about the extremely warped spacetime around black holes, exotic nuclear
matter in neutron stars, and, within the next decade, a unique probe of cosmology at
high redshifts.
The current LIGO detectors will approach the thermodynamic and quantum
mechanical limits of their designs within a few years. Over the next several years,
aLIGO will undergo a modest upgrade, designated “A+”. The aim of this upgrade is
chiefly to lower the quantum (shot) noise through the use of squeezed light, and also
to reduce somewhat the thermal noise from the mirror coatings. This upgrade has the
goal of enhancing the sensitivity by
∼
50% [3].
In this article, we describe a more substantial upgrade, called “LIGO Voyager”,
that will increase the range by a factor of 4 – 5 over aLIGO, and the event rate by
approximately 100 times, to roughly one detection per hour. Such a dramatic change
in the sensitivity should increase the detection rate of binary neutron star mergers to
about 10 per day and the rate of binary black hole mergers to around 30 per day. This
upgraded instrument would be able to detect binary black holes out to a redshift of 8.
The path to LIGO Voyager requires reducing several noise sources, including:
(i) quantum radiation pressure and shot noise,
(ii) mirror thermal noise,
(iii) mirror suspension thermal noise,
(iv) Newtonian gravity noise
All of these noise sources are addressed by the LIGO Voyager design, with the goal of
commissioning and observational runs within a decade.
1.1. Justification
The most significant design changes in LIGO Voyager versus Advanced LIGO can be
traced to the need to reduce the quantum noise in tandem with the mirror thermal
noise.
•
Quantum noise will be reduced by increasing the optical power stored in the arms.
In Advanced LIGO, the stored power is limited by thermally induced wavefront
distortion effects in the fused silica test masses. These effects will be alleviated by
choosing a test mass material with a high thermal conductivity, such as silicon.
•
The test mass temperature will be lowered to 123 K, to mitigate thermo-elastic
noise. This species of thermal noise is especially problematic in test masses
Introduction
6
that are good thermal conductors. Fortunately, in silicon at 123 K, the thermal
expansion coefficient crosses zero, which eliminates thermo-elastic noise. (Other
plausible material candidates, such as sapphire, require cooling to near 0 K to be
free of this noise.)
•
The thermal noise of the mirror coating will be reduced by switching to low
dissipation amorphous silicon based coatings, and by reducing the temperature.
Achieving low optical absorption in the amorphous silicon coatings requires an
increased laser wavelength.
1.2. Design overview
The LIGO Voyager design is illustrated in Figure 1, with critical parameters called
out in Table 1.
The dual-recycled, Fabry-Perot Michelson topology is similar to
Advanced LIGO and A+, with the following additional upgrades. Optical coatings
on the cryogenically-cooled (123 K) test masses will be made from amorphous silicon,
with the lower coating mechanical loss and cryogenic operation reducing the coating
thermal noise. The 200 kg test-masses will be made of crystalline silicon (rather
than fused silica). The absorption spectrum of the test mass materials requires us to
choose a longer wavelength laser. The longer wavelength will also significantly reduce
optical scattering from the mirrors, lowering losses and allowing for higher finesse arm
cavities. The quantum noise (shot noise and radiation pressure) will be reduced by a
combination of frequency-dependent squeezing, heavier test masses, and higher stored
power in the arms. Finally, the environmentally produced Newtonian gravitational
noise [4] will be reduced using seismometer arrays combined with adaptive noise
regression [5, 6].
The LIGO Voyager noise budget and resulting design sensitivity are shown in
Figure 2. Horizon distances for astrophysical sources are illustrated in Figure 3a and
Figure 3b, showing the improvement over the Advanced LIGO design.
Although most optical components will need to be changed to handle the new
wavelength, we plan on reusing the Advanced LIGO hardware and infrastructure
wherever possible (for example, the seismic isolation platforms, vacuum systems,
electronics and infrastructure).
