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\subject{A Thesis submitted for the degree of PHILOSOPHIAE DOCTOR}
\title{Innovative perspectives for seismic isolation of gravitational-wave detectors}
\author{Chiara Di Fronzo}
\publishers{\raggedleft{{\normalsize Institute of Gravitational Wave Astronomy\\ School of Physics and Astronomy\\ University of Birmingham\\ December 2021}}}
\date{}

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\frontmatter
\chapter{Statement of originality}
I confirm that the work presented in this thesis is original and has been entirely carried out by the author, started and completed at the University of Birmingham. The work done in collaboration with other scientific groups and/or abroad has been suitably highlighted throughout the thesis.\\

\noindent
During my second year I collaborated with the Albert Einstein Institute (Hannover) to test a device I designed and built in Birmingham. In the same year, I spent 5 months, between June and November 2019, at LIGO Harford site, working on ideas for improving the stability of the interferometer. This work has been carried on in collaboration with the SEI (SEIsmic) group of Stanford, MIT, Caltech, UoB and LIGO Livingston.

\begin{flushright}
Chiara Di Fronzo
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\chapter{Abstract}

The discovery of gravitational waves opened a new way to look at the Universe and offered new opportunities to shed light on the still unknown aspects of physical sciences. The work presented in this thesis wants to give a contribution to the development of this new type of research: the author chose to focus on the improvement of the instruments able to detect the gravitational waves. This field is important to make the detectors more sensitive, in order to see more gravitational-wave sources and help to complete the mosaic of the astrophysical science. In particular, the detectors currently in use are interferometers, which are especially blind in a range of frequency below 30 Hz: this affects the chance to detect sources emitting in this frequency band.\\ 
This lack of sensitivity is mainly due to seismic motion, and the work exposed in this thesis focussed on new techniques to lower this noise source and allow the instruments to be sensitive below 30 Hz.\\
During the studies, the development and test of devices able to to potentially reduce the seismic motion have been performed, such as optical levers for tilt motion reduction and laser stabilization for low frequency readout; a new concept of the seismic system on one of the interferometers (LIGO) has also been proposed.\\
The optical levers can in principle reduce tilt motion below 1 Hz; the use of capacitive position sensors in a new software configuration for LIGO can help to suppress ground motion by a factor of 3 in order of magnitude below 0.1 Hz. A competitive frequency stabilization to 3.6 $\times$ 10$^3$ Hz/$\sqrt{Hz}$ at 1 Hz for readout at low frequency is possible with a compact and easy to handle setup. These results are promising to provide suppression of the seismic motion in the bandwidth of interest and show that it is possible for a ground-based instrument to be seismically more stable and able to detect gravitational waves where it is now forbidden. 

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    \textit{Ai miei genitori e a mia sorella.}
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\chapter{Acknowledgements}
I am particularly grateful to Dr. Conor Mow-Lowry and the University of Birmingham, for giving me the opportunity and the funding to join the Gravitational waves group and contribute to the development of exciting science. This was also possible thanks to the support of the Royal Astronomical Society and the Institute of Physics, which allowed me to take part to conferences and workshops abroad.\\
During my stay at LIGO Hanford site, I need to warmly thank Caltech for providing me accommodation and travel: this experience was very important for my studies. Thanks to the Albert Einstein Institute (Hannover) for providing their facilities for my tests.\\
The completion of the work presented in this thesis would not have been possible without the action of the UoB, which accepted my application for an extension of my studies: the lockdown in 2020 stopped my lab work and the support of the UoB has been crucial to accomplish my project in the best way.\\

\mainmatter

\tableofcontents
\listoffigures
\addcontentsline{toc}{chapter}{List of Figures}
\listoftables
\addcontentsline{toc}{chapter}{List of Tables}

