\chapter{Introduction}
\label{intro}

In this chapter I will briefly introduce the key concepts that establish the goals of the work presented in this thesis and moved all its steps. My research has been devoted to the enhancement of the instruments currently used to detect gravitational waves, which is one of the most advanced fields of astrophysics research of our time.\\
A detailed structure of the thesis then follows.


\section{Gravitational waves and their detection}

Gravitational waves are an astrophysical event that takes place when massive objects move with a quadrupolar momentum and deform the fabric of spacetime \footnote{An in-depth source about how gravitational waves have been computed and their features is \cite{mag}.}. They have been theorized by Albert Einstein in 1915 and discovered a hundred years later by a joint collaboration of two detectors \cite{nar} \cite{first}, which was worthy of the Nobel Prize for Physics in 2017 \footnote{See Appendix C for some information about the first detection of gravitational waves.}.\\

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The effect of the gravitational-wave radiation is to produce a strain $h$ that induces a deformation of the physical lengths. This strain is typically very small ($h$ $\sim$ 10$^{-21}$), because the strain amplidute scales as $\sim GQ/c^4$, where $G = 6,67 \time 10^{-11}$ Nm$^2$/Kg$^2$, Q is the quadrupole mass moment of the wave and c is the speed of light \cite{mag}. The quadrupole mass moment is directly proportional to the mass of the object involved: masses able to deform the fabric of spacetime and generate gravitational-wave amplitudes detectable on the Earth are of the order of more than the solar mass $M_{\odot}$, so such massive objects need to be looked for in the Universe.\\

\subsection{A challenging detection}
Detecting gravitational waves is particularly challenging, because the effect is very small, and the sensitivity required for an instrument to see it must be suitably high.\\
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 provides information on 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) and Supernova events: this new-born branch of astrophysics will help to fill the gap and increase our knowledge of the Universe.\\

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The detectors currently in use are sensitive to events from sources emitting at frequencies above $\sim$ 30 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 chances to better understand their nature.\\

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The work carried on during my PhD studies and presented 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.


\section{Structure of this thesis}

This thesis presents a study for the enhancement of the detectors for gravitational waves. It is divided into 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 illustrates some features of the detectors useful to fully understand the work done 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.\\

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Chapter 2. In this chapter we will see that there are some gravitational-wave sources emitting at lower frequency to 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.\\

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

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Chapter 4. This chapter contains the first experimental work performed in the first year of my PhD study: an optical lever for the reduction of tilt motion has been designed and built at UoB, and then tested at the AEI. The details of the experiment and the results are explained in detail.\\

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Chapter 5. This chapter is focused entirely on the work done during my collaboration at LIGO Hanford 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 include original computations and tests at the LIGO sites.\\

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Chapter 6. During the last year of my PhD studies, I contributed to the development of a new device for seismic control; in particular, I focused 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 detail.



