The approach given in this thesis to introduce gravitational waves starts from the concept of gravity: gravity is not a force, but it is a property of the spacetime. This statement has been proved by General Relativity.\\
In this chapter we will briefly go through the reason why gravitational waves are an astrophysical phenomenon and how it is possible to detect them.\\
The purpose of the writer is to offer a contribution to the improvement of techniques of gravitational waves detection, extremely sophisticated in practice as well as elegant and straightforward in theory.
\chapter{Introduction}
\label{intro}
\section{Space, time and gravitation}
%RELATIVITA' GENERALE E EEs
%In the first years of XVIII century, the assumption that the fundamental laws of physics were invariant for all inertial observers was undisputed; however, they find hard applications in the electromagnetic theory: this led Einstein to develop the theory of relativity. He found that the Maxwell's equations imply that the electromagnetic fiends propagate in space as waves at the speed of light and that they are not invariant for all inertial observers in the Newtonian dynamics, but they are invariant in a frame were the space and time coordinates are linked together to be a unified system. Thus, for inertial observers moving with different relative velocities, space and time form a four-dimensional structure, called \textit{spacetime}.\\
In this chapter I will briefly introduce the key concept that established the goals of the work exposed in this thesis and moved all its steps. My research has been devoted to the enhancement of the instruments currently in use to detect gravitational waves, which is one of the most advanced fields of astrophysics research of our time.\\
A detailed structure of the thesis is then following.
%\noindent
The replacement of the Newtonian concepts of absolute space and absolute time with the merged concept of \textit{spacetime} introduced the Special Relativity\footnote{It is not in the aims of this work to demostrate the Theory of Relativity: a suggested detailed resource about the important transition between classical to relativistic physics is \cite{wei}.}. In this theory the light speed is assumed as preserved everywhere and every time for all interactions. However, gravitation seems not following this rule: the gravitational attraction seems to be instantaneous, or to propagate with \textit{infinite} speed.\\
%As well as the Newtonian space and time concepts have been modified to adapt to electromagnetic propagation
The Special Relativity then needs to be modified to adapt to gravity, taking into account its features: wherever there is matter, there is a gravitational effect, which is always present and acts as a radial inverse-square law. When trying to apply Newtonian gravitation to Special Relativity, the problem to solve becomes non-linear \cite{nar}; the key feature used by Einstein to adapt Special relativity to the presence of gravitation, is to consider that the permanence of gravitational effects makes gravity to be an intrinsic feature of space and time. Einstein's intuition marks the transition to the General Relativity: gravity is not anymore a force but an effect on the \textit{geometry} of the spacetime.\\
\section{Gravitational waves and their detection}
\noindent
General Relativity is then built on a non-Euclidean geometry able to explain the presence of gravity without considering it as a force: in such a geometry, matter under no force should move in straight like paths with uniform speeds.\\
This is possible if the spacetime is \textit{curved}.
