XXXX-XXXX

1]Graduate School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama,
Meguro-ku, Tokyo 152-8551, Japan 2]LIGO Laboratory , California Institute of
Technology, 1200 East California Boulevard, Pasadena, CA 91125, USA
3]Gravitational Wave Science Project, National Astronomical Observatory of
Japan (NAOJ), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan 4]Advanced
Technology Center, National Astronomical Observatory of Japan (NAOJ), 2-21-1
Osawa, Mitaka City, Tokyo 181-8588, Japan 5]Department of Physics, The
University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 6]Research
Center for the Early Universe (RESCEU), The University of Tokyo, 7-3-1 Hongo,
Bunkyo-ku, Tokyo 113-0033, Japan 7]Earthquake Research Institute, The
University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan
8]Department of Mathematics and Physics, Hirosaki University, Hirosaki City,
Aomori 036-8561, Japan 9]Kamioka Branch, National Astronomical Observatory of
Japan (NAOJ), 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan
10]The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa,
Mitaka City, Tokyo 181-8588, Japan 11]Korea Institute of Science and
Technology Information (KISTI), 245 Daehak-ro, Yuseong-gu, Daejeon 34141,
Republic of Korea 12]National Institute for Mathematical Sciences, 70 Yuseong-
daero, 1689 Beon-gil, Yuseong-gu, Daejeon 34047, Republic of Korea 13]School
of High Energy Accelerator Science, The Graduate University for Advanced
Studies (SOKENDAI), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan
14]Department of Physics, Syracuse University, 900 South Crouse Ave. Syracuse,
NY 13244, USA 15]Department of Astronomy, Beijing Normal University,
Xinjiekouwai Street 19, Haidian District, Beijing 100875, China 16]
Laboratoire Astro Particulea and Cosmology, Universite de Paris, 10, rue Alice
Domon et Leonie Duquet, 75013 Paris, France 17]Department of Applied Physics,
Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180,
Japan 18]Department of Physics, Tamkang University, No. 151, Yingzhuan Rd.,
Danshui Dist., New Taipei City 25137, Taiwan 19]Department of Physics and
Institute of Astronomy, National Tsing Hua University, No. 101 Section 2,
Kuang-Fu Road, Hsinchu 30013, Taiwan 20]Department of Physics, Center for High
Energy and High Field Physics, National Central University, No.300, Zhongda
Rd, Zhongli District, Taoyuan City 32001, Taiwan 21]Department of Physics,
National Tsing Hua University, No. 101 Section 2, Kuang-Fu Road, Hsinchu
30013, Taiwan 22]Institute of Physics, Academia Sinica, 128 Sec. 2, Academia
Rd., Nankang, Taipei 11529, Taiwan 23]LIGO Hanford Observatory, Richland,
Washington 99352, USA 24]LIGO Livingston Observatory, Livingston, Louisiana
70754, USA 25]Department of Applied Physics, The University of Tokyo, 7-3-1
Hongo, Bunkyo-ku, Tokyo 113-8656, Japan 26]Univ. Grenoble Alpes, Laboratoire
d’Annecy de Physique des Particules (LAPP), , Université Savoie Mont Blanc,
CNRS/IN2P3, F-74941 Annecy, France 27]Department of Astronomy, The University
of Tokyo, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan 28]Faculty of
Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata
City, Niigata 950-2181, Japan 29]Department of Physics, Graduate School of
Science, Osaka City University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka
City, Osaka 558-8585, Japan 30]State Key Laboratory of Magnetic Resonance and
Atomic and Molecular Physics, Innovation Academy for Precision Measurement
Science and Technology (APM), Chinese Academy of Sciences, West No. 30, Xiao
Hong Shan, Wuhan 430071, China 31]Department of Physics, Ulsan National
Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan
44919, Republic of Korea 32]Shanghai Astronomical Observatory, Chinese Academy
of Sciences, 80 Nandan Road, Shanghai 200030, China 33]Institute for Cosmic
Ray Research (ICRR), KAGRA Observatory, The University of Tokyo, 5-1-5
Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan 34]Faculty of Science,
University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan
35]Institute for Cosmic Ray Research (ICRR), KAGRA Observatory, The University
of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan
36]College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino
City, Chiba 275-8575, Japan 37]Institute of Astronomy, National Tsing Hua
University, No. 101 Section 2, Kuang-Fu Road, Hsinchu 30013, Taiwan
38]Department of Astronomy & Space Science, Chungnam National University, 9
Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea 39]Department of
Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara
City, Kanagawa 252-5258, Japan 40]Kavli Institute for Astronomy and
Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing
100871, China 41]Graduate School of Science and Engineering, University of
Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan 42]Nambu Yoichiro
Institute of Theoretical and Experimental Physics (NITEP), Osaka City
University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City, Osaka 558-8585,
Japan 43]Japan Aerospace Exploration Agency, Institute of Space and
Astronautical Science, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara City, Kanagawa
252-5210, Japan 44]Department of Physics, Ewha Womans University, 52
Ewhayeodae, Seodaemun-gu, Seoul 03760, Republic of Korea 45]National
Astronomical Observatories, Chinese Academic of Sciences, 20A Datun Road,
Chaoyang District, Beijing, China 46]School of Astronomy and Space Science,
University of Chinese Academy of Sciences, 20A Datun Road, Chaoyang District,
Beijing, China 47]Institute for Cosmic Ray Research (ICRR), The University of
Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan 48]Faculty of
Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555,
Japan 49]Department of Physics, Myongji University, , Yongin 17058, Republic
of Korea 50]Department of Computer Simulation, Inje University, 197 Inje-ro,
Gimhae, Gyeongsangnam-do 50834, Republic of Korea 51]Institute of Particle and
Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK),
1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan 52]School of Physics and
Astronomy, Cardiff University, The Parade, Cardiff, CF24 3AA, UK 53]Instituto
de Fisica Teorica, C/ Nicolas Cabrera, 13-15, 28049 Madrid, Spain
54]Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku,
Nagoya, Aichi 464-8602, Japan 55]Department of Physics, National Cheng Kung
University, No.1, University Road, Tainan City 701, Taiwan 56]School of
Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District,
Wuhan, Hubei, 430072, China 57]National Center for High-performance computing,
National Applied Research Laboratories, No. 7, R&D 6th Rd., Hsinchu Science
Park, Hsinchu City 30076, Taiwan 58]Department of Physics, National Taiwan
Normal University, 88 Ting-Chou Rd. , sec. 4, Taipei 116, Taiwan 59]Istituto
Nazionale di Fisica Nucleare (INFN), Universita di Roma ”La Sapienza”, P.le A.
Moro 2, 00185 Roma, Italy 60]Institute for Photon Science and Technology, The
University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan
61]Department of Physics, University of Wisconsin-Milwaukee, , Milwaukee, WI
53201, USA 62]Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho,
Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan 63]Department of Physics,
University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556,
USA 64]Graduate School of Science and Technology, Niigata University, 8050
Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan 65]Scuola
Normale Superiore Pisa, Piazza dei Cavalieri, 7-56126, Pisa, Italy 66]Sezione
di Pisa, Istituto Nazionale di Fisica Nucleare (INFN), , I-56127 Pisa, Italy
67]Technology Center for Astronomy and Space Science, Korea Astronomy and
Space Science Institute (KASI), 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055,
Republic of Korea 68]Department of Electronic Control Engineering, National
Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City,
Niigata 940-8532, Japan 69]Faculty of Science, Toho University, 2-2-1 Miyama,
Funabashi City, Chiba 274-8510, Japan 70]Graduate School of Science and
Technology, Gunma University, 4-2 Aramaki, Maebashi, Gunma 371-8510, Japan
71]Institute for Quantum Studies, Chapman University, 1 University Dr.,
Orange, CA 92866, USA 72]Accelerator Laboratory, High Energy Accelerator
Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan
73]Faculty of Information Science and Technology, Osaka Institute of
Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan
74]Department of Space and Astronautical Science, The Graduate University for
Advanced Studies (SOKENDAI), 3-1-1 Yoshinodai, Chuo-ku, Sagamihara City,
Kanagawa 252-5210, Japan 75]Centre for Cosmology, Particle Physics and
Phenomenology - CP3, Universite catholique de Louvain, 2, Chemin du Cyclotron
- Box L7.01.05, B-1348 Louvain-la-Neuve, Belgium 76]Research Center for Space
Science, Advanced Research Laboratories, Tokyo City University, 8-15-1
Todoroki, Setagaya, Tokyo 158-0082, Japan 77]Institute for Cosmic Ray Research
(ICRR), Research Center for Cosmic Neutrinos (RCCN), The University of Tokyo,
5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan 78]Department of
Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City,
Kyoto 606-8502, Japan 79]Yukawa Institute for Theoretical Physics (YITP),
Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto
606-8502, Japan 80]Sezione di Napoli, Istituto Nazionale di Fisica Nucleare
(INFN), Strada Comunale Cinthia, 80126 Napoli (NA), Italy 81]Faculty of
Science, Department of Physics, The Chinese University of Hong Kong, Shatin,
N.T., Hong Kong 82]Applied Research Laboratory, High Energy Accelerator
Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan
83]Department of Communications Engineering, National Defense Academy of
Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan
84]Department of Physics, University of Florida, , Gainesville, FL 32611, USA
85]Department of Information and Management Systems Engineering, Nagaoka
University of Technology, 1603-1 Kamitomioka, Nagaoka City, Niigata 940-2188,
Japan 86]Department of Physics and Astronomy, Sejong University, 209
Neungdong-ro, Gwangjin-gu, Seoul 143-747, Republic of Korea 87]Department of
Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street,
Hsinchu, Taiwan 88]Department of Physics, Rikkyo University, 3-34-1
Nishiikebukuro, Toshima-ku, Tokyo 171-8501, Japan 89]International Centre for
Theoretical Physics Asia-Pacific, University of Chinese Academy of Sciences,
100190 Beijing, China