\chapter*{Notations}
\addcontentsline{toc}{chapter}{Notations}
Speed of light:\\
$c = 3 \times 10^8$ m/s\\
Gravitational constant:\\
$G = 6,67 \time 10^{-11}$ Nm$^2$/Kg$^2$\\
Gravitational wave amplitude:\\
$h \sim 10^{-21} $ $1/\sqrt{Hz}$\\
Solar mass:\\
$M_{\odot} = 10^{33}$ g\\
Chirp Mass\\
$M_c = \dfrac{(m_1 \cdot m_2)^{3/5}}{(m_1 + m_2)^{1/5}}$\\
Wave number\\
$k = 2\pi / \lambda$\\
Gravitational acceleration\\
$g = 9.8 m/s^2$\\
Boltzmann constant\\
$k_B = 1.38 \times 10^{-23}$ J/K\\

\chapter*{Acronyms}
\addcontentsline{toc}{chapter}{Acronyms}
AA = Anti-Aliasing\\
ADC = Analogue-to-Digital Converter\\
AEI = Albert Einstein Institute\\
aLIGO = Advanced Laser Interferometric Gravitational-wave Observatory\\
AI = Anti-Imaging\\
ASD = Amplitude Spectral Density\\
BRS = Beam Rotation Sensors\\
BS = Beam Splitter\\
BSC = Basic Symmetric Chamber\\
BH = Black Hole\\
CARM = Common Arm length\\
CDS = Control and Data System\\
CP = Compensation Plate\\
CPS = Capacitive Position Sensors\\
CS = Corner Station\\
DAC = Digital-to-Analogue Converter\\
DARM = Differential Arm Length\\
DCC = Document Control Center\\
DIFF2SE = Differential to Single-Ended\\
ETM = End Test Mass\\
ET = Einstein Telescope\\
FI = Faraday Isolator\\
FIR = Finite Impulse Response\\
HAM = Horizontal Access Module\\
HEPI = Hydraulic External Pre-Isolator\\
HoQI = Homodyne Quadrature Interferometer\\
HP = High Pass filter\\
HSTS = HAM Small Triple Suspension\\
IMBH = Intermediate Mass Black Hole\\
IMC = Input Mode Cleaner\\
IMCL = Input Mode Cleaner Length\\
ISI = Internal Seismic Isolation\\
ITM = Input Test Mass\\
LHO = LIGO Hanford Observaotry\\
LLO = LIGO Livingston Observatory\\
LP = Low Pass filter\\
LSC = Length Sensing and Control\\
LVDT = Linear Variable Displacement Transformer\\
LVK = Ligo-Virgo-Kagra meeting\\
MCA = Mid-Course Assessment\\
MICH = Michelson length\\
MIT = Massachusetts Institute of Technology\\
ND = Neutral-Density (filter)\\
NPBS = Non-Polarizing Beam Splitter\\
NS = Neutron Star\\
OPL = Opltical Path Length\\
PBS = Polarizing Beam Splitter\\
PD = PhotoDiode\\
PR = Power Recycling\\
PRCL = Power Recycling Cavity Length\\
PSD = Power Spectral Density\\
QPD = Quadrant Position Device\\
RIN = Relative Intensity Noise\\
SC = Sensor Correction\\
SR = Signal Recycling\\
SRCL = Signal Recycling Cavity Length\\
STS = Streckheisen Tri-axial Seismometer\\
TEC = Thermo-Electric Controller\\
UoB = University of Birmingham\\

\part{Gravitational-wave frontiers}
\include{GW}
\include{LF}
\include{LIGO}

\part{Lowering seismic motion}
\include{oplevs}
\include{CPSdiff}
\include{laserstab}

\appendix
\include{A}
\include{B}
\include{C}

\backmatter

\begin{thebibliography}{}
\addcontentsline{toc}{chapter}{Bibliography}

%chapt 1

\bibitem{wei} S. Weinberg \textit{Gravitation and Cosmology: principles and applications of the General Theory of Relativity}, John Wiley \& Sons, Inc., 1972