\paragraph{Physics in a curved spacetime}
In General Relativity, the way to describe the physics in the curved spacetime modifies the usual Cartesian coordinate system used to measure the distance $s$ in space and time for two observers in an inertial frame:
\begin{equation}
\centering
ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2
\end{equation}
Gravitational waves are an astrophysical event that takes place when massive objects move and deform the fabric of the spacetime \cite{mag}\footnote{An in-depth source about how gravitational waves have been computed and their features is \cite{mag}.}. They have been theorized by Einstein in 1915 and discovered a hundred years later by a joint collaboration of three detectors \cite{nar}\cite{first}, which was worth of the Nobel Prize for Physics in 2017 \footnote{See Appendix C for some information about the first detection of gravitational waves.}.\\
\noindent
where $c =3\times10^8$ m/s is the speed of light, with the following:
The effect of the gravitational waves when they pass through an object is to produce a deformation on the physical lengths (L). This effect is very small ($\Delta$L/L $\sim$ 10$^{-21}$): masses able to deform the fabric of the spacetime and generate gravitational waves are of the order of more than the solar mass $M_{\odot}$, so they need to be looked for in the Universe.\\
\begin{equation}
\centering
ds^2 = \Sigma_{i,k = 0}^{3} g_{ik}dx^{i}dx^{k}
\label{a}
\end{equation}
\subsection{A difficult detection}
Detecting gravitational waves is particularly hard, because the effect is very small, and the sensitivity required for an instrument to see it must be suitable.\\
The challenging goal of detecting gravitational waves opened a research field dedicated to the development of new technologies, that could help to obtain the sensitivity necessary for the detection to happen.\\
This research is important, because detecting gravitational waves means looking at the sources which produced them. There is still a gap in the knowledge of many astrophysical objects, such as Black Holes (BH), Neutron Stars (NS), Supernova events: this new-born branch of astrophysics will help to fill the gap and increase our knowledge of the Universe.\\
\noindent
where the coordinates are now called $x^i$, with $i$=1,2,3 representing the three space coordinates and $i$=0 is the time coordinate\footnote{From now on we will omit the $\Sigma$ symbol, thanks to the summation convention of indeces: \textit{whenever an index appears as subscribt and superscript in the same expression, it is summed over all values}.} . The new entry is the coefficient $g_{ik}$, which is a series of functions of $x^i$. Eq. \ref{a} describes the geometry of the spacetime: its properties depend on $g_{ik}$, which transforms as a covariant tensor\footnote{A covariant vector is a quantity that transforms as $A'_{k}=\frac{\partial x^i}{\partial x^{'k}} B_i $. A tensor T is defined as the 4 $\times$ 4 product of two vectors and a covariant tensor transforms as $T'_{ik}=\frac{\partial x^m}{\partial x^{'i}}\frac{\partial x^n}{\partial x^{'k}} T_{mn}$.} and it is called \textit{metric tensor} (a simple demonstration of the tensorial property of $g_{ik}$ can be found in \cite{nar}).\\
The detectors currently in use are sensitive to events from sources emitting at frequencies above $\sim$ 10 Hz, but there is still a broad range of frequencies to which the detectors are blind. Looking at different frequencies of emission means looking at different objects emitting gravitational waves. This would broaden the catalogue of observed objects and the changes to better understand their nature.\\
\noindent
%All physical interactions and how they behave in presence of gravitation can be described in this geometry in terms of vectors and tensors and the effect of gravitation enters in a condition of \textit{curved spacetime}:
The defined metric explains how to measure distances, while in order to define parallel vectors in a curved spacetime (and build equations of motion in such conditions), we need functions $\Gamma$ of space and time that can describe variations of components of a vector $B_i$ during a displacement $\delta x^k$ along the curve:
The work carried on during my PhD studies and exposed in this thesis has been dedicated to the improvement of the sensitivity of the detectors at frequencies below 10 Hz, by the development of new ideas and technologies to reduce noise sources affecting the low-frequency bandwidth, in particular the seismic motion.
\begin{equation}
\centering
\delta B_i = \Gamma^{l}_{ik} B_l \delta x^k
\end{equation}
\noindent
that are determined once the metric tensor is known \cite{nar}:
The spacetime curvature is instead described by the Riemann tensor:
This thesis presents a study for the enhancement of the detectors for gravitational waves. It is 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 and illustrate some features of the detectors useful 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.\\
Now that we have the elements describing geometry, displacements, the curvature of the spacetime and the energy distribution, physical interactions can be built on them. In particular, we are interested in the gravitational fields.
\subsection{The Einstein's equations}
%NON DERIVARLE NEL DETTAGLIO, SPIEGA IL METODO EURISTICO
%SPIEGA LE APPROSSIMAZIONI PER MANIPOLARLE
The dynamical equations derivated by Einstein consider the energy-momentum tensor $T_{ik}$ acting as a source of gravity propagating in the spacetime as a wave, having the form of series of wave equations for the metric $g_{ik}$ in presence of curvature\footnote{A heuristic derivation of the Eintein's equations can be found in \cite{nar}, while a derivation based on the non-linear effect of the gravitational fields can be found in \cite{wei}.}:
The Einstein's equations expressed in the form of eq. \ref{EE} are valid in the weak field (or Newtonian) approximation:
\begin{enumerate}
\item The motion of particles is non-relativistic.
