Advanced Interferometric Gravitational-Wave Detectors

The following sections are included:

• Preface
• Contents

This chapter is an introduction to the book. It begins with some history of gravitational waves and describes a few recent measurements of compact binary gravitational wave sources that serve to give a preview of the new field of gravitational wave astronomy as a component of multi-messenger astronomy and astrophysics. After a review of the different techniques being developed to measure gravitational waves (with periods ranging from billions of years to milliseconds), the presentation focuses on terrestrial detection by optical interferometry, which is the main topic of the book. Here, the basic ideas for interferometric detection are developed, followed by an introduction to the various limiting noise sources. Beginning with fundamental limits and the techniques used to measure and reduce them, this chapter ends off by listing technical noise sources that can be reduced by careful engineering and good experimental practice. The various sections below will also direct readers to other chapters in this volume where these topics are discussed in greater detail. The chapter concludes with a brief presentation of challenges and opportunities for the future of the field.

The response of a simple Michelson interferometer to a gravitational wave can be enhanced by implementing Fabry–Perot arm cavities below the cavity pole frequency. The power recycling technique lowers the shot noise level of a Fabry– Perot Michelson interferometer at the expense of increased radiation pressure noise. The signal recycling technique enhances the response of a Michelson interferometer at lower frequencies at the expense of reduced bandwidth. The resonant sideband extraction technique improves the response of a Fabry–Perot Michelson interferometer together with high-finesse arm cavities. Although a power-recycled Fabry–Perot Michelson interferometer can provide the same quantum noise performance as that of the resonant sideband extraction interferometer, the resonant sideband extraction is mostly used for second-generation detectors. One of the reasons is the capability of detuning. The frequency response and the quantum noise of the resonant sideband extraction interferometer can be optimized by displacing the signal extraction mirror by a fraction of the wavelength of the light.

Whereas the challenge to detect the elusive gravitational-wave signal drives the technological design of laser-interferometer gravitational-wave detectors, the identification and characterization of astrophysical sources emitting the gravitational-wave signals require a global network of gravitational-wave detectors. Using the simultaneous observations of a network of detectors has strong scientific motivations: (i) to increase the detection confidence of weak and rare gravitational-wave signals expected to be associated with highly energetic astrophysical phenomena, (ii) to improve signal/source reconstruction and then provide an accurate estimate of the source parameters, and (iii) to enable gravitational waves to be part of the multi-messenger observations of the Universe. It was, indeed, the network of the LIGO interferometers that detected and characterized the first gravitational-wave signals coming from binary black-hole mergers [Abbott et al. (2016c,e, 2017c,d)], opening a new channel for the exploration of the Universe. It was also the network of the LIGO and Virgo interferometers that detected and characterized the first gravitational-wave signal coming from a binary neutron star coalescence [Abbott et al. (2017f)], starting the era of multi-messenger astronomy including gravitational waves [Abbott et al. (2017g)]. This chapter focuses on the importance of a network of gravitational-wave detectors for gravitational-wave detection, gravitational-wave astrophysics and multi-messenger astronomy.

This chapter examines the fundamentals of quantum noise in laser interferometer type gravitational-wave detectors. After defining coherent and squeezed vacuum states, quantum noise in a simple Michelson interferometer is used to introduce shot noise, quantum back-action noise and the standard quantum limit. We discuss how quantum noise limits can be manipulated via internal interaction of the propagating field with mirror dynamics, changing the readout observable, or injecting a squeezed field into the interferometer. We finish with an overview of the current state of the art and outlook, circa 2018.

This chapter reviews some of the important sources of thermal noise that can impact the sensitivity of interferometric gravitational wave observatories. It also reviews current research activities in this area and discusses prospects for future advances in reducing relevant sources of thermal noise.

Gravity gradient noise is generated by mass density changes through fluctuating gravity fields. Ambient seismic noise generated by microseismism, wind or of antropogenic origin is a possible source of such fluctuations. This work gives an overview of the impact of seismic noise and gravity-gradient noise on existing gravitational-wave detectors, and discusses the outlook for third-generation detectors.

Despite their name, non-fundamental noise sources in gravitational-wave detectors are drivers for some of the most basic detector design choices. They are also responsible for most of the commissioning required to reach design sensitivity. In this chapter we provide two typical examples of non-fundamental noise sources and related mitigation techniques. We then discuss general strategies for identifying and eliminating sensitivity-limiting noise sources during detector commissioning.

Control systems play a fundamental role in all interferometric gravitational-wave detectors. In this chapter we introduce the theoretical and mathematical basis for understanding control systems, and the terminology used in the gravitational-wave instrument science community to describe these systems. We also present the fundamental aspects of analog and digital signal processing necessary to work with advanced detector control systems.