\bibitem{mag} M. Maggiore \textit{Gravitational waves - Vol. 1: Theory and Experiments}, Oxford University Press, 2013

\bibitem{nar} J. V. Narlikar \textit{An introduction to Relativity}, Cambridge University Press, 2011

%chapt 2

\bibitem{first} B. P. Abbott, \textit{Observation of Gravitational Waves from a Binary Black Hole Merger}, Phys. Rev. Lett. 116, 061102, 2016

\bibitem{yu} H. Yu et al, \textit{Prospects for Detecting Gravitational Waves at 5 Hz with Ground-Based Detectors}, Phys. Rev. Lett. 120, 141102, 2018

\bibitem{bird} S. Bird et al., \textit{Did LIGO detect dark matter?}, Phys. Rev. Lett. 116, 201301, 2016

\bibitem{branchesi} M. Branchesi, \textit{Multi-messenger astronomy: gravitational waves, neutrinos, photons, and cosmic rays}, 2016 J. Phys.: Conf. Ser. 718 022004

\bibitem{multi} LIGO Scientific Collaboration and Virgo Collaboration, Fermi GBM, INTEGRAL, IceCube Collaboration, AstroSat Cadmium Zinc Telluride Imager Team, IPN Collaboration, The Insight-Hxmt Collaboration, ANTARES Collaboration, The Swift Collaboration, AGILE Team, The 1M2H Team, The Dark Energy Camera GW-EM Collaboration and the DES Collaboration, The DLT40 Collaboration, GRAWITA: GRAvitational Wave Inaf TeAm, The Fermi Large Area Telescope Collaboration, ATCA: Australia Telescope Compact Array, ASKAP: Australian SKA Pathfinder, Las Cumbres Observatory Group, OzGrav, DWF (Deeper, Wider, Faster Program), AST3, and CAASTRO Collaborations, The VINROUGE Collaboration, MASTER Collaboration, J-GEM, GROWTH, JAGWAR, CaltechNRAO, TTU-NRAO, and NuSTAR Collaborations, Pan-STARRS, The MAXI Team, TZAC Consortium, KU Collaboration, Nordic Optical Telescope, ePESSTO, GROND, Texas Tech University, SALT Group, TOROS: Transient Robotic Observatory of the South
Collaboration, The BOOTES Collaboration, MWA: Murchison Widefield Array, The CALET Collaboration, IKI-GW Follow-up Collaboration, H.E.S.S. Collaboration, LOFAR Collaboration, LWA: Long Wavelength Array, HAWC Collaboration, The Pierre Auger Collaboration, ALMA Collaboration, Euro VLBI Team, Pi of the Sky Collaboration, The Chandra Team at McGill University, DFN: Desert Fireball Network, ATLAS, High Time Resolution Universe Survey, RIMAS and RATIR, and SKA South Africa/MeerKAT \textit{Multi-messenger Observations of a Binary Neutron Star Merger} ApJL, 848:L12, 2017

\bibitem{lf1} P. Fritschel, B. Lantz, \textit{Report on the workshop on Low Frequency Noise in LIGO, April 6 -7, 2021}, Low Frequency Workshop, April 2021 DCC L2100055

\bibitem{lf2} ERC Workshop, Frebruary 2021

\bibitem{lf3} Low Frequency Workshop, University of Birmingham, August 2018

\bibitem{lantztalk} B. Lantz, \textit{System-wide upgrades to improve the Seismic Isolation and control of detectors beyond A+}, talk, 2020

\bibitem{goulding} A. D. Goulding et al, \textit{Discovery of a Close-separation Binary Quasar at the Heart of a z$\sim$0.2 Merging Galaxy and Its Implications for Low-frequency Gravitational Waves}, The Astrophysical Journal Letters, 879:L21 (7pp), 2019

\bibitem{whyte} J. S. B. Whyithe et al, \textit{Low-frequency gravitational waves from massive black holes binaries: predictions for LISA and PULSAR timing arrays}, The Astrophysical Journal, 590:691–706, 2003