\item The gravitational fields are weak: $g_{ik}=\eta_{ik}+ h_{ik}$, where the term $\eta_{ik}$ = (-,+,+,+) expresses the flat-space metric and the perturbation is $\mid h_{ik}\mid$$\ll$ 1.
\item The fields change slowly with time, so time derivatives are negligible with respect to space derivatives.
\end{enumerate}
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
This approximation allows to handle the field equations in a linearized condition.
\paragraph{Gravitational-wave radiation}
%RISOLUZIONE DELLE EEs PER TROVARE L'EQ D'ONDA DELLE GWs\\
%SOLUZIONI DELL'EQ D'ONDA: COME SI PROPAGANO LE GW\\
The wave equations in the weak field approximation and under linearized conditions describe the gravitational radiation:
\begin{equation}
\centering
\square\bar{h}_{ik} = -\frac{16\pi G}{c^4}T_{ik},
\label{GW}
\end{equation}
\\
\noindent
where $\square=\eta_{ik}\partial^{i}\partial^{k}$ and $\bar{h}_{ik}= h_{ik}-\frac{1}{2}\eta_{ik}h$.\\
Physically, eqs. \ref{GW} say that bodies acting as sources of gravitational radiation move in a flat spacetime along a trajectory defined by their mutual influence. The gravitational field propagating in waves is known as \textit{Gravitational Waves}.\\
Solutions of the wave equations will tell how the gravitational waves propagate, how they interact with other bodies, the energy carried by the waves and the physical objects that could be gravitational waves sources.\\
If we consider what happens far from the source, i.e. when gravitational waves propagate, we need $T_{ik}$ = 0: in this way we just need to solve $\square\bar{h}_{ik}$ = 0. This gives a matrix-type form of the tensor when the wave propagates along the direction z\footnote{Full computations to derive the solutions of the wave equations for inspiriling masses can be found in \cite{mag}}:
The TT index indicates a Transverse-Traceless condition of the solution. The two amplitudes of the gravitational wave depend on the mass of two objects at distance $r$ from each other \cite{mag}:
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.\\
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
where 0 $< \theta <$$\pi/2$ and $f_{gw}=2\omega/(2\pi)$ is the frequency of the gravitational wave emitted. The mass of the two-system source of $m_1$ and $m_2$ each is defined as \textit{chirp mass}:
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.\\
\begin{equation}
\centering
M_c = \frac{(m_1 m_2)^{3/5}}{(m_1 + m_2)^{1/5}}.
\end{equation}\\
\noindent
Typically, the amplitude of a gravitational wave is of the order of $h \sim10^{-21}$$1/\sqrt{Hz}$, very small: masses able to deform the fabric of the spacetime and generate gravitational waves are of the order of more than the solar mass $M_{\odot}$, so they need to be looked for in the Universe.
%servono masse molto grandi, quindi vanno cercate nell'Universo: possibili candidati
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.
Most of the work exposed in this thesis has been carried on in laboratories and on LIGO sites. In this chapter, I will briefly introduce interferometers and LIGO, and I will explain in details only the structures of LIGO that have been subject of study in this thesis work: this is essential to fully embrace the work exposed in Chapter \ref{CPSdiff} in particular, and in general for the devices described in the whole thesis. The information contained in this chapter will be often referred to throughout the thesis.
\section{Interferometric detectors}
The interaction of gravitation waves with two objects moving along the x axis produces effects on their distance $d = x_2- x_1$:
\begin{equation}
\centering
s \simeq d \left(1 + \frac{1}{2}h_+ \cos\left[\omega \left(t-\frac{z}{c}\right)\right]\right).
\end{equation}
\\
\noindent
So the effect of the gravitational waves can be measured looking at the variation of the distance of the masses involved. A method to do it is to measure the time light takes to travel from one mass to the other: this is the basic principle of the \textit{interferometer}.
