Advanced Interferometers and the Search for Gravitational Waves: Lectures from the First VESF School on Advanced Detectors for Gravitational Waves (Astrophysics and Space Science Library Book 404)

The Search For Gravitational Radiation With Optical Interferometers Is Gaining Momentum Worldwide. Beside The Virgo And Geo Gravitational Wave Observatories In Europe And The Two Ligos In The United States, Which Have Operated Successfully During The Past Decade, Further Observatories Are Being Completed (kagra In Japan) Or Planned (iligo In India). The Sensitivity Of The Current Observatories, Although Spectacular, Has Not Allowed Direct Discovery Of Gravitational Waves. The Advanced Detectors (advanced Ligo And Advanced Virgo), At Present In The Development Phase, Will Improve Sensitivity By A Factor Of 10, Probing The Universe Up To 200 Mpc For Signal From Inspiraling Binary Compact Stars. This Book Covers All Experimental Aspects Of The Search For Gravitational Radiation With Optical Interferometers. Every Facet Of The Technological Development Underlying The Evolution Of Advanced Interferometers Is Thoroughly Described, From Configuration To Optics And Coatings, And From Thermal Compensation To Suspensions And Controls. All Key Ingredients Of An Advanced Detector Are Covered, Including The Solutions Implemented In First-generation Detectors, Their Limitations, And How To Overcome Them. Each Issue Is Addressed With Special Reference To The Solution Adopted For Advanced Virgo, But Constant Attention Is Also Paid To Other Strategies, In Particular Those Chosen For Advanced Ligo. Preface -- Foreword -- Towards Gravitational Wave Astronomy -- The Science Case For Advanced Gravitational Wave Detectors -- Interferometer Configurations -- Pre Stabilized Lasers For Advanced Detectors -- Input Optics System -- Readout, Sensing And Control -- An Introduction To The Virgo Suspension System -- Thermal Noise In Laser Interferometer Gravitational Wave Detectors -- Thermal Effects And Other Wave-front Aberrations In Recycling Cavities -- Stray Light Issues -- A Basic Introduction To Quantum Noise And Quantum-non-demolition Techniques -- The Parametric Instability In Advanced Gravitational-wave Interferometers -- A Third Generation Gravitational Wave Observatory: The Einstein Telescope -- Low Temperature And Gravitation Wave Detectors. Edited By Massimo Bassan. Foreword 6 Preface 7 Contents 11 1 Towards Gravitational Wave Astronomy 13 1.1 Introduction 13 1.2 The Legacy of the First-Generation Interferometric Detectors 14 1.3 Creating a Worldwide Network 16 1.4 Advanced Detectors: The Scenario 16 1.4.1 Advanced LIGO 19 1.4.2 Advanced Virgo 19 1.4.3 KAGRA 21 1.5 Advanced Detectors: The Technologies 21 1.5.1 Optical Configurations 21 1.5.2 Mirrors 22 1.5.3 Vibration Isolation 24 1.5.4 Monolithic Suspensions 25 1.5.5 Laser 27 1.5.6 Thermal Compensation 27 1.5.7 Squeezing 29 1.6 Third Generation: The Einstein Telescope 29 References 31 2 The Science Case for Advanced Gravitational Wave Detectors 33 2.1 Introduction 33 2.2 Generalities 36 2.3 Transients 38 2.3.1 Compact Binary Coalescence 38 2.3.2 Core Collapse Supernovae 45 2.3.3 Scientific Results on Transients 47 2.3.4 Transients in the ADE: Science and Prospects 49 2.4 Continuous Signals 55 2.4.1 Rotating Neutron Stars 56 2.4.2 Stochastic Background 61 2.5 Conclusions 64 References 65 3 Interferometer Configurations 68 3.1 The Interferometer as a Transducer 68 3.1.1 Plane Wave Description of Laser Fields 69 3.1.2 Effect of a Gravitational Wave 70 3.2 The Michelson Interferometer 71 3.2.1 Common and Differential Signals 74 3.2.2 Shot Noise 74 3.3 Improving the Sensitivity: Resonant Fabry-Perot Cavities 75 3.3.1 Static Response of a Fabry-Perot Cavity 76 3.3.2 Frequency Response of a Fabry-Perot Cavity 79 3.4 Increasing the Circulating Power: Power Recycling Technique 81 3.5 Shaping the Optical Response: Signal Recycling Technique 84 3.6 High Power Brings Radiation Pressure 90 3.6.1 Opto-Mechanical Couplings 90 3.6.2 Change in the ITF Optical Response 95 3.7 Beam Optics and High Order Transverse Modes 96 3.7.1 The Paraxial Diffraction Equation 97 3.7.2 Transverse Electro-Magnetic Modes 99 3.7.3 Resonant Cavity Stability and Mode Separation 99 3.8 Stability of Recycling Cavities 103 3.9 Exercises 105 3.9.1 