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The Next Generation of Interferometry: Multi-Frequency Optical Modelling, Control Concepts and Implementation

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The Next Generation of Interferometry: Multi-Frequency Optical Modelling, Control Concepts and Implementation The Next Generation of Interferometry: Multi-Frequency Optical Modelling, Control Concepts and Implementation Vom Fachbereich Physik der UniversitÄat Hannover zur Erlangung des Grades Doktor der Naturwissenschaften { Dr. rer. nat. { genehmigte Dissertation von Dipl.-Phys. Andreas Freise geboren am 24. Mai 1971 in Hildesheim 2003 Referent: Prof. K. Danzmann Korreferent: Prof. W. Ertmer Tag der Promotion: 04. Februar 2003 Druckdatum: 22. Februar 2003 Zusammenfassung Albert Einstein hat in seiner allgemeinen RelativitÄatstheorie die Existenz von Gravitationswellen vorhergesagt. Die direkte Me¼ung dieser Wellen ist eine der gro¼en Herausforderungen der Ex- perimentalphysik. Mit Hilfe eines Netzwerkes von Gravitationswellendetektoren wird es mÄoglich sein, das Universum unabhÄangig von elektro-magnetischer Strahlung zu beobachten. Die Gravita- tionswellenastronomie wird der Kosmologie und der Gravitationsphysik neue, bisher unerreichbare experimentelle Daten zur VerfugungÄ stellen. Zur Zeit werden weltweit funfÄ gro¼e interferometrische Gravitationswellendetektoren gebaut. Sie basieren auf klassischen Instrumenten wie z.B. dem Michelson-Interferometer. FurÄ die Suche nach Gravitationswellen ist allerdings eine extrem hohe, bisher unerreichte Me¼emp¯ndlichkeit notwen- dig. Diese soll durch den Einsatz von weiterentwickelten, optimierten Teilsystemen des Interfero- meters und durch die Entwicklung neuer Interferometertopologien erreicht werden. Diese Arbeit dokumentiert einen wichtigen Teil des Aufbaus des britisch-deutschen Detektors GEO 600, der sich zur Zeit in der Testphase be¯ndet und erste Me¼daten aufnimmt. Im ersten Abschnitt werden das Moden¯lter-System und die Laserfrequenzstabilisierung beschrieben, wel- che im Rahmen dieser Arbeit aufgebaut wurden. Um die benÄotigte extrem hohe Emp¯ndlichkeit zu erreichen, mu¼ der verwendete Laserstrahl bezuglicÄ h rÄaumlicher und zeitlicher Fluktuationen ge¯ltert und stabilisiert werden. Dies wird erreicht durch zwei sequentielle Ringresonatoren, soge- nannte Moden¯lter, mit aufgehÄangten Spiegeln und einer UmlauflÄange von jeweils 8 m. Diese Re- sonatoren ersetzen au¼erdem den ublicÄ hen festen Referenzresonator furÄ die Frequenzstabilisierung des Lasers. Mit Hilfe von Pound-Drever-Hall-Regelungen wurde eine (in-loop) FrequenzstabilitÄat von 100¹Hz=pHz bei 100 Hz erreicht. Die Moden¯lter und die Frequenzstabilisierung arbeiten Äau¼erst zuverlÄassig; es konnte ein kontinuierlicher Betrieb von ubÄ er 120 Stunden demonstriert werden. Die Kontrollsysteme sind automatisiert, so da¼ im Normalbetrieb kein manueller Eingri® erforderlich ist. Im zweiten Teil der Arbeit werden fortschrittliche Interferometermethoden besprochen. GEO 600 wird als erster Detektor das sogenannte Dual-Recycling verwenden, welches die Emp¯ndlichkeit des Detektors erhÄoht und eine Abstimmung auf eine gewunscÄ hte Signalfrequenz der Gravitati- onswelle erlaubt. Dies wird durch einen zusÄatzlichen Spiegel im Interferometerausgang erreicht. Ein solches Interferometer hat drei longitudinale Freiheitsgrade, die mit Hilfe von Modulation- Demodulations-Methoden stabilisiert werden sollen. FurÄ das Design und VerstÄandnis eines Michel- son-Interferometers mit Dual-Recycling ist es zwingend erforderlich, das optische System mit Hilfe einer Modellierung in einem multidimensionalen Parameterraum zu analysieren. Zu diesem Zweck wurde eine numerische Interferometersimulation entwickelt, die es erlaubt, beliebige Laserinterfe- rometer zu simulieren. Das optische System wird hierbei