The interaction of gravitation waves with two objects moving along the x axis produces effects on their distance $d = x_2- x_1$ and hence the effect of the gravitational waves can be measured looking at the variation of the distance of the masses involved.\\
A method to do it is to measure the time light takes to travel from one mass to the other: this is the basic principle of the \textit{interferometer}.
\begin{figure}[h!]
\centering
...
...
@@ -22,7 +15,7 @@ So the effect of the gravitational waves can be measured looking at the variatio
\noindent
As shown in Fig. \ref{itf}, an interferometer is an instrument where a laser beam of wavelength $\lambda$ is split into two beams which propagate in two perpendicular arms of the same length. At the end of each arm, a mirror reflects the beam back to be recombined with the other one. The recombined beam is then deviated to a photodiode.\\
If we consider the length of arms oriented to the x and y directions to be $L_x = L_y = L$, the power measured depends on the difference of path length between the two beams:
If we consider the length of arms oriented to the x and y directions to be $L_x = L_y = L$, the power measured by the photodiode depends on the difference of path length between the two beams \cite{mag}:
\begin{equation}
\centering
...
...
@@ -39,7 +32,7 @@ We know that the effect of a gravitational wave is to modify the distance of two
\end{equation}
\noindent
and hence the key feature of this detector is that the beam coming from the recombined beam brings a phase difference:
and hence the key feature of this detector is that the recombined beam brings a phase difference \footnote{For details about interferometry refer to \cite{mag}.}:
The amplitude of a gravitational wave is typically very small and corresponds to a variation of the arm length of the order of $\Delta L \sim10^{-18}$ m. This means that, if we want to measure a considerable phase shift, the sensitivity of the instrument depends on the length of the arms.
\paragraph{Fabry-Perot cavities}
A useful way to increase the length of the arms is to make the laser beam travel back and forth into an optical cavity delimited by two mirrors, called \textit{Fabry-Perot cavity}: here, thanks to the multiple reflections, the optical path length will be longer, and the field amplitude will increase due to constructive interference. This process returns a longer optical arm length, proportionally to the quality factor of the cavity, which depends on the reflection coefficients of the two mirrors and it is called \textit{Finesse} (F):
A useful way to increase the length of the arms is to make the laser beam travel back and forth into an optical cavity delimited by two mirrors, called \textit{Fabry-Perot cavity}: here, thanks to the multiple reflections, the optical path length will be longer. This process returns a longer optical arm length, proportionally to the quality factor of the cavity, which depends on the reflection coefficients of the two mirrors and it is called \textit{Finesse} (F):
\begin{equation}
\centering
...
...
@@ -81,7 +74,10 @@ The higher is F, the higher is the effective length of the cavity and higher is
The goal of this work is to provide a contribution to the improvement of one of the interferometric detectors in use at present time, based in the USA: the Advanced Laser Interferometric Gravitational-wave Observatory (aLIGO).\\
\noindent
The configuration of aLIGO is shown in Fig. \ref{aligo}: it is a Michelson interferometer provided with Fabry-Perot, power and signal recycling cavities and 4 km-long arms. The light source is a solid-state Nd:YAG laser of wavelength $\lambda$= 1064 nm, injected at a power between 5 - 125 W.\\ The instrument design is extremely intricate in its details: this thesis will provide technical information useful for the understanding of the work made on specific sections of aLIGO.
The configuration of aLIGO is shown in Fig. \ref{aligo}: it is a Michelson interferometer provided with Fabry-Perot, power and signal recycling cavities and 4 km-long arms. The light source is a solid-state Nd:YAG laser of wavelength $\lambda$= 1064 nm, injected at a power between 5 - 125 W.\\
\noindent
The mirrors at the end of each arm, called End Test Masses (ETM), are made of fused silica and they are 34 cm $\times$ 20 cm in size and 40 kg in weight. A photodiode (PD) detects the power at the output. The optic able to split the injected beam into two parts along the arms is called Beam Splitter (BS) and it is placed at 45$^{\circ}$ between the arms.\\
\begin{figure}[h!]
