Quantum Enhancement of a 4 km Laser Interferometer Gravitational-Wave Detector (Springer Theses)

Nominated for Springer Theses by the Gravitational Waves International Committee (GWIC) Winner of 2013 GWIC Thesis Prize – The annual prize for an outstanding Ph.D. thesis based on research in gravitational waves Presents the first ever measurement of squeezing enhancement in a full-scale suspended GW interferometer with Fabry-Perot arms Achieved best sensitivity by any Gravitational Wave detector The annual prize for an outstanding Ph.D. thesis based on research in gravitational waves Presents the first ever measurement of squeezing enhancement in a full-scale suspended GW interferometer with Fabry-Perot arms Achieved best sensitivity by any Gravitational Wave detector The work in this thesis was a part of the experiment of squeezed light injection into the LIGO interferometer. The work first discusses the detailed design of the squeezed light source which would be used for the experiment. The specific design is the doubly-resonant, traveling-wave bow-tie cavity squeezed light source with a new modified coherent sideband locking technique. The thesis describes the properties affecting the squeezing magnitudes and offers solutions which improve the gain. The first part also includes the detailed modeling of the back-scattering noise of a traveling Optical Parametric Oscillator (OPO). In the second part, the thesis discusses the LIGO Squeezed Light Injection Experiment, undertaken to test squeezed light injection into a 4km interferometric gravitational wave detector. The results show the first ever measurement of squeezing enhancement in a full-scale suspended gravitational wave interferometer with Fabry-Perot arms. Further, it showed that the presence of a squeezed-light source added no additional noise in the low frequency band. The result was the best sensitivity achieved by any gravitational wave detector. The thesis is very well organized with the adequate theoretical background including basics of Quantum Optics, Quantum noise pertaining to gravitational wave detectors in various configurations, along with extensive referencing necessary for the experimental set-up. For any non-experimental scientist, this introduction is a very useful and enjoyable reading. The author is the winner of the 2013 GWIC Theses Prize. Related Subjects: Classical and Quantum Gravitation, Relativity Theory, Quantum Optics, Quantum Electronics, Nonlinear Optics, Astronomy, Astrophysics and Cosmology 1 Introduction 1.1 Squeezed States for Gravitational-Wave Detection 1.1.1 Squeezing Magnitude 1.1.2 Audio-Detection Band Fourier Frequencies 1.1.3 Proof-of-Principle Experiments and Application in Gravitational-Wave-Detection Interferometers 1.2 Thesis Overview 1.3 Statement of Contribution 1.4 Publications References Part I Background 2 Gravitational Waves and the Quest for Their Direct Detection 2.1 The Nature of Gravitational Waves 2.2 Ground-Based Gravitational-Wave Interferometric Detectors 2.2.1 Interferometers for Direct Detection 2.2.2 The ``Generation 1.5'' Detectors 2.2.3 Second Generation Detectors 2.2.4 Third Generation Detectors 2.2.5 Strain Sensitivities and Development Timelines 2.3 Noise Sources Affecting Ground-Based Interferometers 2.3.1 Quantum Noise 2.3.2 Thermal Noise 2.3.3 Seismic Noise 2.3.4 Gravity Gradient Noise 2.3.5 Other Noise Sources 2.4 Summary References 3 Quantum Optics and Light 3.1 Light Quantisation 3.1.1 The Quantised Electromagnetic Field 3.1.2 Quadrature Operators 3.1.3 The Heisenberg Uncertainty Principle and Quantum Noise 3.1.4 The Number Operator 3.2 Important States of Light 3.2.1 The Coherent State 3.2.2 The Vacuum State 3.2.3 The Squeezed State 3.2.4 Non-minimum Uncertainty States 3.3 Pictorial Representations of the States of Light 3.3.1 Classical Phasor and Classical Sideband Diagrams 3.3.2 Quantum