KAGRA Collaboration

# Performance of the KAGRA detector during the first joint observation with
GEO 600 (O3GK)

H. Abe  R. X. Adhikari  T. Akutsu  M. Ando  A. Araya  N. Aritomi  H. Asada  Y.
Aso  S. Bae  Y. Bae  R. Bajpai  S. W. Ballmer  K. Cannon  Z. Cao  E. Capocasa
M. Chan  C. Chen  D. Chen  K. Chen  Y. Chen  C-Y. Chiang  Y-K. Chu  J. C.
Driggers  S. E. Dwyer  A. Effler  S. Eguchi  M. Eisenmann  Y. Enomoto  R.
Flaminio  H. K. Fong  V. V. Frolov  Y. Fujii  Y. Fujikawa  Y. Fujimoto  M.
Fukushima  D. Gao  G.-G. Ge  S. Ha  I. P. W. Hadiputrawan  S. Haino  W.-B. Han
K. Hasegawa  K. Hattori  H. Hayakawa  K. Hayama  Y. Himemoto  N. Hirata  C.
Hirose  T-C. Ho  B-H. Hsieh  H-F. Hsieh  C. Hsiung  H-Y. Huang  P. Huang  Y-C.
Huang  Y.-J. Huang  D. C. Y. Hui  S. Ide  B. Ikenoue  K. Inayoshi  Y. Inoue
K. Ito  Y. Itoh  K. Izumi  C. Jeon  H.-B. Jin  K. Jung  P. Jung  K. Kaihotsu
T. Kajita  M. Kakizaki  M. Kamiizumi  N. Kanda  T. Kato  K. Kawabe  K.
Kawaguchi  C. Kim  J. Kim  J. C. Kim  Y.-M. Kim  N. Kimura  Y. Kobayashi  K.
Kohri  K. Kokeyama<EMAIL_ADDRESS>A. K. H. Kong  N. Koyama  C.
Kozakai  J. Kume  Y. Kuromiya  S. Kuroyanagi  K. Kwak  E. Lee  H. W. Lee  R.
Lee  M. Leonardi  K. L. Li  P. Li  L. C.-C. Lin  C-Y. Lin  E. T. Lin  F-K. Lin
F-L. Lin  H. L. Lin  G. C. Liu  L.-W. Luo  M. Ma’arif  E. Majorana  Y.
Michimura  N. Mio  O. Miyakawa  K. Miyo  S. Miyoki  Y. Mori  S. Morisaki  N.
Morisue  Y. Moriwaki  A. Mullavey  K. Nagano  K. Nakamura  H. Nakano  M.
Nakano  Y. Nakayama  T. Narikawa  L. Naticchioni  L. Nguyen Quynh  W.-T. Ni
T. Nishimoto  A. Nishizawa  S. Nozaki  Y. Obayashi  Y. Obuchi  W. Ogaki  J. J.
Oh  K. Oh  M. Ohashi  T. Ohashi  M. Ohkawa  H. Ohta  Y. Okutani  K. Oohara  S.
Oshino  S. Otabe  K.-C. Pan  A. Parisi  J. Park  F. E. Peña Arellano  S. Saha
S. Saito  Y. Saito  K. Sakai  T. Sawada  Y. Sekiguchi  L. Shao  Y. Shikano  H.
Shimizu  R. Shimizu  K. Shimode  H. Shinkai  T. Shishido  A. Shoda  K. Somiya
I. Song  R. Sugimoto  J. Suresh  T. Suzuki  T. Suzuki  T. Suzuki  H. Tagoshi
H. Takahashi  R. Takahashi  S. Takano  H. Takeda  M. Takeda  M. Tamaki  K.
Tanaka  T. Tanaka  T. Tanaka  S. Tanioka  A. Taruya  T. Tomaru  T. Tomura  L.
Trozzo  T. Tsang  J-S. Tsao  S. Tsuchida  T. Tsutsui  T. Tsuzuki  D.
Tuyenbayev  N. Uchikata  T. Uchiyama  A. Ueda  T. Uehara  K. Ueno  G. Ueshima
F. Uraguchi  T. Ushiba  M. H. P. M. van Putten  J. Wang  T. Washimi
<EMAIL_ADDRESS>C. Wu  H. Wu  T. Yamada  K. Yamamoto
<EMAIL_ADDRESS>T. Yamamoto  K. Yamashita  R. Yamazaki  Y. Yang
S.-W. Yeh  J. Yokoyama  T. Yokozawa  T. Yoshioka  H. Yuzurihara  S. Zeidler
M. Zhan  H. Zhang  Y. Zhao  Z.-H. Zhu  [  [  [  [  [  [  [  [  [  [  [  [  [
[  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [
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###### Abstract

KAGRA, the kilometer-scale underground gravitational-wave detector, is located
at Kamioka, Japan. In April 2020, an astrophysics observation was performed at
the KAGRA detector in combination with the GEO 600 detector; this observation
operation is called O3GK. The optical configuration in O3GK is based on a
power recycled Fabry-Pérot Michelson interferometer; all the mirrors were set
at room temperature. The duty factor of the operation was approximately 53%,
and the strain sensitivity was $3\times 10^{-22}$ $/\sqrt{\rm{Hz}}$ at 250 Hz.
In addition, the binary-neutron-star (BNS) inspiral range was approximately
0.6 Mpc. The contributions of various noise sources to the sensitivity of O3GK
were investigated to understand how the observation range could be improved;
this study is called a “noise budget.” According to our noise budget, the
measured sensitivity could be approximated by adding up the effect of each
noise. The sensitivity was dominated by noise from the sensors used for local
controls of the vibration isolation systems, acoustic noise, shot noise, and
laser frequency noise. Further, other noise sources that did not limit the
sensitivity were investigated. This paper provides a detailed account of the
KAGRA detector in O3GK including interferometer configuration, status, and
noise budget. In addition, strategies for future sensitivity improvements such
as hardware upgrades, are discussed.

F32

##  1 Introduction

In 2015, the era of gravitational-wave (GW) astrophysics began when the
Advanced Laser Interferometer Gravitational-Wave Observatory (Advanced LIGO)
detectors observed a binary black hole merger Abbott et al. [2016] in their
first observing run (O1). In addition, a binary neutron star merger was
detected by the Advanced LIGO and Advanced Virgo detectors Abbott et al.
[2017] in their second observing run (O2). With improved astrophysical
sensitivity, 35 candidate GWs, including neutron star-black hole binary
mergers Abbott et al. [2021a] and extremely unbalanced mass binary mergers
Abbott et al. [2020] were discovered in the second half of the third observing
run (O3b) Abbott et al. [2021b].

The KAGRA detector is the world’s fourth large-scale GW detector located in
Japan Akutsu et al. [2019a, 2021a]. Two distinctive features of KAGRA include
the use of cryogenic mirrors to reduce thermal noise and its construction at
the underground site to isolate from seismic motions are two distinctive
features of KAGRA. The project was funded in 2010, and the underground tunnel
excavation was completed in 2014 Uchiyama et al. [2014]. In October 2015,
significant infrastructure installation was completed. The KAGRA detector
commissioning that aimed at the first astronomical observation commenced after
the cryogenic test operation in 2018 Akutsu et al. [2019b]. The detector noise
was reduced by 4.5 orders of magnitude by this commissioning Akutsu et al.
[2021a]. After the commissioning, the KAGRA detector was continuously operated
for the observing run from 8:00 UTC on April 7 to 0:00 UTC on April 21, 2020.
Initially, KAGRA had planned to join the LIGO-Virgo O3 observation. However,
while KAGRA was still under commission, O3 was suspended on March 27, 2020,
because of the COVID-19 pandemic. Fortunately, the GEO 600 detector Dooley et
al. [2016], Lough et al. [2021] was online when KAGRA initiated the observing
run. Thus, we could conduct a joint observation GEO 600-KAGRA (O3GK). During
O3GK, the binary-neutron-star (BNS) range, which is the observable distance of
gravitational wave from binary-neutron-star coalescence Finn and Chernoff
[1993], of the detectors KAGRA and GEO 600 were 0.6 Mpc and 1.0 Mpc in the
median, respectively LVK [2022].

This study discusses the performance of the KAGRA detector in O3GK, which
considers the limiting factors of the sensitivity. It is essential to argue
the possible noise reduction strategies for the subsequent observing runs to
improve the detector sensitivity to contribute to the astrophysical searches.

##  2 Overview of the KAGRA detector configuration during O3GK

The optical configuration of the KAGRA detector, sensing and control sequence
for the operation, calibration scheme, and operational status during O3GK are
explained in this section as an introduction to the noise coupling topic
discussed in Section 3.

###  2.1 Interferometer configuration during O3GK

Figure 1: Schematic of the KAGRA interferometer. A pre-stabilized laser (PSL)
acquires phase modulation sidebands at 16.87 MHz and 45.00 MHz in the super-
clean PSL room for signal extraction techniques (such as the Pound-Drever-Hall
method Drever et al. [1983]). Thereafter, using a triangular input-mode
cleaner (IMC), the beam is spatially cleaned. An input Faraday isolator (IFI)
is used to prevent the laser beam from returning to the PSL from the main
interferometer. The input mode-matching telescope (IMMT) mirrors shape the
laser spatial mode to match with the main interferometer. The power-recycling
mirrors (PRM, PR2, and PR3), beam splitter (BS), and input test masses (ITMX
and ITMY) form the power recycling cavity (PRC) to enhance the laser power
inside the interferometer. The BS is used to split the beam into two in the X
and Y directions. The input test mass X (ITMX), end test mass X (ETMX), input
test mass Y (ITMY), and end test mass Y (ETMY) form the 3-km Fabry–Pérot
cavities in the X and Y arms, respectively. The two signal-recycling mirrors
(SR2 and SR3) served only as the steering mirrors in O3GK. The SRM (with 30%
power transmittance) was installed at downstream of the SR2; however, it is
misaligned to prevent a cavity formation in O3GK, and it is not shown in this
figure. The output mode-matching telescopes (OMMTs) match the spatial mode
with the output mode-cleaner (OMC) that cleans the spatial mode and rejects
unwanted RF sideband fields at the detection port. An output Faraday isolator
(OFI) is implemented just upstream of the OMC. The DC photodetector (DC PD)
detects the degree of freedom of the differential arm length (DARM), which is
a GW channel. The other sensing signals are obtained from three detection
ports: reflection (REFL), pick-off port of the power recycling cavity (POP),
and anti-symmetric (AS) ports (the DC PD part in this figure). Four length
degrees of freedom (right bottom inset) must be controlled to operate the
interferometer. The interferometer mirrors are suspended using vibration
isolation systems (VISs) to attenuate unwanted movements of the mirrors caused
by ground motion. There are four different types of VIS in KAGRA. The left
bottom inset summarizes VIS’s and suspended mirrors.

The interferometer configuration during O3GK is based on a power-recycled
Fabry–Pérot–Michelson interferometer, as shown in as Fig. 1. The optical path
differences between the two L-shaped orthogonal arms caused by the space–time
perturbations are detected at the anti-symmetric (AS) port (the DC PD part in
Fig. 1) where the interference fringe is controlled to be dark. In the
Fabry–Pérot cavities, the phase change of the laser field is accumulated for
the cavity storage time and enhanced. Fig. 1 shows that the power-recycling
mirrors (PRM, PR2, and PR3), beam splitter (BS), and input test masses (ITMX
and ITMY) form the power recycling cavity (PRC) that enhances the circulating
laser power in the interferometer, and this helps improve the signal-to-noise
ratio for the shot noise. The laser was composed of a non-planar ring
oscillator, Mephisto 500NEFC (Coherent), and a fiber laser amplifier, PSFA-10
mw-40 W-1064 (Coherent/Nufern), operating at 1064 nm. The nominal laser power
injected to the interferometer (before PRM) was about 5 W during the run.

Optical cavities comprising the complex interferometer need to be controlled
to ensure that the cavities are in resonance with the carrier light for
operating the power-recycled Fabry–Pérot–Michelson interferometer as a GW
detector. The phase difference between the reflected beams from the two arms
also needs to be controlled, and therefore, the AS port is kept dark to ensure
the best signal-to-noise ratio for the GW detection. In total, there are four
length degrees of freedom to control: the differential length of the arm
cavities and corresponding to the GW degree of freedom (DARM), common length
of the arm cavities (CARM), differential motion between the BS and each input
test mass (MICH), and the length of the power-recycling cavity (PRCL). The
bottom-right inset in Fig. 1 summarizes all degrees of freedom.

Moreover, the sensing and control schemes described in Ref. Aso et al. [2013]
are applied. Radio frequency (RF) sideband fields at two different frequencies
(16.87 MHz and 45.00 MHz) are generated by electro-optic modulators in the
pre-stabilized laser (PSL) system to determine the multiple length degrees of
freedom of the interferometer Yamamoto et al. [2019]. In addition, the
modulation for the length sensing of the IMC (13.78 MHz) is applied. The light
fields are detected and demodulated at the REFL, POP, and AS ports. Signals
sensitive to a specific degree of freedom are used as error signals for the
feedback control loops. The GW signals (or DARM signals) are detected as
slight DC power changes at the OMC transmission port known as the DC readout
scheme Fricke et al. [2012]. The OMC is a bow-tie shape optical cavity to
clean the spatial mode and it rejects unwanted RF sideband fields at the AS
port. The parameter sets of the optical properties are summarized in Table 1.

