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\title{Innovative perspectives for seismic isolation of gravitational-wave detectors}
\author{Chiara Di Fronzo}
\date{}
\titlehead{A Thesis submitted for the degree of Philosophiae Doctor}
\publishers{School of Physics and Astronomy\\Gravitational Waves Department\\ University of Birmingham}

\begin{document}
\maketitle

\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.

\begin{flushright}
Chiara Di Fronzo
\end{flushright}

\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 8 $\times$ 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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\chapter*{}
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    \vspace*{1cm}
    \textit{Ai miei genitori e a mia sorella.}
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\clearpage

\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.\\
%The completion of the work presented in this thesis would not have been possible without the action of the University of Birmingham, 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.\\


\tableofcontents
\listoffigures
\listoftables

\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

\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\\

\mainmatter

\chapter*{Structure of this thesis}

This thesis presents a study for the enhancement of the detectors for gravitational waves. It is then divided in two parts: Part 1 introduces the context of the work done and frames the study into the specific field of the low frequency window; this part is crucial to fully embrace the study performed in the laboratories. Part 2 is entirely focussed on the work done during the years between 2017 and 2021, covering the experience at LIGO Hanford and at the Albert Einstein Institute. This part includes the details of the experiments performed and their results.\\

\noindent
Chapter 1. This chapter briefly introduces the gravitational waves as the astrophysical phenomenon proposed by Albert Einstein in 1915 and discovered in 2017.\\

\noindent
Chapter 2. In this chapter we will see that there are some gravitational-wave sources emitting at lower frequency for which the current detectors are blind: it is in this frame that the experiments proposed in this thesis have been done. The final and ambitious goal is to improve the sensitivity of the detectors at lower frequencies.\\

\noindent
Chapter 3. This chapter describes briefly how an interferometric detector for gravitational waves works. In particular, the detector LIGO for which this work collaborated is illustrated. Specific details of the instruments on which the author has contributed are explained and referred to throughout the experimental work of the following chapters.\\

\noindent
Chapter 4. In this chapter there is the first experimental study performed in the first year of my PhD study: an optical lever for the reduction of tilt motion has been design and build at UoB, and then tested at the AEI. The details of the experiment and the results are explained in details.\\

\noindent
Chapter 5. This chapter is focussed entirely on the work done during my collaboration at LIGO Hanford site in 2019: during the O3a and O3b runs I had the chance to contribute to the improvement of the detectors by studying a new configuration of the seismic system in order to make the instrument more stable and allow a longer observing time. The details of this study includes original computations and tests on LIGO sites.\\

\noindent
Chapter 6. During the last year of the PhD studies, I contributed to the development of a new device for seismic control; in particular, I focussed on the stabilization in frequency of the laser source of the device, making use of new technology and advanced techniques. The experiment has been fully carried out at UoB between September 2020 and September 2021 and it is described in details.\\

\noindent
There are three appendices useful to make the work more complete: appendix A illustrates the work done at LIGO Hanford laboratory in building the suspensions for the A+ upgrade; appendix B gives some useful directions about control loops and block diagrams; appendix C aims to celebrate the first gravitational wave discovery.

\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}{}

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

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

%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{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{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{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{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{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

\end{thebibliography}

%\chapter*{Grazie!}
%Personal acknowledgements

\end{document}