Phasor Diagram 3.3.3 Quantum Sideband Diagram 3.4 A Quantum Treatment of Optical Components 3.4.1 Linearisation of Operators 3.4.2 A Partially Transmissive Mirror 3.4.3 Photodetection 3.5 Optical Cavities 3.5.1 Quantum Langevin Equations of an Optical Cavity 3.5.2 Reflected and Transmitted Fields 3.5.3 Noise Variances of the Reflected and Transmitted Fields 3.6 Summary References 4 Quantum Noise in Gravitational-Wave Detectors and Applied Squeezed States 4.1 Quantum Noise in Measurement 4.1.1 Amplitude Quadrature Uncertainty---Radiation Pressure Noise 4.1.2 Phase Quadrature Uncertainty---Photon Shot Noise (Shot Noise) 4.1.3 The Standard Quantum Limit (SQL) 4.2 Main Source of Quantum Noise in Gravitational-Wave Measurement 4.3 Simple Michelson Interferometers 4.3.1 Input-Output Relations for Quantum Noise 4.3.2 Squeezing in Simple Michelson Interferometers 4.4 Power-Recycled Fabry-Perot Michelson Gravitational-Wave Detectors 4.4.1 Additions to the Simple Michelson Configuration 4.4.2 Quantum Noise in a Lossless Power-Recycled Michelson 4.4.3 Arm Cavities and Power-Recycling Effect on Quantum Noise 4.4.4 Squeezing Enhancement of a Lossless Power-Recycled Michelson 4.4.5 Power-Recycled Michelson with Optical Losses 4.4.6 Squeezing in a Power-Recycled Michelson with Optical Losses 4.5 Dual-Recycled Fabry-Perot Michelson Gravitational-Wave Detectors 4.6 Implications and Assumptions 4.6.1 Signal-to-Noise Ratio 4.6.2 Contributing Noise Sources Other Than Quantum Noise 4.6.3 Squeezing Injection Optical Losses 4.6.4 Frequency Dependent Squeezing and the Heisenberg Uncertainty Principle 4.6.5 Squeezing and Optical Filter Cavities 4.7 Summary References 5 Squeezed State Generation for Gravitational-Wave Detection 5.1 Squeezed Light Source Overview 5.2 Laser Input Stages 5.3 Nonlinear Optical Stages 5.3.1 Nonlinear Optical Interactions 5.3.2 .2 Nonlinear Cavity Quantum Langevin Equations 5.3.3 Second Harmonic Generator (SHG) 5.3.4 Optical Parametric Oscillator (OPO) 5.3.5 Classical Behaviour of the OPO 5.3.6 Semiclassical Behaviour of the OPO 5.3.7 The OPO and the Auxiliary Field 5.4 Detection Stage (Purple Section) 5.4.1 Balanced Detection Schemes 5.4.2 Balanced Homodyne Detection (HD) 5.5 Filtering and Stabilisation Stages 5.5.1 Mode Cleaner (MC) 5.5.2 Mach-Zehnder Interferometer (MZ) 5.6 Control Stages 5.6.1 DC Voltage Subtraction Locking 5.6.2 Offset Frequency Locking 5.6.3 Pound-Drever-Hall Locking 5.7 Summary References Part II The Doubly Resonant, Travelling-WaveSqueezed Light Source 6 The Doubly Resonant, Travelling-Wave Squeezed Light Source 6.1 Design Properties of the Optical Parametric Oscillator 6.1.1 Bow-Tie Travelling-Wave Cavity 6.1.2 Doubly Resonant Cavity 6.1.3 Wedged Nonlinear Media 6.2 The Doubly Resonant, Travelling-Wave OPO Cavity 6.3 Modified Coherent Sideband Locking 6.3.1 Coherent Sideband Locking 6.3.2 Modified Coherent Sideband Locking 6.4 Properties Affecting Squeezing Magnitude Measurement 6.4.1 Optical Losses 6.4.2 Spatial Mode Mismatch 6.4.3 Squeezing Measurement Efficiency 6.4.4 Squeezing Ellipse Phase Noise 6.4.5 Squeezing/Antisqueezing as a Function of OPO Nonlinear Parametric Gain 6.5 Properties Affecting Squeezed State Detection at Low Frequencies 6.5.1 Detection Electronics 6.5.2 Homodyne Detection Balancing 6.5.3 Backscattered Light Interferences 6.6 Upgrades to the Squeezed Light Source 6.7 The DB-OPO Squeezed Light Source 6.8 Results from the DB-OPO Squeezed Light Source 6.8.1 Summary of Measurement Parameters 6.8.2 Squeezing Phase Noise Measurement 6.8.3 Time Series Measurement 6.8.4 First Measurement of Greater than 10dB Squeezing Across the Audio Gravitational-Wave Detection Band 6.8.5 Inferred Squeezing Magnitude 6.9 Summary References 7 Backscatter Tolerance of a Travelling-Wave Optical Parametric Oscillator 7.1 Backscattered Light 7.2 Theoretical Analysis of an OPO Cavity Backscattered-Light