The interferometer mirrors are suspended using vibration isolation systems
(VISs) composed of multiple mechanical stages to attenuate unwanted movements
of the mirrors caused by ground motion. As mentioned in the inset of Fig. 1,
there are four different types of VIS in KAGRA. The test masses (ETMX, ETMY,
ITMX, and ITMY) are suspended by Type-A suspensions that are 13-m tall 9-stage
pendulums. The first five stages are called Type-A towers, which are at room
temperature Okutomi [2019], Fujii [2020]; and the last four stages are called
cryopayload, which can be cooled down Ushiba et al. [2021]. The BS, SR2, and
SR3 are suspended by Type-B suspensions, which have a two-stage payload under
a three-stage seismic isolation system that includes inverted pendulums Akutsu
et al. [2021c]. The PRM, PR2, and PR3 are suspended by Type-Bp suspensions and
are similar to Type-B suspensions except without the inverted pendulums
Akiyama et al. [2019]. Small auxiliary mirrors (IMC mirrors, IMMT1, 2, and
OMMT1, 2) are suspended by Type-C suspensions, which are simple double-
pendulums originally designed for TAMA300 detector Takahashi and Arai [2002].
Moreover, the aluminum breadboard of the OMC cavity was suspended by three
blade springs made of maraging steel in O3GK.

One key feature of KAGRA to reduce thermal noise is the cryogenic technique
Akutsu et al. [2021a, 2019b] to cool the cryopayloads. Before O3GK, all
cryogenic systems were already installed. The cryopayloads were connected to
the pulse tube cryocoolers by soft heat links made of pure aluminum to conduct
the heat from the cryopayloads to the cryocolers. Further, additional VISs
specially designed for the heat links were installed to avoid transferring
ground vibrations. However, the cryopayloads were at room temperature during
O3GK because the sensitivity was not yet limited by mirror thermal noise.
These cryocoolers will operate in future observations, and the sapphire mirror
(TM) temperature will be approximately 20 K.

The suspension controls (Sections 3.1.1 and 3.2.1) and interferometer controls
(Section 2.2) are performed using the real-time digital control system
originally developed by LIGO. Analog signals from the instruments are
converted to digital signals using the analog-to-digital converter (ADC)
cards, and they are filtered using digital servo filters. The digital control
signals are converted to analog signals using the digital-to-analog converter
(DAC) cards and fed back to the relevant actuators. Control loops that require
broad control bandwidths are performed in analog, whereas the digital system
continue to obtain the monitoring signals. Furthermore, the real-time digital
control system is integrated into the data acquisition system, and together,
they are called the control and data acquisition system (CDS) Bork et al.
[2020].

Length | IMC | 53.30 m
---|---|---
| Power-recycling cavity | 66(1) m
| X arm | 3000 m
| Y arm | 3000 m
| Schnupp asymmetry | 3.36(1) m
RF sideband frequency | IMC modulation | 13.78 MHz
| 1st modulation | 16.87 MHz
| 2nd modulation | 45.00 MHz
Modulation index | IMC modulation | not measured
| 1st modulation | 0.23(2) rad
| 2nd modulation | 0.23(2) rad
Power recycling gain | 11(1)
Arm cavity finesse | X arm | 1410(30)
| Y arm | 1320(30)
Table 1: Measured parameters of the KAGRA interferometer during O3GK. The test
masses were maintained at room temperature.

###  2.2 Lock acquisition

Lock acquisition is a control sequence that simultaneously achieves the
resonances of all cavities in the interferometer and the dark fringe at the AS
port. The mirrors move larger than resonance widths of cavities, and
therefore, each cavity must be controlled within its linear regime (where it
is said “the cavity is locked”) because the responses of the light fields
strongly depend on the resonant conditions of the cavities in the
interferometer. The laser interferometer can be operated as a GW detector only
when all length degrees of freedom are locked.

The lock acquisition scheme of the KAGRA detector is similar to the Advanced
LIGO scheme Staley et al. [2014] but with two differences. First, there is no
signal-recycling cavity; therefore, there is one less degree of freedom to
control. Second, the optical configuration of the arm length stabilization
(ALS) system is different. The ALS system utilizes an auxiliary green visible
laser that is phase locked to the PSL light with a doubled frequency of the
PSL light; this green laser independently controls the arm cavities from the
resonant conditions of the main IR laser. As described in Ref. Akutsu et al.
[2020a], in KAGRA, the green laser beams are injected through the backside of
the PR2 and SR2 mirrors. In LIGO, the green laser beams go into the arm
cavities through the ETMs.

The main optics of the interferometer are initially aligned before the lock
acquisition procedure, as follows. Each arm cavity is independently aligned
such that the high-visibility flashes of green light are observed by the PD at
each transmission port and the CCD camera looking at each end mirror surface
Akutsu et al. [2021b], whereas all the other mirrors are misaligned. After
recording the optimal angles of ETMX, ITMX, ETMY, and ITMY mirrors, the short
Michelson interferometer (composed of the BS, ITMX, and ITMY mirrors) is
configured, and the BS is aligned to attain the high visibility of the
Michelson interferometer. Then, the PRM is aligned in the PRC configuration.

The PRM is misaligned after recording its optimized angle by confirming the
PRC flashes; the interferometer is configured as a Fabry–Pérot–Michelson
interferometer. In this configuration, the arm cavities are maintained non-
resonant for the main IR beam by the ALS system. The common arm signals of the
ALS (ALS CARM) and the differential arm signals (ALS DARM) are fed back to the
frequency of the main laser to which the green laser is phase locked and the
differential motion of the end test masses (ETMX and ETMY), respectively. The
ALS system adds an offset to the ALS CARM such that the arm cavities are at
off resonance. This scheme is useful because the sign of the carrier fields in
the PRC and the short Michelson interferometer section (the central part)
depends on the resonant condition of the arm cavities. The sign of the carrier
field does not switch because of maintaining the arm cavities non-resonant for
the carrier field; therefore, the signs of the PRCL and MICH length signals do
not switch during the lock acquisition of the central part of the
interferometer.

The PRM is subsequently realigned to configure the power-recycled
Fabry–Pérot–Michelson interferometer with non-resonant Fabry–Pérot cavities.
The PRCL and MICH are locked using the third harmonic demodulation signals
(“3f signals”) that are less sensitive to the sign switch of the carrier field
Arai et al. [2000]. The incident power to the arm cavities are stabilized when
the MICH and PRCL degrees of freedom are locked by the $3f$ signals. With the
MICH and PRCL being locked by the $3f$ signals, the arm cavities are brought
to their resonances by reducing the offsets on ALS CARM and DARM signals;
then, the control signals are transitioned to the Pound-Drever-Hall (PDH)
Drever et al. [1983] signals obtained at REFL and AS ports for CARM and DARM,
respectively.

Finally, the DARM length signal is switched from the demodulated signal to the
DC readout signal with the DARM offset of about 17 pm. The error signal of the
OMC cavity length is obtained by dithering the OMC length and demodulating the
detected signal, and by feeding it back to the PZT attached to one of the four
mirrors of the OMC.

The entire locking procedure is automated using the state machine Guardian
Graef Rollins [2016] developed by the Advanced LIGO project. This locking
sequence takes about 20-30 min depending on exactitude of the initial
alignment and on environmental conditions such as the degree of ground
motions. Further details regarding control scheme will be presented in our
future paper on the detector commissioning.

###  2.3 Alignment control

The alignment degrees of freedom for the interferometer must be controlled
Barsotti et al. [2010] in addition to the length degrees of freedom (Sec.
2.2). Mirror misalignment is gradually induced by external disturbances such
as ground motions, and this affects the long-term stability and noise coupling
for the DARM degree of freedom. The following three alignment sensing and
control schemes are used in GW detectors: RF wavefront sensors Fritschel et
al. [1998], alignment dithering K. Kawabe [1994], and beam spot centering. In
O3GK, an alignment dither system (ADS) was implemented for local alignment
control. The ADS method uses mechanical modulation in the mirror’s angular
degrees of freedom and the lock-in detection.

During O3GK, PR3, BS, and IMMT2 were intentionally excited in angular degrees
of freedom (i.e., in pitch and yaw). The RF signal at the POP port was
demodulated at 90 MHz to obtain the build-up of the 45 MHz sideband field in
the PRC; this was again demodulated at the angular excitation frequencies
(lock-in detection). Thus, ADS loops were used to maximize the buildup of the
45 MHz sideband; consequently, the carrier and 16 MHz sideband fields were
also maximized in the PRC.

###  2.4 Calibration and sensitivity

Detector sensitivity in displacement is reconstructed by calibrating detector
outputs in the DARM control loop using the interferometer response and coil-
magnet actuator functions. The details of the O3GK calibration are described
in Refs. LVK [2022], Akutsu et al. [2021b]. The calibrated data used in this
study are derived in a real-time digital control system with infinite impulse
response filters that simulate the pre-measured optical response and actuator
functions with an error of approximately 15% in magnitude. However, this
calibration does not consider any time-dependent factors of the interferometer
response induced by, for example, alignment drifts, because this calibration
pipeline aims to realize only detector commissioning and monitoring.

Using the calibrated data, astrophysical BNS inspiral ranges were calculated,
as depicted in Fig. 2. The BNS inspiral range represents the detection range
of the volume- and orientation-averaged inspiral signals from a 1.4 solar mass
BNS inspiral at a signal-to-noise ratio of 8 Finn and Chernoff [1993]. The
presented BNS inspiral range was calculated during the observation, using the
calibrated data derived from the above-mentioned method without considering
any redshift effect because the expected BNS inspiral range was less than 1
Mpc.

Figure 2:  BNS inspiral range of the KAGRA detector during O3GK, from 8:00 UTC
on April 7, 2020. The median BNS inspiral range during the observation was 0.6
Mpc. The detector was non-operational during the latter part of days 5 to day
7 because of a storm.

###  2.5 Duty factor

The interferometer occasionally experiences lockloss wherein the control loops
can no longer maintain the cavity resonances. This is attributed to various
factors such as significant seismic activities and global misalignment caused
by interferometer mirrors drifting away over time. The global misalignment is
believed to cause also sensitivity degradation even if it does not break the
lock; however, it is still under investigation.

The KAGRA detector was operational for approximately 53% of the entire time of
the observation run time. This duty factor of GEO 600 was 78%, which results
in a 45% coincident time of the two detectors.

As depicted in Fig. 2, the interferometer was not operational around day 6 and
day 7 because of the high seismic activity at 0.1–0.3 Hz bandwidth, known as
the micro-seismic motion. For KAGRA, the micro-seismic activity is excited by
the waves in the sea of Japan and the Pacific Ocean. During day 2, the micro-
seismic motion was as high as 1–2 $\mu$m/s Kokeyama and the KAGRA
collaboration [2020]. The other occasional downtime was caused by earthquakes,
abnormal behavior of the control loops, and gradual drifts of the
interferometer alignment. Once the interferometer lost control, the entire
lock acquisition sequence was repeated automatically by the Guardian. The
initial alignment was manually performed before the automatic lock acquisition
depending on the interferometer condition (for instance, when the visibility
of the short Michelson interferometer was degraded).