%chapt 3

\bibitem{ligo} Advanced LIGO Systems Group, \textit{Advanced LIGO Systems Design}, DCC document T010075-v3, 2017

\bibitem{abb} B. P. Abbott et al, \textit{GW150914: The Advanced LIGO Detectors in the Era of First Discoveries}, Phys. Rev. Lett. 116, 131102, 2016

\bibitem{mar} D. Martynov et al., \textit{The Sensitivity of the Advanced LIGO Detectors at the
Beginning of Gravitational Wave Astronomy}

\bibitem{mat} F. Matichard et al, \textit{Seismic isolation of Advanced LIGO: Review of strategy, instrumentation and performance}, Class. Quantum Grav. 32 185003, 2015

\bibitem{kisseltalk3} J. Kissel, \textit{On	Seismic	Isolation in 2nd Generation	Detectors}, GWADW talk, 2012, dcc.ligo.org/LIGO-G1200556

\bibitem{lsc} K. Izumi, D. Sigg, \textit{Advanced LIGO: length sensing and control in a dual recycled interferometric gravitational wave antenna}, 2017 Class. Quantum Grav. 34 015001


%oplev

\bibitem{mca} C. Di Fronzo \textit{Optical sensors for improving low-frequency performance in GW detectors}, Mid-Course Assessment, University of Birmingham, 2018

\bibitem{poster2} C. Di Fronzo et al., \textit{Optical Lever for interferometric inertial isolation}, poster, LVC meeting, Maastricht 2018, https://dcc.ligo.org/LIGO-G1801693 

\bibitem{lantz} B. Lantz et al., \textit{Estimates of HAM-ISI motion for A+}, T1800066-v2, March 2018, https://dcc.ligo.org/LIGO-T1800066 

\bibitem{cooper} S. Cooper et al., \textit{Ham ISI model}, Technical note, University of Birmingham, March 2018, https://dcc.ligo.org/LIGO-T1800092

\bibitem{sina} S. M. Köhlenbeck, \textit{Towards the SQL Interferometer Length Stabilization at the AEI 10 m-Prototype}, PhD thesis, Gottfried Wilhelm Leibniz Universität Hannover, 2018

\bibitem{luise} L. KranzHoff for the AEI group, \textit{A novel vertical inertial sensor for with phasemeter readout}, poster, LVK September 2021

\bibitem{tuyen} D. Tuyenbayev, \textit{Extending the scientific reach of Advanced LIGO by compensating for temporal variations in the calibration of the detector.}, PhD thesis, University of Texas, 2017

\bibitem{venka} Venkateswara et al., \textit{Subtracting tilt from a horizontal-seismometer using a ground-rotation-sensor}, Bulletin of the Seismological Society of America (2017) 107 (2): 709-717

\bibitem{jones} R.V. Jones et al., \textit{Some developments and applications of optical levers}, 1961 J. Sci. Instrum. 38 37

\bibitem{agatzuma} K. Agatsuma, \textit{Optical lever for KAGRA}, GW monthly seminar at Tokyo, 2014

\bibitem{lantz2} B. Lantz et al. \textit{Review: Requirements for a Ground Rotation Sensor to Improve Advanced LIGO}, Bulletin of the Seismological Society of America, Vol. 99, No. 2B, 2009

\bibitem{collette} C. Collette et al. \textit{Review: Inertial Sensors for Low-Frequency Seismic Vibration Measurement}, Bulletin of the Seismological Society of America, Vol. 102, No. 4, 2012

\bibitem{clark} D. E. Clark, \textit{Control of Differential Motion Between Adjacent Avanced LIGO Seismic Isolation Platforms}, PhD thesis, Stanford University, 2013

\bibitem{aston} S. M. Aston at al., \textit{Update on quadruple suspension design for Advanced LIGO}, Class. Quantum Grav., 29 (2012) 235004 (25pp)