\centering
...
...
@@ -91,7 +87,7 @@ The configuration of aLIGO is shown in Fig. \ref{aligo}: it is a Michelson inter
\end{figure}
\noindent
The fused silica mirrors at the end of each arm, called End Test Masses (ETM), are 34 cm $\times$ 20 cm in size and 40 kg in weight. A photodiode (PD) detects the power at the output. The optic able to split the injected beam into two parts along the arms is called Beam Splitter (BS) and it is placed at 45$^{\circ}$ between the arms.\\
The instrument design is extremely intricate in all its details: this thesis will provide technical information useful for the understanding of the work made on specific sections of aLIGO.\\
There are two LIGOs in the USA, one in Hanford (WA) and one in Livingston (LA): some of the work that will be presented in the next chapters has been physically done in Hanford, in remote collaboration with Livingston team.
\subsection{LIGO sensitivity and noise sources}
...
...
@@ -117,12 +113,12 @@ Noise sources make LIGO blind in some frequency windows: current technological l
\end{figure}
\noindent
Noises can be of fundamental, technical and environmental origin. Fundamental noises come from first principles, and they determine the ultimate design sensitivity of the instrument. They include thermal and quantum noises, and they cannot be reduced without a major instrument upgrade. Quantum noise includes shot noise of the sensors, causing power fluctuations, and radiation pressure, resulting in a physical displacement of the test masses. Thermal noise arises from the suspensions and the optical coatings and dominates in the 5-100 Hz frequency range.\\
Noises can be of fundamental, technical and environmental origin. Fundamental noises come from first principles, and they determine the ultimate design sensitivity of the instrument. They include thermal and quantum noises, and they cannot be reduced without a major instrument upgrade which involves structural changes. Quantum noise includes shot noise of the sensors, causing power fluctuations, and radiation pressure, resulting in a physical displacement of the test masses. Thermal noise arises from the suspensions and the optical coatings and dominates in the 5-100 Hz frequency range.\\
Technical noises arise from electronics, control loops, charging noise and other effects; environmental noises include seismic motion, acoustic and magnetic noises: these noises can be reduced once identified and carefully studied.\\
\noindent
This thesis focuses on the improvement of the seismic isolation system, which noises affect the inertial sensors placed on the suspension benches and the stabilization of the resonant cavities, which in turn limit the sensitivity of the detector in the low frequency bandwidth. The goal id to provide solutions to reduce seismic motion and improve the detector sensitivity.
This thesis focuses on the improvement of the seismic isolation system, which noises affect the inertial sensors placed on the suspension benches and the stabilization of the resonant cavities, which in turn limit the sensitivity of the detector in the low frequency bandwidth. The goal is to provide solutions to reduce seismic motion and improve the detector sensitivity.
\section{LIGO seismic isolation system}
Every optic needs to be stable with respect to seismic motion, because movements in the mirrors will cause unwanted displacement of the laser beam on the optical surface, resulting in noise during the laser travel into the cavities and then at the output. The main mirrors (test masses and beam splitter) are suspended from a stabilized bench and every suspension chain is placed in vacuum chambers called \textit{Basic Symmetric Chamber} (BSC). The auxiliary optics are placed on optical benches enclosed in the \textit{Horizontal Access Module} (HAM) chambers.
...
...
@@ -139,7 +135,7 @@ The HAMs provide five levels of isolation, among which there is the Internal Sei
\begin{figure}[h!]