As depicted in Fig. 3, a majority of the observation segments had an
operational time duration of less than 15 min. They correspond to about 10% of
the total operational time. We expect to improve the operational duration once
the global angular control system with wavefront sensors is implemented.

Figure 3:  Histogram of the operational duration during O3GK.

##  3 Noise Budget

Figure 4: Top: Various noise sources in the KAGRA detector during the O3GK run
(April 12th, 2020). The measured sensitivity (orange curve) and summation of
various noise sources (solid black curves) are displayed. Each noise source
(depicted in multiple colors) is estimated using online monitoring channels
and pre-measured transfer functions. Bottom: Measured sensitivity (orange
curve) and known line frequencies (vertical lines). The values of each
frequency are listed in the Appendix A.

For noise reduction, it is necessary to evaluate the noise sources and their
couplings; this study is called “noise budget.” KAGRA has already provided
noise budgets for the first operation using a simple Michelson interferometer
configuration in March and April 2016 Akutsu et al. [2018], and, for the first
cryogenic operation in April and May 2018 Akutsu et al. [2019b]. A similar
study was repeated for the power-recycled Michelson interferometer
configuration at room temperature of O3GK. Each noise contribution in the
noise budget (top panel of Fig. 4) and the reduction strategies are explained
in the following sections from lower to higher frequencies. In each frequency
region, the largest contribution is displayed primarily, and the identified
peaks (bottom panel of Fig. 4) are also explained. The measured sensitivity
can be explained by adding the effects of each noise.

The estimated noise curves in the sensitivity are evaluated as follows: the
amplitude spectral density of the witness channel for a certain noise
contribution and the transfer function from this witness channel to the GW
channel (DARM) are measured. For the latter, the sinusoidal signal is injected
intentionally, and the ratio of the Fourier components at the DARM to the
witness channel is evaluated. In some cases, the simulated transfer functions
or the theoretical formula of the noise contribution are adopted.

###  3.1 Noise contribution below 50 Hz

Below 50 Hz, the noise of the photocoupler position sensors for Type-A
suspension’s local control limited the sensitivity. The other noise
contributions (seismic motion through Type-A tower and vibrations through the
heat links) and the resonant peaks of the Type-A suspension are also
discussed. Although Newtonian noise can be one of the limiting noise sources
for the terrestrial detectors in this frequency region, it is not discussed
here because it is sufficiently smaller than the KAGRA design sensitivity
owing to the underground site Badaracco et al. [2021].

####  3.1.1 Control noise of the cryopayload part of the Type-A suspensions

All mirrors shown in Fig. 1 are isolated from the seismic motion in the GW
frequency band because of the VISs. In contrast, around the resonant
frequencies of the suspensions of VISs, which are lower than the GW frequency,
the mechanical resonances enhance the vibration. Local damping controls were
implemented to suppress the vibration of the suspensions. The local sensors
monitor the internal vibration, relative motions between suspension parts or
motion relative to the ground. The sensor signals are used to reduce the
resonant motion via appropriate feedback loops.

A simplified drawing of the Type-A suspension is depicted in Fig. 5. For the
Type-A suspensions, the feedback force is applied to the Marionette (MN),
intermediate-mass (IM), and sapphire mirror (TM) with the coil magnet
actuators. In this scheme, the sensor noise applied to the suspensions through
the feedback system contaminates the GW signals. The local damping for the
longitudinal direction (which is the optical axis) on the mirror, IM, and MN
stages was intended to be used only during the lock-acquisition phase and to
be turned off in the observation mode to avoid sensor noise coupling. However,
in O3GK, local damping was applied to the MN stage to reduce the residual
longitudinal motion of the mirrors.

Figure 5: Schematic of Type-A suspension Okutomi [2019], Fujii [2020]. The
suspension is a multiple-stage pendulum with a total height of 13 m. The
Type-A tower is at room temperature while the cryopayload is cooled down to
cryogenic temperature. The foot of the inverted pendulum for horizontal
vibration isolation is fixed to the ground, and it suspends a four-stage
pendulum at room temperature. For vertical vibration isolation, each inverted
pendulum and suspension stage has geometric anti-spring (GAS) filters
Bertolini et al. [1999]. The bottom of this pendulum, the bottom filter (BF),
suspends four stages of the pendulum at the cryogenic temperature. The
platform at the top of the cryopayload has leaf springs for the vertical
vibration isolation, and it suspends the marionette (MN), intermediate mass
(IM), and sapphire mirror (TM). The IM has four sapphire blade springs for
vertical vibration isolation. The photocoupler position sensors (“photo-
sensors”) to monitor the internal vibration resonances of the cryopayload were
implemented as the local damping sensors Ushiba et al. [2021]. Coil magnet
actuators are installed to apply feedback force on the MN, IM, and TM for
local damping and lock acquisition. The damping filters were implemented to
reduce the free-swinging motion in the inverted pendulum, GAS filters, BF, MN,
and IM. Further, the sensor correction system was implemented to reduce the
contamination of the seismic noise at the inverted pendulum stage Fujii
[2020].

In O3GK, the photocoupler position sensors (“photo-sensors”) of cryopayload
were adopted as the local damping sensors Ushiba et al. [2021]. These sensors
monitored the internal vibration resonances of the cryopayload. The feedback
signals were sent to the actuators to control the position and angle of the
MN.

A transfer function from the feedback signal of the MN stage to the DARM was
measured before O3GK. The photo-sensor noise contribution to the DARM was
estimated using the online witness channel of the MN photo-sensor in the O3GK
observation; it was multiplied by the transfer function. We observed that the
amplitude of each TM motion caused by the photo-sensor noise was different in
the four test masses in O3GK. Among the four, the photo-sensor for ITMX was
the noisiest, and it limited the O3GK sensitivity to below 50 Hz.

Although local sensors would not be used for longitudinal motion in the final
phase of the KAGRA project where the sensitivity is considerably better, they
will still be necessary in the near future. We plan to substitute the photo-
sensors with optical levers for MN damping to sense the motion relative to the
ground; the investigation is in progress. Another method for improvement is to
increase the sensitivity of the photo-sensors by modifying the driving and
readout circuits. With improved photo-sensors, it is essential to modify the
damping loop to reduce the feedback gain at higher frequencies (i.e., in the
GW band) to lower the sensor noise coupling.

####  3.1.2 Seismic noise through Type-A tower

As a unique key feature, the KAGRA detector is located in a 200-m deep
underground site where the seismic motion at the GW frequency is reduced by
approximately $1/100$ compared to the surface Akutsu et al. [2021a].

In addition, the VISs were installed to isolate the main KAGRA mirrors from
the seismic motion. They isolate the vibration of the mirrors in the
horizontal (along the laser beam) and vertical directions of the mirrors. The
laser beam is not exactly perpendicular to the vertical direction because the
arm baselines have a slope inclination of $1/300$ for an underground water
drain. Moreover, imperfections in the vibration isolation suspensions convert
the vertical motions into horizontal motions. The actual coupling factor was
measured to be 1% from the vertical to horizontal motions at the mirror stage
of Type-A suspensions Shoda [2020]. Multiple stage pendulums and an inverted
pendulum are adopted for horizontal vibration isolation. The geometric anti-
spring (GAS) filters are deemed effective for vertical vibration isolation
Bertolini et al. [1999]. For Type-A suspensions, each pendulum stage at the
room temperature has a GAS filter, and in total, there are five GAS filters in
a Type-A tower.

Figure 6: (left) Amplitude spectral density of seismic motion measured by
seismometers in the KAGRA site on April 12th, 2020. (right) Estimated noise
contribution of seismic motion through the Type-A tower and the vibration
through the heat links. The coupling from the vertical seismic motions to the
longitudinal direction was assumed to be 1%. These noise contributions are
lower than the sensitivity in O3GK, as indicated in the right inset. Although
seismic motions through the ETMY Type-A tower are higher than the design
sensitivity, they reduce after restoration. Vibrations through the heat links
are sufficiently low because of the heat link vibration isolation system
(HLVIS).

The previously explained seismic noise through the Type-A tower was estimated
as follows: the ground motions measured using the three-axis seismometers
placed near the ETMX and ETMY in O3GK Akutsu et al. [2021b] are multiplied by
the modeled transfer functions from the ground to the mirror (ETMX or ETMY).
All Type-A towers had some parts that did not work in O3GK, among which ETMY
was extremely ineffective because three GAS filters were stuck. In contrast,
the ETMX Type-A tower was effective. We calculate the seismic noise under
these conditions; the results are displayed in Fig. 6. The seismic noise in
O3GK was dominated by the vertical vibration of the ETMY Type-A tower. The
seismic contribution of ETMX Type-A tower already met the KAGRA design goal in
O3GK, and as such, the seismic contribution of Type-A suspensions is expected
to be lower than the KAGRA design sensitivity once the ongoing repairs of
Type-A suspensions are complete.

####  3.1.3 Vibration through heat links

Cryogenic mirrors are the key feature of the KAGRA design for reducing thermal
noise. Although these mirrors are not cooled during O3GK, heat links (made of
aluminum thin wires) are installed to connect the cryocooler and cryopayload
for future cooling. Heat link vibration isolation system (HLVIS) was
introduced to avoid these links from propagating the vibrations because of
seismic motion, cryocoolers, or compressors Yamada [2021].

The noise projection depicted in Fig. 6 is calculated as the product of a
measured vibration of the radiation shield111This vibration was measured about
2.5 years before O3GK when the cryostat was evacuated in room temperature, and
all cryocoolers were in operation. and a simulated transfer function from the
radiation shield to the TM through an HLVIS. This vibration projection is
lower than the KAGRA design sensitivity.

####  3.1.4 Eigenmodes of the Type-A suspensions

The resonances of the Type-A suspension eigenmodes appeared in the observed
sensitivity as various peaks. Only identified peaks are listed in this paper;
however, some unknown lines are also observed. Not all expected peaks are
observed, and this is most likely because the background noise is larger than
the peaks at some frequencies. In this section, eigenmodes below approximately
50 Hz are discussed. The violin modes of Type-A suspensions, above 150 Hz, are
discussed in Sec. 3.3.2.

Local damping systems were implemented to suppress the resonant motions;
however, they were not perfectly eliminated. The TM, IM, and MN stages were
intentionally (and independently) excited through the corresponding actuators
and monitored using the local sensors to identify the resonant frequencies of
Type-A suspensions. The results of these measurements were compared with a
mathematical model of a Type-A suspension Okutomi .

As depicted in the bottom plot of Fig. 4, five peaks at approximately 21 Hz,
23 Hz, 40 Hz, 45 Hz, and 55 Hz constitute the eigenmodes of the Type-A
suspensions. The peak frequencies are listed in Appendix A. These resonant
peak excitations can be caused by the couplings of the degrees of freedom in a
servo control system (for example, longitudinal motion and pitch, yaw
rotation); the decoupling (reduction of coupling) is necessary.

###  3.2 Noise contribution between 50 Hz and 100 Hz

The noise of the local damping control in Type-Bp suspensions between 50 Hz
and 100 Hz was dominant in the sensitivity. The other noise sources in this
frequency range included the control noise from Type-B suspensions, cross-
coupled control noise from auxiliary length degrees of freedom, and the
electronic noise from DACs and coil drivers, and the mains AC power supply.

####  3.2.1 Control noise of Type-B/Bp suspensions

Simplified schematics of Type-B and -Bp suspensions are shown in Fig. 7. Like
the Type-A suspensions, the largest noise contribution from the Type-B and -Bp
suspensions to the sensitivity included the control noise from the local
damping loops on the mirror stage. For Type-B and -Bp, the local sensors used
for the control included optical levers for measuring the displacement of the
position and angle to ground, in contrast to the photo-sensors that monitor
the internal motions of the Type-A suspensions.