\bibitem{shapiro} B. Shapiro, \textit{Brief Introduction to Advanced LIGO Suspensions}, LAAC Talk, August 2014, https://dcc.ligo.org/LIGO-G1400964

%cpsdiff

\bibitem{proposal} C. Di Fronzo et al., \textit{Proposal for an experiment at LHO: Locking PRCL to IMCL}, proposal, 2019, DCC T1900656-v2

\bibitem{technote1} C. Di Fronzo et al., \textit{Reducing differential motion using CPS sensors}, technical note, 2019, DCC T1900777-v1

\bibitem{chiatalk} C. Di Fronzo, \textit{Reducing differential motion of Advanced LIGO seismic platforms to improve interferometer control signals}, talk, LVK September 2020

\bibitem{biscans} S. Biscans et al., \textit{Control strategy to limit duty cycle impact of earthquakes on the LIGO gravitational-wave detectors}, arXiv:1707.03466, 2017

\bibitem{kisseltalk1} J. Kissel, \textit{On Relaxing Our Demand for Single IFO Duty Cycle}, talk, 2019, DCC G1901125-v1

\bibitem{peletalk} A. Pele' \textit{Lockloss status at beginning of O3 (LLO)}, Talk, dcc.ligo.org/LIGO-G1901122

\bibitem{biscanstalk} S. Biscans, \textit{Global seismic control}, talk, GWADW 2019

\bibitem{biswas} A. Biswas et al., \textit{New methods to assess the impact of seismic events on LIGO detector duty cycle}, 2019, 	arXiv:1910.12143

\bibitem{kisselthesis} J. Kissel, \textit{Calibrating and improving the sensitivity of the LIGO detectors}, PhD thesis, 2010

\bibitem{adl2} LIGO Scientific Collaboration \textit{Advanced Ligo}, LIGO-P1400177-v5

\bibitem{kisseltalk2} J. Kissel, \textit{Advanced LIGO Active Seismic Isolation}, talk, 2011

\bibitem{technote2} C. Di Fronzo et al., \textit{Reducing differential motion of Advanced LIGO seismic platforms to improve interferometer control signals: block diagrams and maths}, technical note, 2020, DCC T2000108-v1

\bibitem{technote3} C. Di Fronzo et al., \textit{Reducing differential motion of Advanced LIGO seismic platforms to improve interferometer control signals:analysis of feasibility}, technical note, 2020, DCC T2000365-v2

\bibitem{jenne} J. Driggers, \textit{Noise Cancellation for Gravitational Wave Detectors}, PhD thesis, 2016

\bibitem{llo} A. Pele' et al., \textit{ECR: Differential CPS and cavity offload}, proposal, 2019, DCC E1900330-v1

\bibitem{lhotest} LHO and SEI team \textit{The impact of CPS differential controls on scattered light glitches in O3b}, alog.ligo-wa.caltech.edu/aLOG/index.php?callRep=56293

\bibitem{lhotest2} LHO team \textit{Turned off CPS DIFF} alog.ligo-wa.caltech.edu/aLOG/index.php?callRep=53926

\bibitem{lantztech} B. Lantz et al., \textit{Estimates of HAM-ISI motion for A+}, technical note, 2018, DCC T1800066-v2

\bibitem{hammodel} S. Cooper et al., \textit{Ham ISI Model}, technical note, 2018


%6D

\bibitem{poster} C. Di Fronzo et al, \textit{A 6D inertial isolation system}, ET Symposium, 2019, poster, https://dcc.ligo.org/LIGO-G1900741

\bibitem{6d} C.M. Mow-Lowry, D. Martinov, \textit{A 6D interferometric inertial isolation system}, 2019 Class. Quantum Grav. 36, 24 

\bibitem{lisa} L Barsotti et al, \textit{Alignment sensing and control in advanced LIGO} 2010 Class. Quantum Grav. 27 084026