\centering
\includegraphics[scale=0.9]{images/HAM.png}
\caption[Advanced LIGO HAM chamber design]{Schematic (a) and CAD model (b) of a HAM chamber \cite{mat}. Suspensions of auxiliary optics provide levels of passive isolation above 10 Hz. The ISI platforms where the suspensions live are optical tables actively isolated via low noise inertial sensors at low frequency ($\sim0.1 Hz$). The hydraulic attenuators of the \textit{Hydraulic External Pre-Isolator} (HEPI) and the geophones gives isolation from ground motion.}
\caption[Advanced LIGO HAM chamber design]{Schematic (a) and CAD model (b) of a HAM chamber \cite{mat}. Suspensions of auxiliary optics provide levels of passive isolation above 10 Hz. The ISI platforms where the suspensions live are optical tables actively isolated via low noise inertial sensors at low frequency ($\sim0.1$ Hz). The hydraulic attenuators of the \textit{Hydraulic External Pre-Isolator} (HEPI) and the geophones gives isolation from ground motion.}
\label{ham}
\end{figure}
...
...
@@ -149,7 +145,7 @@ The BSCs have a similar design as the HAMs, but they have two stages of ISI to s
\begin{figure}
\centering
\includegraphics[scale=0.9]{images/BSC.png}
\caption[Advanced LIGO BSC chamber design]{Schematic (a) and CAD model (b) of a BSC chamber \cite{mat}. The active isolation is similar to the one exposed for HAM chambers. The two ISIs provide two stages of isolation while and the suspensions are design to be quadruple pendulums, for a total of seven levels of isolation.}
\caption[Advanced LIGO BSC chamber design]{Schematic (a) and CAD model (b) of a BSC chamber \cite{mat}. The active isolation is similar to the one exposed for HAM chambers. The two ISIs provide two stages of isolation while the suspensions are designed to be quadruple pendulums, for a total of seven levels of isolation.}
@@ -216,7 +216,7 @@ The performances of the setup depend strongly on the HoQIs because they are the
\paragraph*{Tested noise sources}
There are several noise sources to take into account: air currents and vibrations from electronics and cables have been reduced placing the optical setup into a foam box and moving the electronic devices suitably. Cables have been isolated from the table and the breadboard by rubber feet.\\
\noindent
The test in Fig. \ref{sound} shows that the setup is sensitive to acoustic noise: we injected a sound at 75 Hz and both HoQIs clearly detected it. Moreover, we found out that HoQI1 is detected some noise around 22 Hz that HoQI2 is not able to sense: the two peaks in the figure are present in every condition of the laboratory and part of the day. The source of this noise is still under investigation: it could be a permanent sound in the lab non audible by humans. The fact that only HoQI1 can detected could be due to its position with respect to the noise source: it might be closer to it than HoQI2. Imperfections in the optics and general setup of the HoQIs are also taken into account.\\
The test in Fig. \ref{sound} shows that the setup is sensitive to acoustic noise: we injected a sound at 75 Hz and both HoQIs clearly detected it. Moreover, we found out that HoQI1 is detecting some noise around 22 Hz that HoQI2 is not able to sense: the two peaks in the figure are present in every condition of the laboratory and time of the day. The source of this noise is still under investigation: it could be a permanent sound in the lab non audible by humans. The fact that only HoQI1 can detected could be due to its position with respect to the noise source: it might be closer to it than HoQI2. Imperfections in the optics and general setup of the HoQIs are also taken into account.\\
\begin{figure}[h!]
\centering
...
...
@@ -237,7 +237,7 @@ The behaviour of the two HoQIs has been tested in loop and out of loop, to check
This test shows that HoQI2 is in general noisier than HoQI1, especially above 1 Hz: this affects laser stabilization measurement and loop stability, thus it has been deeply investigated. The higher intensity fluctuations of laser2 can partially explain the reason of HoQI2 noise.
\begin{figure}[h!]
%\centering
\centering
\includegraphics[scale=0.3]{images/hoqisOLCL.png}
\caption[In-loop test of HoQIs performances]{In-loop test of HoQIs performances. The out-of-loop traces (cyan and purple) are following the free running frequency noise trace (blue) as expected, while when the loop is closed the HoQI outputs (green and red) show that the controllers are pushing the expected gain (orange). There is an evident un-match with the orange trace below 0.4 Hz and this is likely due to loop leakage.}
@@ -135,31 +135,6 @@ 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}
...
...
@@ -183,10 +158,10 @@ There are three appendices useful to make the work more complete: appendix A ill
\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
\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