Figure 7: Schematic of Type-B (left) and Type-Bp (right) suspensions. Both
suspensions comprise a room-temperature payload and GAS filters for vertical
isolation. Further, the Type-B suspension has an inverted pendulum for the
horizontal isolation. The payload contains the MN, recoil mass (not shown in
the figure), and fused silica mirror. Coil magnet actuators are installed to
apply a feedback force on the mirror stage. Optical levers are equipped on the
mirror stage to monitor the pitch, yaw, and longitudinal motion of the mirror.
Details of Type-B and -Bp suspensions are presented in Ref. Akutsu et al.
[2021c] and Ref. Akiyama et al. [2019], respectively.

The transfer functions from the feedback signals of the mirror stages to the
DARM were measured before O3GK to calculate the noise contribution. The local
control noise contribution of the Type-B/Bp suspensions to the DARM was
estimated using the feedback signals measured during O3GK, and it was
multiplied by the transfer functions. Only BS was considered for the noise
budget for Type-B suspensions because SRM was misaligned and SR2 and SR3 were
used only as steering mirrors. The noise contribution from the Type-Bp
suspensions includes the three power-recycling mirrors. For Type-B, the
contributions along the longitudinal, pitch, and yaw directions were added in
the quadrature. For Type-Bp, only the contributions from pitch and yaw were
added because the contribution along the longitudinal direction was
negligible.

The top panel of Fig. 4 represents the contributions from the Type-B
suspension (purple) and Type-Bp suspensions (blue). The noise contribution
from the Type-Bp suspensions was larger than that from the Type-B suspension
above 50 Hz; the control noise from the Type-Bp suspensions limits the
sensitivity between 60 Hz to 100 Hz.

Control filters must be redesigned to minimize the noise for future
improvements. One strategy is to use a high-gain band-pass filters only near
mechanical resonances.

####  3.2.2 Coupling from the auxiliary length degrees of freedom

The power-recycled Fabry–Pérot–Michelson interferometer has four length
degrees of freedom as shown in Fig. 1. Although they are ideally independent
of each other, a certain amount of coupling exists. Further, there is an
inevitable MICH-to-DARM coupling because the DARM error signal is
fundamentally sensitive to the MICH degree of freedom because both are the X
and Y arm’s differential degrees of freedom. In addition, the PRCL degree of
freedom couples to the DARM motion through the interferometer’s practical
imperfections. The sensing noise of the MICH and PRCL sensors are re-injected
to the DARM control loop through the crosstalk.

We assume that the DARM error signal can be represented by the summation of
the real DARM signal and the sum of the contributions of auxiliary degrees of
freedom through (unmodeled) linear transfer functions from the control loops
in an auxiliary degree of freedom to the DARM loop to evaluate the crosstalk
between auxiliary degrees of freedom and DARM. The re-injected sensing noise
is subtracted using the transfer function from the control point of the
auxiliary degree of freedom loop to the DARM error point Allen et al. [1999],
Meadors et al. [2014] by the feed-forward method. Here, MICH and PRCL control
signals were subtracted from the DARM through ITMX (as an actuator), using the
pre-measured and fitted corresponding transfer functions.

The real-time feed-forward subtraction successfully improved the sensitivity
between 80 Hz and 200 Hz by approximately an order of magnitude. The residual
contribution is depicted in salmon and light magenta colors in the top plot of
Fig. 4. With the feed-forward subtraction, the PRCL-to-DARM contribution was
no longer directly limited the sensitivity; however, it was still one of the
major noise sources between 50 Hz and 80 Hz, and the MICH-to-DARM coupling was
slightly lower than the other noise sources in the frequency region. There is
a possibility to double-count the Type-B and -Bp’s control noise in the MICH
and PRCL lines in the top panel of Fig. 4, because some of the MICH and PRCL
noise may be from the suspension control noise. In future commissioning, a
similar feed-forward online subtraction will be adopted, wherein an additional
degree of freedom (the SRC length) will be included.

####  3.2.3 DAC and coil driver noise

Coil magnet actuators are used to control the positions and angles of the
suspended mirrors Michimura et al. [2017]. Control signals from the real-time
control system are transmitted to actuators through the DACs and driver
circuits. Any noises caused by the DACs and drivers are converted to the force
applied by the coil magnet actuator to the suspended mirrors. Only the DAC
noise is considered because the noise from the driver circuits is known to be
a few magnitude lower than that of the DAC.

Amplitude spectral density at the DAC output with a null DAC input was
measured and multiplied by a pre-measured transfer function from the DAC
output to the DARM to evaluate the noise contribution. All DAC noise
contributions from the Type-A, -B, and -Bp suspensions were evaluated.

Therefore, the noise contribution from the Type-A suspensions was the largest
by a factor of 10. The DAC noise from Type-A suspensions is presented in the
top panel of Fig. 4. Although it was still lower than the observed
sensitivity, DAC noise reduction is necessary in the next observing run.
Whitening and de-whitening filters were installed to avoid the DAC noise of
the suspensions; the number of the filters will be increased in the future. If
necessary, low-noise drivers with 100 times lower driving power will be used
when the observed sensitivity approaches the design sensitivity of KAGRA.

####  3.2.4 Mains AC power

The mains AC power at the KAGRA site (located in the western part of Japan) is
100 Vrms, 60 Hz, and all electronics, even AC-DC converters, originally
operate with the same specifications. Therefore, the mains power and its
harmonics can appear in any analog circuits as electrical noise, e.g., in PDs
and actuators. Such noise is reduced to as low as possible by eliminating the
AC devices and placing the AC-DC converters in a room away from the
interferometer.

An ADC channel with no connected sensor was used as a witness channel to
evaluate its contribution to the DARM signal. Coherence between the ADC
witness channel and DARM signals had clear peaks at $f=60n$ Hz
($n=1,2,3,...$), of which only $n=1$ was dominant in the DARM (the bottom
panel in Fig. 4). We plan to install voltmeters for AC and DC power lines to
obtain more detailed noise investigation and mitigation in future
observations.

###  3.3 Noise contribution between 100 Hz and 400 Hz

Acoustic noise contributes significantly between 100 Hz and 400 Hz. We
observed the fundamental violin modes (transverse standing waves of the
sapphire fibers that suspended TMs) as a number of peaks.

####  3.3.1 Acoustic noise

Acoustic vibration originates from many apparatuses in the experimental site
including air-conditioners, vacuum pumps, and electrical devices. This
acoustic field induces the mechanical vibration of a vacuum chamber and duct,
optical table, or in-air optics, and it can contaminate the interferometer
signal as scattered light noise or other noise. The acoustic field (i.e., the
sound pressure) $G_{\mathrm{mic}}(f^{\prime})$ was measured using microphones
located in the experimental site; they are one of the physical environmental
monitoring (PEM) systems used to monitor environmental conditions. Details of
the KAGRA PEM are reported in Ref. Akutsu et al. [2021b].

The power spectral density of the acoustic noise in the DARM
$G_{\mathrm{acoustic}}(f)$ is evaluated using

$\displaystyle G_{\mathrm{acoustic}}(f)=\int R(f,f^{\prime})\times
G_{\mathrm{mic}}(f^{\prime})df^{\prime},$ (1)

where $R(f,f^{\prime})$ denotes a response function, and
$G_{\mathrm{mic}}(f^{\prime})$ represents the power spectral density of the
microphone signal. This model considers the frequency conversion effect and
when the frequency conversion does not occur, the equation is simplified as

$\displaystyle G_{\mathrm{acoustic}}(f)=C^{2}(f)\times G_{\mathrm{mic}}(f),$
(2)

where $C(f)$ denotes a coupling function.

The measurements for the $R(f,f^{\prime})$ for the PSL room and power-
recycling (PR) booth were performed using single line acoustic injection in
the post-commissioning term (June 2020). In the PR booth, the frequency
conversion was confirmed, and the response function model in Eq. (1) was
applied to noise projection. However, in the PSL room, frequency conversion
was not observed, and the coupling function model in Eq. (2) was applied.
Further details are described in Ref. Washimi et al. [2021].

The hammering tests for the vacuum systems and optical tables (around the IMC
and PRCL) were performed to identify where the acoustic field affected the
interferometer signal. Finally, the largest contribution to the O3GK
sensitivity was identified as the scattered light in the vacuum bellows
between the IMC and IFI chambers (Fig. 1).

The acoustic noise limited the O3GK sensitivity in some frequencies between
100 Hz and 400 Hz. Therefore, the following approaches are planned to reduce
them in the next observation: (1) Introduction of soundproofing material at
the experimental site to reduce the acoustic field, (2) Mitigation of
scattered light propagation using new optical baffles and beam dumps inside
and outside the vacuum enclosure in addition to the currently installed ones
Akutsu et al. [2016], (3) Acoustic contamination in the DARM signal subtracted
by independent component analysis performed in the iKAGRA study Akutsu et al.
[2020b].

####  3.3.2 Violin modes of sapphire fibers

Peaks observed at approximately 180 Hz, 420 Hz, and 740 Hz include the violin
modes, which are the transverse standing waves of sapphire fibers that suspend
the TM. The masses of fibers cause back actions on the center of the mirror. A
single violin-mode peak can be indicated as 32 peaks in the sensitivity [4
(number of mirrors) $\times$ 4 (number of fibers for each mirror) $\times$ 2
(two degrees of freedom of the transverse vibration for each fiber)]. The
number of modes observed can be less than 32, because some of these modes
cannot be observed when the mirror motion induced by fiber vibrations is
parallel to the mirror surface.

Frequencies of violin modes were derived from the equation of elastic fiber
motions under tension by gravity González and Saulson [1994]. The dissipation
in the fiber is expected to be dominated by thermoelastic damping because the
KAGRA interferometer was at room temperature in O3GK, as described in Sec.
3.3.3. Q-values of the violin modes were calculated from the equation of the
violin mode motions and the thermoelastic damping formula. The calculated
Q-values of the violin modes cannot be lower than the measured value. Q-values
are lower When there are other types of dissipation in or around the fiber.
The parameters of sapphire suspensions used for violin modes calculation are
as follows Akutsu et al. [2021a]: the mass of the TM is 22.8 kg; the length
and diameter of a sapphire fiber is 350 mm and 1.6 mm, respectively. The
material properties of sapphire are summarized in Table 3.

From the observation data, the violin mode peaks in Fig. 8 are evaluated by
fitting the power spectral density with

$G_{\rm
violin}(f)=\sum_{i}\frac{G_{i}f_{i}^{2}\varGamma_{i}^{2}}{(f^{2}-f_{i}^{2})^{2}+f^{2}\varGamma_{i}^{2}},$
(3)

where $i$, $G_{i}$, $f_{i}$, $\varGamma_{i}=f_{i}/Q_{i}$, and $Q_{i}$ denote
the index for each peak, peak value, peak frequency, FWHM, and Q-value for
each peak, respectively. The results in Table 2 are consistent with the
theoretical expectation of the violin modes. The number of peaks are less than
or equal to 32. The values of the peak frequencies are listed in the Appendix
A.

Although we expect the excited violin modes observed in O3GK to be thermal
fluctuations of the suspension, further investigation is required. If the
violin-mode vibration is dominated by thermal fluctuation, the amplitude of
the violin modes can be suppressed by cooling.