Etalon Effect 105 References 106 4 Pre-stabilized Lasers for Advanced Detectors 107 4.1 Brief Introduction on the Laser 107 4.2 Laser Sources for Gravitational Wave Interferometric Detection 110 4.3 Getting Stable HP Lasers 112 4.4 HP Laser Candidates 113 4.5 Laser Pre-stabilizations 119 4.6 Conclusion 121 References 122 5 Input Optics System 124 5.1 Introduction 124 5.2 Radio Frequency Modulation System 125 5.2.1 Electro-Optic Effect 126 5.2.2 Acousto-Optic Effect 131 5.2.3 Advanced Virgo Modulator 136 5.3 Faraday Isolation 136 5.3.1 Faraday Effect 137 5.3.2 Advanced Virgo Faraday Isolator 138 5.4 Input Mode Cleaner Cavity 142 5.5 Reference Cavity System 147 5.6 Beam Pointing Control 148 5.6.1 Beam Jitter 148 5.6.2 Beam Jitter Control System 149 5.7 Input Power Control System 150 5.8 Mode Matching Telescope 152 5.8.1 Optical Telescope 153 5.9 Future Improvements 154 5.9.1 Input Beam Monitoring System 155 5.9.2 Thermally Deformable Mirrors 157 5.10 Advanced Ligo Input Optics 159 References 160 6 Readout, Sensing, and Control 161 6.1 Foundations of the Problem 161 6.2 How to Measure the Laser Field Phase Change 162 6.2.1 Heterodyne Detection 162 6.2.2 Pound-Drever-Hall Technique 164 6.2.3 Frontal Modulation 168 6.2.4 The Schnupp Asymmetry 169 6.2.5 Phase Noise 170 6.2.6 Homodyne Detection 171 6.3 Longitudinal Control of the Interferometer 173 6.3.1 The Problem of Lock Acquisition 175 6.3.2 Laser Frequency Stabilization 176 6.4 Angular Control 177 6.5 A Brief Introduction to Feedback Control Systems 180 6.5.1 Linear Systems 181 6.5.2 Simple Feedback System 182 6.5.3 Response to Variations of the Input Signal 186 6.5.4 Stability 188 6.5.5 Bode and Nichols Plots 192 6.5.6 Fabry--Perot cavity 194 6.6 Actuation: How to Apply Forces to the Mirrors 195 6.6.1 Hierarchical Control 196 6.7 Exercises 199 6.7.1 Dither Control 199 References 200 7 An Introduction to the Virgo Suspension System 201 7.1 Introduction 201 7.2 The Harmonic Oscillator as a Mechanical Filter 202 7.3 The Real Suspension Systems in Gravitational Wave Interferometers 204 7.3.1 The Virgo Superattenuator 206 7.3.2 The Inverted Pendulum 206 7.3.3 The Top Ring and the Filter 0 208 7.3.4 The Seismic Filters 210 7.3.5 The Magnetic Anti-Spring 212 7.3.6 The Filter 7 213 7.4 The Last Stage Suspension 215 7.4.1 Overview of the Last Stage Suspension 215 7.4.2 The Last Stage Suspension and the Local Control of the Mirror 216 7.4.3 The Real Design of Last Stage Suspension Elements 219 7.4.4 Last Stage Suspension and Thermal Noise 219 7.4.5 The Monolithic Suspensions 223 7.4.6 The Last Stage Suspension in Advanced Virgo 228 References 231 8 Thermal Noise in Laser Interferometer Gravitational Wave Detectors 232 8.1 Introduction 232 8.2 The Fluctuation-Dissipation Theorem 234 8.3 Application to the Harmonic Oscillator 235 8.4 Pendulum Thermal Noise 239 8.5 Thermal Noise in Continuous Systems 242 8.6 Substrate Thermal Noise, Thermo-Elastic Noise, and Thermo-Refractive Noise 245 8.7 Coating Thermal Noise 248 8.8 Conclusions 255 References 255 9 Thermal Effects and Other Wavefront Aberrations in Recycling Cavities 257 9.1 Introduction to Thermal Effects 257 9.1.1 Thermal Lensing 258 9.1.2 Consequences of Thermal Effects 263 9.2 Compensation of Thermal Effects in Virgo 266 9.2.1 General Guidelines 266 9.2.2 The Virgo Scheme 266 9.3 Adaptive Optical System for Advanced Virgo 269 9.3.1 Thermal Effects in Advanced Detectors 269 9.3.2 TCS Noise Coupling 271 9.3.3 TCS in Advanced Virgo 272 9.3.4 Other Sources of Wavefront Aberrations in Advanced Virgo Recycling Cavities 274 9.3.5 Sensing Wavefront Aberrations in Recycling Cavities 276 9.4 Conclusions 279 References 280 10 Stray Light Issues 281 10.1 The Stray Light Displacement Noise 281 10.2 Stray Light Coupling Mechanisms 282 10.3 Experimental Evidences and Measurements 287 10.4 Stray Light Noise Mitigation 290 10.4.1 Core Optics Small Angle Scattering 290 10.4.2 Core Optics Wide Angle Scattering 291 10.4.3 External Optics Back-Scattering 292 10.5 Future Prospects 293 References 295 11 A Basic Introduction to Quantum Noise and Quantum-Non-Demolition Techniques 297 11.1 How to Approach This Chapter 297 11.2 The Basics of Quantum Noise 298 11.2.1 Principles for Building a GW Detector 298 11.2.2 Photon Shot Noise and Quantum Radiation Pressure Noise 