\bibitem{hoqi} S. Cooper et. al, \textit{A compact, large-range interferometer for precision measurement and inertial sensing}, 2018 Class. Quantum Grav. 35 095007

\bibitem{sam} S. Cooper, \textit{Breaking the Seismic Wall: How to Improve Gravitational Wave Detectors at Low Frequency}, PhD thesis, University of Birmingham, 2019

\bibitem{rio} $https://rio-lasers.com/1064-nm-laser-module/$

\bibitem{riologbook} Test of the lasers at UoB $https://lnx0.sr.bham.ac.uk:8081/ifo/371$

\bibitem{adj} $https://www.photonicsolutions.co.uk/upfiles/ADJUSTIKFiberLaserLG13Dec17.pdf$

\bibitem{mephi} $https://edge.coherent.com/assets/pdf/COHR\_ MephistoNPRO$

%appendix B

\bibitem{freise} Andreas Freise, \textit{The Next Generation of Interferometry: Multi-Frequency Optical Modelling, Control Concepts and Implementation}, Appendix B \textit{Control loops}, PhD thesis, 2003

\bibitem{wiki} https://en.wikipedia.org/wiki/Control-system

%appendix C
\bibitem{ligocalt} ligo.caltech.edu \textit{Observation Of Gravitational Waves From a Binary Black Hole Merger}

\bibitem{cavaglia} M. Cavaglia, \textit{Logo slide with institution names}, DCC G1300394

\bibitem{duty1} Buikema A. et al., \textit{Sensitivity and Performance of the Advanced LIGO Detectors in the Third Observing Run}, https://dcc.ligo.org/LIGO-P2000122

\bibitem{duty2} Davis D. et al., \textit{LIGO Detector Characterization in the Second and Third Observing Runs}, https://dcc.ligo.org/LIGO-P2000495

\end{thebibliography}

%\chapter*{Grazie!}
%\addcontentsline{toc}{chapter}{Grazie!}
%On a personal note, \textit{grazie} Conor for always being supportive, it was important in the hardest times! Grazie, with great respect.\\
%
%\noindent
%To my best friend here in the UK: \textit{grazie} Sam for your presence, your help, your effort to endure the enormous emotional baggage of this stubborn Italian one, who wanted to be your friend at all costs. I know it was not easy, I will not forget it.\\
%
%\noindent
%\textit{Grazie} to all my PhD colleagues who shared the stress and the fun of this experience with me. Riccardo, thanks for pushing me to go further, do better, stay stronger. George, thank you for the chess \& Czech classes, you opened my mind. Amit, your positivity is always contagious, thank you for sharing it!\\
%
%\noindent
%I really need to thank all the people on LIGO Hanford, who made me feel included and part of a great family. \textit{Grazie} Jenny, Jim, Rahul and Jeff B. for your infinite patience and for teaching me so much of LIGO; and I was very lucky to meet Dripta, an amazing housemate and friend, thank you for all the time you chose to share with me.\\
%\textit{Grazie} to my family in Seattle, zia Claudia, zio Carlo, Rossana \& Jim, Carla \& Wayne, who helped me to feel at home during my stay in the USA.\\
%
%\noindent
%To my friends in Italy: Vero \& Ludo, Alice \& Anna Paola, Martina, Francesca, Edo \& Nani, \textit{grazie} for your incredible will to stay close to me despite the 2000 km-distance.\\
%Angela and Anna, \textit{grazie} for your presence and friendship in Birmingham.\\
%
%\noindent
%A mio nonno, zio Marco e zia Laura, zia Flora e zio Vincenzo, grazie per avermi riempito di affetto e di cibo, sono stati indispensabili.\\
%Ai miei genitori e a mia sorella, grazie per avermi sempre incoraggiato, ascoltato le mie lamentele e sopportato la distanza durante questi 4 anni cosi' importanti per me.


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