Figure 8: Fitting results for the violin mode (top : 1st, middle : 2nd, bottom : 3rd modes) peaks in the power spectrum density (PSD) of the DARM sensitivity. The black and red curves are the observed PSD and fitting result, respectively. | 1st mode | 2nd mode | 3rd mode
---|---|---|---
Number of identified peaks | 27 | 30 | 31
Peak frequency (theory) | 175 Hz | 410 Hz | 732 Hz
Peak frequency (mean) | 180.10 Hz | 420.84 Hz | 752.47 Hz
Peak frequency (lowest) | 173.02 Hz | 404.96 Hz | 721.27 Hz
Peak frequency (highest) | 184.39 Hz | 429.80 Hz | 767.44 Hz
Q-value (theory) | $2.7\times 10^{4}$ | $4.7\times 10^{4}$ | $7.0\times 10^{4}$
Q-value (mean) | $1.30\times 10^{4}$ | $1.80\times 10^{4}$ | $2.12\times 10^{4}$
Q-value (std. dev.) | $2.0\times 10^{3}$ | $3.7\times 10^{3}$ | $6.9\times 10^{3}$
Table 2: Evaluated parameters of the violin mode peaks. Young’s modulus |  $4.0\times 10^{11}$ Pa
---|---
Poisson ratio | 0.29
Density |  $4.0\times 10^{3}$ kg/m3
Thermal expansion |  $5.4\times 10^{-6}$ /K
Specific heat |  $7.73\times 10^{2}$ J/K/kg
Thermal conductivity | 46 W/m/K
Table 3: Material properties of sapphire at room temperature.

####  3.3.3 Thermal noise of the sapphire fibers and sapphire mirrors

The suspended mirrors receive a random energy flow from the heat bath. This
random energy flow shifts the fibers suspending the mirrors and deforms the
surfaces of the mirrors. The arm length fluctuates because of these motions.
They are the fundamental noise sources, and they are called the thermal noise
of the suspension and mirror. The details are explained in Ref. Akutsu et al.
[2021a] and the formulae are briefly explained as follows.

The fluctuation-dissipation theorem predicts the relationship between the
thermal fluctuation and dissipation in the system. A solid exhibits two types
of internal dissipation: (i) Thermoelastic damping, which is the thermal
relaxation caused by inhomogeneous strain and thermal expansion; the strength
of this damping has a frequency dependence. (ii) Structure damping; the
damping strength is almost independent of the frequency. The dissipation in
the KAGRA TMs at room temperature is dominated by the thermoelastic damping in
the substrate and the structure damping in the reflective coating. The thermal
noise (power spectral density) caused by thermoelastic damping in a mirror
substrate at room temperature is described in Ref. Braginsky et al. [1999]

$G_{\rm substrate}=\frac{64}{\sqrt{\pi}}{\alpha_{\rm sub}}^{2}(1+\sigma_{\rm
sub})^{2}\frac{k_{\rm B}T^{2}}{\left(\rho_{\rm sub}C_{\rm
sub}\right)^{2}}\frac{\kappa_{\rm sub}}{{w_{0}}^{3}}\frac{1}{(2\pi f)^{2}},$
(4)

the parameters $\alpha_{\rm sub}$, $\kappa_{\rm sub}$, $C_{\rm sub}$,
$\rho_{\rm sub}$, and $\sigma_{\rm sub}$ denote the thermal expansion
coefficient, thermal conductivity, specific heat capacity, density, and
Poisson ratio of the mirror substrate, respectively. These values are
summarized in Table 3. The parameters $f$, $w_{0}$, $k_{\rm B}$, and $T$
denote the frequency, beam radius at the mirror (35 mm Akutsu et al. [2021a]),
Boltzmann constant, and temperature, respectively. For KAGRA’s sapphire
substrate mirrors in O3GK (room temperature), Eq. (4) is rewritten as the
amplitude spectral density

$\sqrt{G_{\rm substrate}}=2.5\times 10^{-20}[{\rm m}/\sqrt{\rm
Hz}]\left(\frac{100~{}{\rm Hz}}{f}\right).$ (5)

The power spectral density of the coating thermal noise is written as
(assuming Young’s modulus and Poisson ratio of the coating are similar to
those of the substrate)

$G_{\rm coating}=\frac{16k_{\rm B}T(1+\sigma_{\rm sub})(1-2\sigma_{\rm
sub})(d_{\rm ITM}+d_{\rm ETM})\phi_{\rm coating}}{\pi E_{\rm
sub}{w_{0}}^{2}(2\pi f)},$ (6)

where $E_{\rm sub}$, $d_{\rm ITM}$, $d_{\rm ETM}$, and $\phi_{\rm coating}$
denote Young’s modulus of the substrate, thickness of coating of ITM (3.7
$\mu$m) and ETM (6.5 $\mu$m), and loss angle of the coatings ($4\times
10^{-4}$), respectively Akutsu et al. [2021a]. For KAGRA O3GK, Eq. (6) can be
rewritten in the amplitude spectral density as

$\sqrt{G_{\rm coating}}=2.2\times 10^{-20}[{\rm m}/\sqrt{\rm
Hz}]\left(\frac{100~{}{\rm Hz}}{f}\right)^{1/2}.$ (7)

The simplified formula, Eq. (6), underestimates (1.8 times) the coating
thermal noise because of the differences in the elastic properties between the
sapphire and coating. Equation (7) considers this difference between the
substrate and coating Crooks et al. [2002]. For simplicity, Fig. 4 shows the
square root of quadrature summation of Eqs. (5) and (7) as the yellow curve;
this summation did not limit O3GK sensitivity.

The dissipation in the TM’s suspension is dominated by thermoelastic damping
in their sapphire fibers. In this case, the dissipation can be derived from
the theory of elasticity and the elastic and thermal properties of the
sapphire fibers. A simplified expression of the power spectral density of the
thermal noise in its pendulum mode is

$\displaystyle G_{\rm pendulum}$ $\displaystyle=$ $\displaystyle\frac{16k_{\rm
B}Tg}{m(2\pi f)^{5}\ell_{\rm fiber}}\phi_{\rm
fiberthermo}\times\sqrt{\frac{4\pi E_{\rm fiber}}{mg\ell_{\rm
fiber}^{2}}}\left(\frac{d_{\rm fiber}}{4}\right)^{2},$ (8)
$\displaystyle\phi_{\rm fiberthermo}$ $\displaystyle=$
$\displaystyle\frac{\alpha_{\rm fiber}^{2}E_{\rm fiber}T}{\rho_{\rm
fiber}C_{\rm fiber}}\frac{f/f_{0}}{1+(f/f_{0})^{2}},$ (9) $\displaystyle
f_{0}$ $\displaystyle=$ $\displaystyle 2.16\frac{\kappa_{\rm fiber}}{\rho_{\rm
fiber}C_{\rm fiber}d_{\rm fiber}^{2}},$ (10)

where $g$ and $m$ denote the gravitational acceleration and the mass of the
TM, respectively; $\ell_{\rm fiber}$, $E_{\rm fiber}$, and $d_{\rm fiber}$
denote the length, Young’s modulus, and diameter of the sapphire fiber,
respectively; $\phi_{\rm fiberthermo}$ denotes the loss angles by
thermoelastic damping of the fiber; and $\alpha_{\rm fiber}$, $\rho_{\rm
fiber}$, $C_{\rm fiber}$, and $\kappa_{\rm fiber}$ denote the thermal
expansion coefficient, density, specific heat capacity, and thermal
conductivity of the fibers, respectively.

This simplified formula is appropriate when the fibers are thin. In the case
of KAGRA, it is not true because the fiber must be thick to extract the heat
generated in the mirror. The elasticity of the sapphire fibers are considered
as shown in Ref. González and Saulson [1994]. For the KAGRA sapphire
suspension at room temperature, the amplitude power spectrum between 10 Hz and
100 Hz is approximated as follows ($f_{0}$ is approximately 13 Hz)

$\sqrt{G_{\rm pendulum}}=6.0\times 10^{-18}[{\rm m}/\sqrt{\rm
Hz}]\left(\frac{30~{}{\rm Hz}}{f}\right)^{3}.$ (11)

The violin modes appear above 100 Hz. The suspension thermal noise derived by
these formulae is presented in the gray line in the top panel of Fig. 4, which
indicates that the suspension thermal noise did not limit O3GK sensitivity.
Around 100 Hz, the thermal noise was approximately ten times lower than the
O3GK sensitivity. For future operations, thermal noise reduction by cooling is
inevitable. The thermal noise at 100 K is approximately one order of magnitude
lower than at room temperature Akutsu et al. [2021a]. The thermal noise is
approximately three times lower than that at 100 K when the temperature is 22
K (the KAGRA specification value).

###  3.4 Noise contribution above 400 Hz

Above 400 Hz, the main noise contributions originated from the light. Between
400 Hz and 2 kHz, the shot noise dominated the sensitivity. Above 2 kHz, the
laser frequency noise contributed significantly.

####  3.4.1 Shot Noise

The quantum fluctuation of the photon number at a PD (DC PD in Fig. 1) is
called shot noise. We evaluated the shot noise using two different formulae
(an experimental and a theoretical one), and we confirmed that the results are
consistent. The result from the theoretical formula is shown in Fig. 4. The
experimental formula includes the measured interferometer response. For the
theoretical formula, the interferometer response is represented by the optical
gain and cavity pole frequency. The experimental formula of the power spectral
density of the mirror displacement equivalent noise caused by shot noise is
expressed as

$G_{\rm shot}=\frac{2hcP_{\rm DC}}{\lambda|H_{\rm int}|^{2}},$ (12)

where $H_{\rm int}$ denotes the interferometer response from the mirror
displacement to the light power change at the PD. $h,c,P_{\rm DC}$, and
$\lambda$, represent the Planck constant, speed of light, average DC component
of the power at the PD, and wavelength of the light, respectively. We derived
the shot noise from the measured values, $P_{\rm DC}$ and $H_{\rm int}$.
Values $P_{\rm DC}$ and $H_{\rm int}$ depend on the operation condition of the
interferometer (amount of the local oscillator field and the contrast defect).
The theoretical shot noise power spectral density $G_{\rm shot}$ is
represented when the amplitude of the local oscillator is sufficiently larger
than the contrast defect as follows

$\displaystyle G_{\rm shot}$ $\displaystyle=$ $\displaystyle\frac{h\lambda
c}{32{\cal G_{\rm p}}P\delta{\cal F}^{2}}\left[1+\left(\frac{f}{f_{\rm
cut}}\right)^{2}\right],$ (13) $\displaystyle f_{\rm cut}$ $\displaystyle=$
$\displaystyle\frac{c}{4L{\cal F}}.$ (14)

Parameters ${\cal G_{\rm p}},P,\delta,L$, and ${\cal F}$ denote PR gain,
injected light power at the PRM, optical power transmittance between the BS
and DC PD in Fig. 1, and the length and finesse of the arm cavities,
respectively. The averaged value of the measured finesse of the two 3-km arm
cavities is $1.4\times 10^{3}$. The measured finesse implies that the cut-off
frequency is 18 Hz, and the amplitude spectral density of the shot noise in
O3GK is represented by

$\sqrt{G_{\rm shot}}=3.8\times 10^{-20}[{\rm m}/\sqrt{\rm
Hz}]\left[1+\left(\frac{f}{\rm 18~{}Hz}\right)^{2}\right]^{1/2},$ (15)

where ${\cal G_{\rm p}}=11$, $P=5.3~{}$W, and $\delta=0.04$. The estimated
shot noise level derived from Eq. (15) is depicted as a black dashed curve in
the upper plot of Fig. 4. The shot noise limited the observed sensitivity
between 400 Hz and 2 kHz. Only 4% of the interfered light at the BS
($\delta$=0.04) arrived at the PD. We investigated what causes such a low
optical transmittance. The SRM (details are in caption of Fig. 1)
transmittance is 30%. The total transmittance of OFI and OMC was 36%. In
addition, unknown transmittance reduction (approximately 40%) was observed.
The total transmittance (products of transmittance of each part) is 4%.