1.3. Article overview
This article presents a detailed description of the LIGO Voyager design with the goals
of (a) investigating the feasibility of all the required technology, largely illustrated in
Figure 1, and highlighting those technological areas that require further research and
(b) describing all the key noise contributions illustrated in the noise budget in Figure 2
(and thus determining the LIGO Voyager sensitivity).
‡
1/
e
2
intensity
§
Round-trip loss; see section 5.2
Introduction
7
Filter cavity
PSL
λ
=2000 nm
PRM
3.1kW
152W
3MW
FCFI
ITMX
ETMY
ETMX
ITMY
BS
SQZ
OFI
SRM
Balanced
homodyne
detection
cryogenic
shields
⨉
4 200 kg silicon test mass
with amorphous silicon coating
cooled down to 123K
4km
FP cavity
arm
4km FP cavity arm
silicon
compensation plates
OMC2
OMC1
F
IGURE
1:
A simplified schematic layout of LIGO Voyager. Dual-recycled Fabry-Perot Michelson
(DRFPMI) with frequency dependent squeezed light injection. The beam from a 2μm pre-
stabilized laser (PSL), passes through an input mode cleaner (IMC) and is injected into
the DRFPMI via the power-recycling mirror (PRM). Signal bandwidth is shaped via the
signal recycling mirror (SRM). A squeezed vacuum source (SQZ) injects this vacuum into
the DRFPMI via an output Faraday isolator (OFI) after it is reflected off a filter-cavity to
provide frequency dependent squeezing. A Faraday isolator (FCFI) facilitates this coupling
to the filter cavity. The output from the DRFPMI is incident on a balanced homodyne
detector, which employs two output mode cleaner cavities (OMC1 and OMC2) and the
local oscillator light picked off from the DRFPMI. Cold shields surround the input and end
test masses in both the X and Y arms (ITMX, ITMY, ETMX and ETMY) to maintain a
temperature of 123 K in these optics. The high-reflectivity coatings of the test masses are
made from amorphous silicon.
Introduction
8
10
1
10
2
10
3
Frequency [Hz]
10
−
25
10
−
24
10
−
23
10
−
22
Strain [1/
√
Hz]
aLIGO O3
aLIGO
A+
Quantum Vacuum:
P
in
= 152 W;
ζ
sqz
= 10 dB
Seismic: aLIGO/10
Newtonian Gravity: 10x subtraction
Suspension Thermal: 123 K Si blades & ribbons
Coating Brownian:
α
-Si:SiO
2
φ
coat
= 5
.
5e-5
Substrate Thermo-Refractive
Substrate Brownian: 123 K Si mirror (200 kg)
Residual Gas: 3 nTorr of H
2
Total
F
IGURE
2:
LIGO Voyager noise curve compared to Advanced LIGO during O3, and the Advanced
LIGO and A+ design goals.
The structure of the paper is as follows. In Section 2, we examine the feasibility of
using large, cryogenically-cooled (123 K) silicon test masses and identify the substrate
thermo-refractive noise, shown in the noise budget, as the limiting noise source
associated with the test mass. Section 3 describes an amorphous-silicon based coating
design that delivers the coating Brownian noise curve shown in the noise budget
and also identifies coating absorption as a key obstacle that must be overcome. The
numerous factors that enter into the choice of 2000 nm as the laser wavelength are
described in detail in Section 4. Quantum noise as a limiting noise source and the
feasibility of injecting 10 dB of frequency-dependent squeezed vacuum at 2000 nm
are considered in Section 5. The suspension thermal noise (associated with the use
of silicon blades and ribbons) is described in Section 6. This section also explores
the practicality of manufacturing these silicon blades and ribbons. In Section 7, we
review the development of mid-IR laser sources and find no significant impediment to
producing a thulium- or holmium-based 220 W, low-noise, single-frequency, 2000 nm
laser within the next 10 years. Section 8 explores configurations of LIGO Voyager
that are optimized for high-frequency astrophysical sources, given the considerable
tunability of the quantum noise curve and interferometer optical configuration. Finally,
cryogenic considerations are discussed in Section A.