Fabry–Perot cavities are ubiquitous in advanced interferometric gravitational-wave detectors. Among their applications, they are used to enhance the gravitational-wave signal, to filter laser noises and to remove unwanted spatial modes from the detector’s output. The goal of this chapter is to provide a description of the properties of Fabry–Perot cavities in the context of a gravitational-wave detector and an introduction to Gaussian beams.

A brief review of the properties of lasers required for use in gravitational-wave interferometers as well as a historical summary of the research conducted to meet these requirements are presented. This chapter serves as a prerequisite for the Advanced LIGO pre-stabilized laser design effort (Chapter 17). The last section touches very briefly on the research efforts underway to meet the needs for laser performance of future gravitational-wave interferometers.

The requirements for electro-optic modulators and photodiodes for advanced interferometric gravitational-wave detectors are very specialized. Commercially, available devices are usually not suitable for those detectors. In this chapter we give an overview of the aspects that need to be considered when building custom devices. We will show the characteristics of electro-optic modulators, and how they are used to create modulation sidebands and can be designed to satisfy the strict detector requirements. We also show how unwanted modulation effects can be avoided. Several electro-optic modulator-specific applications in gravitational-wave detectors will be addressed. In the second part of the paper we will show the characteristics of photodetectors, inherent and external noise sources, and how basic low noise photodetector circuits can be used to address the strict requirements of advanced gravitational-wave detectors.

This chapter provides an introduction to laser interferometer simulations for advanced gravitational-wave detectors. The single optical components involved in these detectors are simple, but in combination, can produce new complex systems. The stringent requirements on the sensitivity of the instruments demand accurate predictions and prevent us from artificially reducing the complexity of our models. Over the years the gravitational-wave research community has developed its own set of simulation packages adapted for the specific requirements of this field. In this chapter we aim to provide insight into the features and limitations of the existing models and the algorithms on which they are based. Our aim is to give an overview of the typical optical simulation tools developed to support the design, commissioning and characterization of advanced detectors. At the same time we hope to provide enough details so that interested readers would be able to program a basic optical model themselves. We also provide a dedicated webpage www.gwoptics.org/AdvDetectorBook with code samples accompanying this chapter. The code is presented in the form of Python notebooks that contain simple interactive examples for the main modeling methods discussed below.

It is easy to forget that the transformational discoveries made by terrestrial gravitational-wave detectors depended, first of all, on ignoring the effects of Earth’s atmosphere on the instruments. This tacit (but so far, accurate) assumption is perhaps a tribute to the innovative engineering embodied in vacuum systems enclosing current interferometric detectors. Here, we will revisit the fundamental interactions at the root of vacuum requirements, examine different solutions proposed and implemented so far, and consider the implications for larger and more sensitive future instruments.

Advanced detectors operating at design sensitivity (and beyond) will still produce noise with quasi-periodic and transient components that limit the sensitivity of the instruments and can mimic or overlap gravitational-wave signals. This chapter introduces non-Gaussian noise common to detectors and describes diagnostic methods that integrate gravitational-wave search techniques with instrumentation methods. Together, these techniques increase the rate and fidelity of gravitational-wave observations.

In conceptual descriptions of interferometric detectors of gravitational waves (GW) the test masses are assumed to be freely falling, a condition which cannot be fully realized in ground based detectors. What the experimentalists try to achieve instead, in order to make the detector work, is to have test masses which are, within a certain frequency range, basically freely falling in the direction defined by the laser beams. Facilitating this partial free-fall is the aim of seismic isolation systems.

In this chapter we describe the designs used for the suspension systems for Advanced LIGO and Advanced Virgo, which support the test masses that serve as the mirrors for the interferometers. These systems are attached to the last stage of the seismic isolation systems for the detectors. Their designs are chosen to minimize thermal noise, residual seismic noise and technical noise, while allowing control of position and orientation of the test masses, and enabling the interferometers to function. Advanced LIGO and Advanced Virgo differ in their approach to seismic isolation and control. Thus, although the final stages of the suspension systems have clear similarities, there are significant differences in the overall suspension systems. Hence we discuss the designs of the two systems separately. In a concluding section we compare the two systems and note that although the two projects have taken different approaches in certain areas, there are key concepts that show similarities and that both designs should meet their requirements.

Advanced interferometric gravitational-wave detectors (GWDs) set highly demanding requirements on their laser light sources. Even though laser manufacturers for GWDs pay high attention to a low noise design (see Chapter 10), none of the laser parameters as delivered have adequate stability to allow direct injection of the laser beam into the power-recycling cavity of the GWD (see Chapter 2 for optical layouts of GWDs). Hence, special preparation of the laser beam is required, which is often conceptually divided according to whether the components of the stabilized laser reside in the air or in an ultra-high vacuum system. The latter is based on filtering and control via 10–100-m long optical resonators, the so-called input mode-cleaner (see Chapter 18). The laser beam preparation outside the vacuum is typically called the pre-stabilization and constitutes the main topic of this chapter.