We will proceed to increase the optical transmittance between the BS and DC
PD. The shot noise amplitude is expected to be reduced by a factor of 4-5 when
the transmittance is close to unity. Further, we plan to introduce a higher
power laser (more than 50 W at the BS) and resonant sideband extraction (RSE,
details are provided in Ref. Akutsu et al. [2021a], Mizuno et al. [1993]) in
the near future. For the latter, it is necessary to align the SRM.

####  3.4.2 Radiation Pressure Noise

Radiation pressure noise is caused by the quantum fluctuation of the photon
number at the test masses. The sapphire main mirrors receive a back action
force by photons in the laser light; the photon number fluctuation changes the
force and position of the sapphire main mirrors. The power spectral density of
the radiation pressure noise in the mirror displacement is expressed as

$G_{\rm radiation}=\left(\frac{2}{m(2\pi f)^{2}}\frac{2{\cal
F}}{\pi}\right)^{2}\frac{8h{\cal G_{\rm
p}}P}{c\lambda}\left[1+\left(\frac{f}{f_{\rm cut}}\right)^{2}\right]^{-1},$
(16)

where $m$ denotes the mass of the TM. The calculated amplitude spectral
density for the KAGRA detector in O3GK is

$\sqrt{G_{\rm radiation}}=6.2\times 10^{-17}[{\rm m}/\sqrt{\rm
Hz}]\left(\frac{1~{}{\rm Hz}}{f}\right)^{2}\left[1+\left(\frac{f}{18~{}{\rm
Hz}}\right)^{2}\right]^{-1/2}.$ (17)

This noise did not limit O3GK sensitivity as are shown in Fig. 4. While the
radiation pressure noise increases with laser power, it decreases with the
introduction of the SRM in the RSE configuration. Consequently, the radiation
pressure noise in design sensitivity and that in O3GK observation are
comparable.

####  3.4.3 Laser frequency noise

A Michelson interferometer is a precise length measurement device with the
wavelength as a ruler. The fluctuation of the wavelength (or frequency) is the
measurement limit of the interferometer. In an ideal case, the laser frequency
noise does not contaminate the GW signal because its effect is common to the
two arms and is canceled in the DARM. In contrast, the frequency fluctuation
appears in the CARM. The CARM signal is used as the reference for frequency
stabilization because CARM does not include any GW signals and the 3-km arm
cavities are the longest and most stable frequency references in the KAGRA
interferometer.

In the actual senario, the above assumption is not perfectly accurate and
there is coupling from CARM to DARM because of the asymmetry of both arms,
such as by the differences in the length and finesse. The amplitude spectral
density of the CARM error signal was detected and the transfer function from
the CARM error signal to the DARM was measured to evaluate the frequency noise
contribution. The laser frequency noise contribution in the DARM is
represented by the product of the amplitude spectral density and transfer
function. The calculated laser frequency noise was dominant above 2 kHz in
O3GK as presented as a light green curve in the upper plot of Fig. 4.

The coupling between CARM and DARM was measured and observed to be larger than
the expected level derived using the simulation model that included known or
assumed differences in the transmittance of the ITMs, finesse of the arm
cavities (as depicted in Table 1), reflected light phase map, and transmission
wavefront error map that essentially displays the non-uniformity of the
optical thickness of the mirror Somiya et al. [2019]. A possible cause of the
larger CARM-DARM coupling is the birefringence of the test mass mirrors.
Further studies on birefringence are in progress. A lower noise in the CARM
error signal and a higher servo gain for frequency stabilization are necessary
for a better frequency noise level. Below 1 kHz, the laser frequency noise is
limited by the technical noise of the control loop (such as dark current
noise) of the PD to obtain the CARM error signal. The technical noise
contribution decreases if the light power at the PD increases because the CARM
error signal is proportional to the light power while the technical noise is
independent of the light power. The signal-to-noise ratio can improved for
several times compared to the current level by increasing the laser power at
the PD for the frequency stabilization in the future. Further, installing a
vacuum system for the CARM PD will help reduce the noise caused by air
turbulence on the laser beam. The gain of the servo filter needs further
optimization in the high-frequency region above 1 kHz to suppress the
frequency noise further.

####  3.4.4 Laser intensity noise

There is an intentional offset in the light power at the PD (DC PD in Fig. 1)
for the DC readout to extract GW signals. Further, the Michelson
interferometer asymmetry introduces some laser power to the PD. Here, the
intensity change imprinted by the GW signal cannot be distinguished from the
laser intensity fluctuations. In KAGRA, the intensity is monitored using an
in-air PD that receives the transmitted beam through IMMT1 shown in Fig. 1 to
suppress the laser intensity noise. The monitored intensity is used to adjust
the injected power to the interferometer by using an acousto-optic modulator
(AOM) installed in the PSL system. Nevertheless, some residual fluctuations
still exist.

The transfer function from the error signal of the intensity monitor refers to
the DARM to evaluate the intensity noise contribution, and the intensity
fluctuation in this error signal is measured. The product of the transfer
function and the fluctuation is the intensity noise contribution to the DARM.

Although the calculated intensity noise contribution did not limit the
sensitivity of O3GK, further reduction is necessary. The reduction strategies
of the intensity stabilization system include reducing the coupling from the
intensity fluctuation to DARM, and suppressing the intensity fluctuation. For
the former, the interferometer asymmetry must be as low as possible, like in
the case of the laser frequency noise on behalf of KAGRA collaboration [2021].
For the latter, one serious issue includes the intensity fluctuation at IMMT1
without intensity stabilization to be higher than that of the laser source.
Therefore, there must be noise sources between the laser source and the IMMT1
transmission, and these must be removed. Further, the introduction of a
higher-power laser will contribute to a lower intensity fluctuation. A higher
power is useful in suppressing the shot noise in the intensity fluctuation
monitor. The number of PDs will be increased from two to four to receive
higher monitoring power. Another noise source in the intensity monitor could
be the beam jitter. We found that the injected beam jitter caused fluctuations
in the error signal obtained at the intensity monitoring PD. The possible
reasons are the inhomogeneous quantum efficiency on the receiving area and
beam position vibration of the photodiodes. We plan to install a jitter
stabilization system with quadrant PDs and piezo actuators placed before the
intensity monitoring PDs to mitigate the beam jitter. We plan to place the
optics for the intensity stabilization system in a vacuum chamber to further
suppress intensity monitor noise.

####  3.4.5 OMC PD dark noise

The OMC is a bow-tie shaped cavity in Fig. 1 used to filter unwanted RF
sideband fields and higher-order spatial modes generated by the interferometer
imperfections. The DARM signals containing the GW signals are extracted as the
change in the transmitted power through the OMC. The signal of the PD
receiving this light contains noises from the ambient light fluctuations,
photodiode dark current, electric circuit noises of the transimpedance
amplifier, noise of the ADC, and so on. The sum of those background noises is
called the “OMC PD dark noise.”

The PD output was measured without laser light to evaluate this noise. This
was performed after the observation run and was converted to the DARM-
equivalent value with calibration parameters used for the observation run,
assuming that dark-current noise and electrical noise did not drastically
change between the observation period and the measurement. This dark noise was
discovered to be lower than the observed noise in O3GK as shown in the light
gray curve in the upper plot in Fig. 4.

In future observing runs, the signal-to-noise ratio of the PD will be improved
by stronger signals with a higher laser power of the input beam.

###  3.5 Injected lines

Sinusoidal signals (lines) were intentionally injected to monitor the status
of the interferometer. These injected lines are shown in the bottom panel of
Fig. 4; they are discussed here even though some of them were not used during
the observation but appeared in the sensitivity. The list of line frequencies
is provided in the Appendix A.

####  3.5.1 Alignment dither system (ADS)

IMMT2, BS, and PR3 were excited with angular degrees of freedom for the ADS.
In addition, SR3 was excited and controlled for the green beam alignment to
maximize the arm transmission of the green beam. For the same purpose, PR3
excitation was used for the green beam alignment. As represented by the dark
green lines in the bottom panel of Fig. 4, the angular excitation described in
Sec. 2.3 was coupled to the sensitivity because of the imperfect alignment or
mis-centered beam spots. The excitation frequencies were 20–45 Hz.

####  3.5.2 Beam Position Centering (BPC)

BPC was intended; however, no BPC control loops were used during the observing
run due to technical reasons. The pitch and yaw excitation applied to the
input and end mirrors persisted and coupled into the sensitivity, as
represented by the light green lines in the bottom plot of Fig. 4 at
approximately 1 kHz, which were selected to avoid the mechanical resonance of
the suspensions.

####  3.5.3 Calibration lines for DARM displacement

During the observation, the calibration lines are injected in two ways to
monitor the time-dependence of the calibration factor of DARM displacement.
One is through the coil magnet actuators for controlling the positions and
angles of each end test mass mirrors, with the frequencies of 28.3 Hz and 30.7
Hz for ETMX and ETMY, respectively. The other is through the photon calibrator
Akutsu et al. [2021b] for the ETMX mirror, with frequencies of 29.5 Hz, 79.7
Hz, and 859.7 Hz.

####  3.5.4 Calibration lines for MICH/PRCL Feed-forward

MICH and PRCL were excited at 66.6 Hz and 63.1 Hz, respectively, to monitor
the time-dependence of the transfer function from them to DARM. These lines
can be used to calibrate the transfer functions in the offline analysis.

####  3.5.5 Reducing the effects of injection lines

The ADS or BPC lines will not be used once global alignment control Fritschel
et al. [1998] is implemented in future observation runs. However, the
calibration lines cannot be removed at the hardware level because of their
functions; however, they can be subtracted at software processing such as
during DARM reconstruction or some offline analysis because the actuation
powers are also recorded.

##  4 Future Prospects

The noise contributions in the KAGRA detector during the O3GK run were
studied, and the noise mitigation strategies were discussed. The new
challenges and issues to be expected in the near future are summarized.

The optical configuration will be significantly upgraded from the power-
recycled Fabry–Pérot–Michelson interferometer to the RSE which has an
additional SRC at the AS port in next observing runs. This will help broaden
the sensitive bandwidth for GW signals. A high-power laser source is planned
to be installed for reducing the shot noise level because the high-frequency
region of RSE sensitivity will be still limited by the shot noise, similar to
the current case.

Another major upgrade will be lowering the thermal noise drastically by
performing a cryogenic operation. Investigations to cool down without problems
(for example, ice layer on mirror surface Akutsu et al. [2021a]) are in
progress.