300 11.2.3 The Standard Quantum Limit 301 11.3 A Simple Graphical Tool to Understand Quantum Noise 301 11.3.1 The Quadrature Picture 301 11.3.2 The Ball on a Stick Picture 303 11.4 Squeezed Light Injection 306 11.5 Homodyne Readout and Variational Readout 309 11.6 Frequency-Dependent Squeezing 311 11.7 Optical Springs and Optomechanical Rigidity 314 11.8 Speedmeter Topologies 316 11.9 Challenges Towards Sub-SQL Interferometry 318 References 319 12 The Parametric Instability in Advanced Gravitational-Wave Interferometers 321 12.1 Radiation-Pressure Effects 321 12.1.1 Optomechanical Dynamics 322 12.1.2 Experimental Results: Optical Damping 323 12.1.3 Optomechanical Instability 325 12.2 Three-Mode Parametric Effects 325 12.2.1 From Two-Mode to Three-Mode Effects 326 12.2.2 Experimental Demonstration of Three-Mode Coupling 327 12.2.3 Toward Table-Top Demonstrations of the PI 328 12.3 Computing the PI in Large-Scale Interferometers 330 12.3.1 Finite-Element Computation of the Parametric Gain 331 12.3.2 Feedback Approach and Monte-Carlo Estimate of the Gain 332 12.4 Mitigation Strategies 333 12.4.1 Passive Damping 333 12.4.2 Active Damping with an Electrostatic Drive 334 12.4.3 Active Damping with Optical Feedback 335 12.5 Conclusion 336 References 336 13 A Third Generation Gravitational Wave Observatory: The Einstein Telescope 338 13.1 Introduction 338 13.2 Scientific Targets of ET 339 13.3 The Einstein Gravitational Wave Telescope Project 341 13.3.1 Seismic Noise 343 13.3.2 Newtonian Noise 346 13.3.3 Thermal Noise 351 13.3.4 Quantum Noise 355 13.4 Infrastructures, Geometries, and Topologies 361 References 364 14 Low Temperature and Gravitation Wave Detectors 368 14.1 Introduction 368 14.2 Cryogenics 370 14.2.1 The Cryofluids 373 14.2.2 The Cryocooler 379 14.2.3 Cooling Strategy Comparison 384 14.3 The Cryogenic Payload 385 14.3.1 Payload Thermal Input and Heat Extraction 387 14.4 Conclusion 391 References 391 "The search for gravitational radiation with optical interferometers is gaining momentum worldwide. Beside the VIRGO and GEO gravitational wave observatories in Europe and the two LIGOs in the United States, which have operated successfully during the past decade, further observatories are being completed (KAGRA in Japan) or planned (ILIGO in India). The sensitivity of the current observatories, although spectacular, has not allowed direct discovery of gravitational waves. The advanced detectors (Advanced LIGO and Advanced Virgo), at present in the development phase, will improve sensitivity by a factor of 10, probing the universe up to 200 Mpc for signal from inspiraling binary compact stars. This book covers all experimental aspects of the search for gravitational radiation with optical interferometers. Every facet of the technological development underlying the evolution of advanced interferometers is thoroughly described, from configuration to optics and coatings, and from thermal compensation to suspensions and controls. All key ingredients of an advanced detector are covered, including the solutions implemented in first-generation detectors, their limitations, and how to overcome them. Each issue is addressed with special reference to the solution adopted for Advanced VIRGO, but constant attention is also paid to other strategies, in particular those chosen for Advanced LIGO"-- Page 4 of cover Front Matter....Pages i-xii Towards Gravitational Wave Astronomy....Pages 1-20 The Science Case for Advanced Gravitational Wave Detectors....Pages 21-55 Interferometer Configurations....Pages 57-95 Pre-stabilized Lasers for Advanced Detectors....Pages 97-113 Input Optics System....Pages 115-151 Readout, Sensing, and Control....Pages 153-192 An Introduction to the Virgo Suspension System....Pages 193-223 Thermal Noise in Laser Interferometer Gravitational Wave Detectors....Pages 225-249 Thermal Effects and Other Wavefront Aberrations in Recycling Cavities....Pages 251-274 Stray Light Issues....Pages 275-290 A Basic Introduction to Quantum Noise and Quantum-Non-Demolition Techniques....Pages 291-314 The Parametric Instability in Advanced Gravitational-Wave Interferometers....Pages 315-331 A Third Generation Gravitational Wave Observatory: The Einstein Telescope....Pages 333-362 Low Temperature and Gravitation Wave Detectors....Pages 363-387