The light which is injected into the main interferometer in all advanced ground-based laser interferometric gravitational-wave detectors comes from high-power lasers operating at near infrared wavelengths, with powers exceeding 100 W. Their frequency stability in the detection frequency band with respect to their relevant references, the arm cavities, is unrivaled by any other experimental method. Similarly, the relative intensity noise (RIN) of the laser beams, especially at lower frequencies of the detection band, defines the state of the art in laser power stabilization. Their spatial eigenmode is very close to an ideal Gaussian mode. This chapter describes the input optics of the advanced detectors that prepare and inject these near ideal laser beams into the main interferometers.

The choice of materials used to construct an interferometric gravitational-wave detector, or any precision measurement device, is of critical importance. The materials are significant in setting sensitivity limits, especially through thermal noise. Materials also influence the mechanical resonances, connections between subsystems, thermal and optical behavior, controls, and many technical noise sources. We describe the manufacture and properties of materials important for second-generation interferometric gravitational-wave detectors; fused silica glass used for optics substrates, suspension and the low index material of the optical coatings, and amorphous tantalum oxide, with and without titania as a dopant, used for the high index material in the coatings. We detail the creation of the detector core optics, from shaping and polishing through coating and characterization. We then briefly describe the installation of these optics and provide tables that enumerate the properties of the Advanced LIGO, Advanced Virgo and KAGRA core optics.

Length sensing can be seen as the core objective of interferometry, aiming at an as precise as possible measurement of length and length fluctuations. For an interferometric gravitational-wave detector, the quantity containing gravitational-wave information is derived from an ultra-sensitive measurement of differential length fluctuations of the long arms. In this chapter we will describe methods to deduce length signals for advanced gravitational-wave detectors and discuss aspects of length control. We will further look at the non-trivial process of lock acquisition, as well as the readout of the gravitational-wave signal.

This chapter describes one of the most difficult aspects of operating a gravitational-wave interferometer: the alignment sensing and control of the interferometer optics. How to properly sense and control the angular degrees of freedom of a suspended interferometer has been an active topic of research for about three decades. The current generation of advanced detectors have been stably operated during their first two observing runs, O1 and O2. Nevertheless, there are still significant challenges to overcome. Here is a glimpse of the complexity of the interferometer alignment sensing and control scheme, globally referred to as ASC.

Prior to this chapter, all discussions of interferometer optical design and operation have for the most part assumed ideal optical elements. This chapter discusses wavefront distortion from non-ideal optical elements, its adverse effects on interferometer performance and the sources of wavefront distortion. It also reviews the design of a control system for compensation.

Previous chapters in this volume have presented the major components of the Advanced LIGO and Advanced Virgo interferometers, describing their specific roles. Establishing a design that can reach the desired interferometer performance goals, both in terms of sensitivity and operational uptime, falls into the domain of detector system design. This chapter presents the approaches and considerations in developing the overall interferometer design, as well as examining some of the trade-offs and subsystem interplay that must be considered as the design develops.

This chapter describes how Advanced LIGO came to be, as a case study for planning and managing large-scale scientific infrastructure projects. A short history is given along with motivations for the scope, timing and project structure. The key documents, tools and organizational bodies that enabled the project to be executed successfully are described. Several specific systems aspects — contamination, testing, configuration and quality control, and fault recording — are mentioned. Lastly, the project management approach is reviewed.

If civilization were to be wiped out and only a single statement could be left behind in stone for future scientists to use, as they rebuilt civilization and invented gravitational-wave detectors to reach out into the universe, it would be this: “Think carefully and holistically about your detector before building it such that no part is neglected as being ‘too small’ or having a coupling at ‘second order’”…

The direct detection of gravitational waves (GWs) and the beginning of GW astronomy were made possible by the success of the second generation of GW detectors: Advanced LIGO and Advanced Virgo. Further developments of these interferometers are required to achieve design sensitivity and extend their detection range. However, in order to contribute to future high-precision multi-messenger astronomy and to reach cosmological distances in the observation of GW sources, the construction of a third generation of GW observatories is indispensable. The Einstein Telescope (ET) in Europe and Cosmic Explorer (CE) in the US are planned to be the first nodes of a future network of 3G observatories. Some of the key design and technology elements of the ET project and the initial ideas of the CE concept are presented in this chapter.

The straightforward way to reduce thermal noise of a gravitational-wave interferometer is to reduce the physical temperature of mirrors while keeping their mechanical loss low. Since the mirrors are usually suspended by thin fibers in vacuum, this can be a delicate undertaking. The concept of this kind of cryogenic mirror is introduced and the development of practical interferometers is described.

The following section is included:

• Index