Commissioning of the high-power operation is challenging. Interferometer
mirrors absorb the laser power, and hot spots are created in the optics when
the input power is high. Further, hot spots distort the wavefronts of the
laser beam through local refractive index changes and the thermal expansion of
the mirror material Ryan Christopher [2003]. However, these thermal effects
are negligible for the cryogenic sapphire mirrors Tomaru et al. [2002].
Therefore, sapphire mirrors must be cooled prior to the power increase
Degallaix [2012]. In addition, because the thermal aberration effects in room
temperature optics (e.g., beamsplitter) are experimentally unknown for the
KAGRA detector, we must investigate these effects in order to identify its
noise behavior at room temperature. If such thermal aberration effects are
problematic for the interferometer operation, active thermal compensation
systems Brooks et al. [2016] maybe necessary for the future. Other issue
related to the high-power laser is the parametric instability Braginsky et al.
[2001] that causes the unstable sapphire mirror elastic vibration and
excitation of higher optical modes in the 3-km cavities. Although the number
of unstable modes is an order magnitude less than those of LIGO and Virgo
Yamamoto et al. [2008], the suppression system for the cooled sapphire mirrors
is necessary and being studied.

There remain a few unsolved issues for future commissioning. An unexpected
large coupling from laser frequency and intensity noise to the sensitivity was
observed in O3GK, and it is likely to remain because of large asymmetries
between the X and Y arm cavities. Asymmetries between the two arms may be
responsible for the couplings from the auxiliary degrees of freedom (as
presented in Sec. 3.2.2). As discussed in Sec. 3.4.3, the birefringence of the
sapphire substrate is a possible cause of the asymmetries. Further
investigation to characterize the birefringence effect is in progress.

In the upgraded detector, noise couplings may change and have to be re-
evaluated. Noise sources that are not observed in O3GK may be complicated at a
better sensitivity. According to the experiences in Advanced LIGO and Advanced
VIRGO, scattering light noise and angle-to-length coupling noise may appear in
a broad frequency range and between 10 Hz to 100 Hz, respectively. Additional
optical baffles and beam dumps are being prepared for various places in the
vacuum enclosure and on the optical tables in the air to mitigate the
scattered light. The angle-to-length coupling noise problem will be addressed
by a new global angular sensing and control scheme for the KAGRA detector.

The KAGRA noise was reduced by 4.5 orders of magnitude in O3GK compared with
the first cryogenic operation in 2018 Akutsu et al. [2019b]. The measured
sensitivity can be explained by adding up the effect of each noise, and the
noise reduction strategies are discussed. Based on these studies, the KAGRA
sensitivity will be improved for the next observing run aiming to contribute
to the GW astrophysics.

## Acknowledgment

This work was supported by MEXT, JSPS Leading-edge Research Infrastructure
Program, JSPS Grant-in-Aid for Specially Promoted Research 26000005, JSPS
Grant-in-Aid for Scientific Research on Innovative Areas 2905: JP17H06358,
JP17H06361 and JP17H06364, JSPS Core-to-Core Program A. Advanced Research
Networks, JSPS Grant-in-Aid for Scientific Research (S) 17H06133 and 20H05639
, JSPS Grant-in-Aid for Transformative Research Areas (A) 20A203: JP20H05854,
the joint research program of the Institute for Cosmic Ray Research,
University of Tokyo, National Research Foundation (NRF), the Mitsubishi
Foundation, Computing Infrastructure Project of KISTI-GSDC in Korea, Academia
Sinica (AS), AS Grid Center (ASGC) and the Ministry of Science and Technology
(MoST) in Taiwan under grants including AS-CDA-105-M06, Advanced Technology
Center (ATC) of NAOJ, Mechanical Engineering Center of KEK, the LIGO project,
the Virgo project, and Terri Pearce. Finally, we would like to thank all of
the essential workers in the KAGRA observatory; we would not have been able to
complete this work without them.

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##  Appendix A List of the identified lines

Frequency [Hz] | Type
---|---
15.30 | ADS (SR3, Yaw)
20.99 | ETMX eigenmode (Vertical, RM-chain 1st)
21.36 | ITMY eigenmode (Vertical, RM-chain 1st)
22.10 | ADS (IMMT2, Yaw)
23.39 | ETMX eigenmode (Roll, TM-chain 1st)
23.39 | ETMY eigenmode (Roll, TM-chain 1st)
23.39 | ITMX eigenmode (Roll, TM-chain 1st)
23.54 | ITMY eigenmode (Roll, TM-chain 1st)
23.83 | ETMY eigenmode (Vertical, RM-chain 1st)
25.40 | ADS (SR3, Pitch)
26.10 | ADS (BS, Yaw)
29.50 | DARM Calibration (ETMX PCal)
28.30 | DARM Calibration (ETMX actuator)
30.70 | DARM Calibration (ETMY actuator)
30.10 | ADS (PR3, Yaw)
38.10 | ADS (IMMT2, Pitch)
39.75 | ITMY eigenmode (Transverse, TM-chain)
39.36 | Type-A eigenmode (Vertical, TM-chain)
39.75 | ITMY eigenmode (Vertical, TM-chain)
40.13 | Type-A eigenmode (Vertical, TM-chain)
42.10 | ADS (BS, Pitch)
45.23 | ETMX eigenmode (Pitch, TM-chain 2nd)
45.48 | ITMY eigenmode (Pitch, TM-chain 2nd)
46.07 | ITMX eigenmode (Pitch, TM-chain 2nd)
46.10 | ADS (PR3, Pitch)
54.19 | ETMX eigenmode (Roll, TM-chain 2nd)
54.33 | ETMY eigenmode (Roll, TM-chain 2nd)
54.51 | ITTM eigenmode (Roll, TM-chain 2nd)
55.27 | ITMX eigenmode (Roll, TM-chain 2nd)
60.00 | AC power line
63.10 | PRCL feed foword
66.60 | MICH feed foword
79.70 | DARM Calibration (ETMX PCal)
Table 4: List of the identified lines. Frequency [Hz] | Type
---|---
173.021 | Violin mode (1st) of a cryo-payload
174.035 | Violin mode (1st) of a cryo-payload
176.510 | Violin mode (1st) of a cryo-payload
177.929 | Violin mode (1st) of a cryo-payload
178.295 | Violin mode (1st) of a cryo-payload
178.387 | Violin mode (1st) of a cryo-payload
178.425 | Violin mode (1st) of a cryo-payload
178.539 | Violin mode (1st) of a cryo-payload
179.052 | Violin mode (1st) of a cryo-payload
179.247 | Violin mode (1st) of a cryo-payload
179.762 | Violin mode (1st) of a cryo-payload
179.833 | Violin mode (1st) of a cryo-payload
180.061 | Violin mode (1st) of a cryo-payload
180.093 | Violin mode (1st) of a cryo-payload
180.253 | Violin mode (1st) of a cryo-payload
180.625 | Violin mode (1st) of a cryo-payload
180.902 | Violin mode (1st) of a cryo-payload
180.962 | Violin mode (1st) of a cryo-payload
181.615 | Violin mode (1st) of a cryo-payload
181.661 | Violin mode (1st) of a cryo-payload
182.093 | Violin mode (1st) of a cryo-payload
182.139 | Violin mode (1st) of a cryo-payload
182.543 | Violin mode (1st) of a cryo-payload
182.959 | Violin mode (1st) of a cryo-payload
183.427 | Violin mode (1st) of a cryo-payload
184.314 | Violin mode (1st) of a cryo-payload
184.387 | Violin mode (1st) of a cryo-payload
404.961 | Violin mode (2nd) of a cryo-payload
408.562 | Violin mode (2nd) of a cryo-payload
414.901 | Violin mode (2nd) of a cryo-payload
415.482 | Violin mode (2nd) of a cryo-payload
416.433 | Violin mode (2nd) of a cryo-payload
416.998 | Violin mode (2nd) of a cryo-payload
418.844 | Violin mode (2nd) of a cryo-payload
419.270 | Violin mode (2nd) of a cryo-payload
419.512 | Violin mode (2nd) of a cryo-payload
419.721 | Violin mode (2nd) of a cryo-payload
419.906 | Violin mode (2nd) of a cryo-payload
Table 5: List of the identified lines. Frequency [Hz] | Type
---|---
420.296 | Violin mode (2nd) of a cryo-payload
420.644 | Violin mode (2nd) of a cryo-payload
421.157 | Violin mode (2nd) of a cryo-payload
421.269 | Violin mode (2nd) of a cryo-payload
421.325 | Violin mode (2nd) of a cryo-payload
421.659 | Violin mode (2nd) of a cryo-payload
421.744 | Violin mode (2nd) of a cryo-payload
422.415 | Violin mode (2nd) of a cryo-payload
422.540 | Violin mode (2nd) of a cryo-payload
422.642 | Violin mode (2nd) of a cryo-payload
422.949 | Violin mode (2nd) of a cryo-payload
424.255 | Violin mode (2nd) of a cryo-payload
424.658 | Violin mode (2nd) of a cryo-payload
425.184 | Violin mode (2nd) of a cryo-payload
425.798 | Violin mode (2nd) of a cryo-payload
427.256 | Violin mode (2nd) of a cryo-payload
427.454 | Violin mode (2nd) of a cryo-payload
427.662 | Violin mode (2nd) of a cryo-payload
429.796 | Violin mode (2nd) of a cryo-payload
520.00 | BPC (PRM, Pitch) since April 18
550.00 | BPC (PR2, Yaw) since April 18
580.00 | BPC (PR3, Pitch) since April 18
610.00 | BPC (PRM, Yaw) since April 18
640.00 | BPC (PR2, Pitch) since April 18
670.00 | BPC (PR3, Yaw) since April 18
721.271 | Violin mode (3rd) of a cryo-payload
728.291 | Violin mode (3rd) of a cryo-payload
739.319 | Violin mode (3rd) of a cryo-payload
743.367 | Violin mode (3rd) of a cryo-payload
743.762 | Violin mode (3rd) of a cryo-payload
746.132 | Violin mode (3rd) of a cryo-payload
746.455 | Violin mode (3rd) of a cryo-payload
746.707 | Violin mode (3rd) of a cryo-payload
747.163 | Violin mode (3rd) of a cryo-payload
749.812 | Violin mode (3rd) of a cryo-payload
Table 6: List of the identified lines. Frequency [Hz] | Type
---|---
750.900 | Violin mode (3rd) of a cryo-payload
751.171 | Violin mode (3rd) of a cryo-payload
751.249 | Violin mode (3rd) of a cryo-payload
753.344 | Violin mode (3rd) of a cryo-payload
753.651 | Violin mode (3rd) of a cryo-payload
754.724 | Violin mode (3rd) of a cryo-payload
755.729 | Violin mode (3rd) of a cryo-payload
756.340 | Violin mode (3rd) of a cryo-payload
756.750 | Violin mode (3rd) of a cryo-payload
756.786 | Violin mode (3rd) of a cryo-payload
756.885 | Violin mode (3rd) of a cryo-payload
758.686 | Violin mode (3rd) of a cryo-payload
759.405 | Violin mode (3rd) of a cryo-payload
760.548 | Violin mode (3rd) of a cryo-payload
762.359 | Violin mode (3rd) of a cryo-payload
762.611 | Violin mode (3rd) of a cryo-payload
762.930 | Violin mode (3rd) of a cryo-payload
764.139 | Violin mode (3rd) of a cryo-payload
766.052 | Violin mode (3rd) of a cryo-payload
767.439 | Violin mode (3rd) of a cryo-payload
859.70 | DARM Calibration (ETMX PCal)
980.00 | BPC (ETMY, Pitch)
1010.00 | BPC (ETMX, Yaw)
1040.00 | BPC (ITMY, Pitch)
1070.00 | BPC (ITMX, Yaw)
1100.00 | BPC (ETMY, Yaw)
1130.00 | BPC (ETMX, Pitch)
1160.00 | BPC (ITMY, Yaw)
1190.00 | BPC (ITMX, Pitch)
Table 7: List of the identified lines.