Reflectivity 7.3 Determining the Intrinsic Isolation Rr 7.3.1 Balanced Homodyne Measurement to Determine RCoup 7.3.2 Experimental Layout and Result 7.4 Bi-directional Scatter Distribution Function (BSDF) of the OPO 7.5 Verification of the Intrinsic Isolation with Squeezing Measurement 7.5.1 Noise Coupling to Squeezing Measurement 7.5.2 Squeezing with Injected Reverse-Beam Field 7.6 Discussion 7.6.1 Uncertainty in RCoup and Improving Measurements 7.6.2 Improving the Intrinsic Isolation 7.7 Summary References Part III The LIGO H1 Squeezed LightInjection Experiment 8 Overview of the LIGO Squeezed Light Injection Experiment 8.1 Project Background 8.2 The Enhanced LIGO Gravitational-Wave Detector . 8.2.1 The Enhanced LIGO H1 Detector 8.2.2 Hardware Installed for Squeezing Injection 8.2.3 Squeezed-Light Injection Path 8.2.4 Sensitivity of the Enhanced LIGO H1 Interferometer 8.3 The LIGO H1 Squeezed Light Source 8.4 The LIGO H1 Optical Parametric Oscillator 8.5 Squeezing Measurement with the Diagnostic Homodyne Detector 8.6 Summary References 9 Squeezing-Enhancement of a 4km LIGO Gravitational-Wave Detector 9.1 Squeezing Ellipse Phase Noise 9.1.1 Phase Noise from the LIGO Squeezed Light Source 9.1.2 Phase Noise Due to the Interferometer Control Sidebands 9.1.3 Phase Noise of the Squeezed Interferometer 9.1.4 Beam Pointing and Phase Noise 9.1.5 Summary of Phase Noise Results 9.2 Interferometer Squeezing Detection Efficiency 9.2.1 Squeezing/Antisqueezing as a Function of OPO Nonlinear Gain Using Interferometer Readout 9.2.2 Verification of the Interferometer Squeezing Detection Efficiency 9.2.3 Injection Hardware Optical Losses in HAM4 9.2.4 Optical Losses in HAM6---Output Mode Cleaner Mode-Matching Losses and Transmission Throughput 9.2.5 Results of Squeezing Detection Efficiency Verification Tests 9.2.6 Comparison to the OPO Nonlinear Gain Result 9.3 Squeezing-Enhanced Interferometer Sensitivity 9.4 Surpassing the Joint-Scientific Data Run Sensitivity Above 250Hz 9.5 Squeezing and Interferometer Input Power 9.6 Inferred Squeezing Improvement 9.6.1 Inferred Squeezing from the LIGO Squeezed Light Source 9.6.2 Inferred Level of Squeezing-Sensitivity Enhancement 9.7 Improvements for applying Squeezing in Future Gravitational-Wave Detectors 9.7.1 Reducing Sources of Squeezing Ellipse Phase Noise 9.7.2 Improving Squeezing Detection Efficiency 9.8 Summary References 10 Backscattered-Light Impact in a Squeezing-Enhanced Gravitational-Wave Detector 10.1 Backscattered Light from the Interferometer as Port 10.2 Theoretical Derivations and Experiments Overview 10.2.1 Backscattered-Light Theory 10.2.2 Scattered Light and OPO Nonlinear Gain 10.3 Experiment Conditions 10.3.1 Installed Hardware for Backscatter Noise Mitigation 10.3.2 Seismic and Acoustic Environment of the Squeezer Table 10.4 Evidence of the Backscattered Light Mechanism 10.5 Large Displacement Measurement 10.6 BSDF of the H1 Optical Parametric Oscillator 10.7 Small Displacement Measurement 10.8 Consistency Between Large Displacement and Small Displacement Measurements 10.9 Backscatter Improvements for Future Gravitational-Wave Detectors with Squeezing 10.10 Summary References 11 Results Summary, Recommendations and Future Work 11.1 Summary of Squeezed-Light Source Apparatus Development Results 11.2 Summary of LIGO Squeezed Light Injection Experiment Results 11.3 Summary of Recommended Development Work Towards Squeezed-Future Gravitational-Wave Detectors 11.3.1 Improving Squeezing Detection Efficiency 11.3.2 Reducing Sources of Squeezing Ellipse Phase Noise 11.3.3 Reducing Backscattered Light 11.4 Future Work References Appendix AQuantum Noise and Squeezingin Dual-Recycled Michelson Interferometers Appendix BInitial Analysis and Repair of the EnhancedLIGO H1 Output Mode Cleaner Appendix CSupplementary Information for theBackscatter-Light Experiments at LIGO Index