durch ein lineares Gleichungssystem be- schrieben, welches numerisch gelÄost wird. Die Simulation unterstutztÄ unter anderem Modulation- Demodulations-Techniken und hÄohere transversale Moden. Des weiteren wurden im Rahmen dieser Arbeit weiterfuhrendeÄ Topologien untersucht, wovon hier das Xylophon-Interferometer vorgestellt wird. Dieses Interferometer stellt eine direkte Erweiterung zum Dual-Recycling dar, die es ermÄoglicht, die Form der Emp¯ndlichkeitskurve zu optimieren und somit die Emp¯ndlichkeit in einem gewÄahlten Frequenzbereich zu maximieren. Stichworte: Gravitationswellendetektor, Frequenzstabilisierung, Dual Recycling i ii Summary Albert Einstein predicted the existence of gravitational waves in his theory of general relativ- ity. The direct measurement of gravitational waves is one of the most challenging projects in experimental physics. A network of detectors would be able to muster the sky independently of electro-magnetic waves. Gravitational-wave astronomy will provide fascinating new data for cosmology and gravitational physics. To date, ¯ve large-scale interferometric gravitational-wave detectors are being build worldwide. These detectors make use of classic optical instruments such as the Michelson interferometer. The detection of gravitational waves, however, requires an extremely good sensitivity. We aim to achieve the required sensitivity by optimising the subsystems of the interferometer and by using new interferometer topologies. This work describes important contributions to the British-German detector GEO 600, which is currently commissioned and records ¯rst data. First, the mode cleaners and the laser frequency stabilisation are discussed. These systems have been constructed and commissioned within this work. In order to guarantee a good sensitivity, the laser beam has to be ¯ltered in space and time before it enters the Michelson interferometer. Two ring cavities with suspended mirrors and an optical path length of 8 m each have been installed as so-called mode cleaners. In addition, these cavities replace the commonly used rigid reference cavity of the laser frequency stabilisation. By using Pound-Drever-Hall control loops, an (in-loop) frequency stability of 100¹Hz=pHz at 100 Hz was achieved. The mode cleaners and the frequency stabilisation system work reliably; a continuous operation of more than 120 hours could be demonstrated. The control systems have been automated so that no human interaction is required during normal operation. In the second part of this work, advanced interferometer concepts are discussed. GEO 600 will be the ¯rst large-scale detector to use Dual Recycling. By installing an additional mirror in the in- terferometer output, the shot-noise-limited sensitivity of the detector is enhanced. Furthermore, the detector can then be tuned to a chosen signal frequency (of the gravitational wave). The Dual-Recycled Michelson interferometer has three longitudinal degrees of freedom that are to be controlled using modulation-demodulation techniques. It is essential for the design and under- standing of such an interferometer to analyse the optical system using a multi-parameter model. Consequently, a numerical simulation has been developed: A user-de¯ned interferometer topology is described by a linear system of equation that is then solved numerically. The simulation com- putes a variety of output signals such as error signals and transfer functions; transverse modes of the light or modulation-demodulation schemes can be included in the analysis. During this work, further advanced interferometer concepts were investigated, and the Xylophone interferometer is introduced here. This interferometer represents a direct extension to a Dual- Recycled Michelson interferometer; it allows to optimise the shape of the shot-noise spectral density and thus maximise the sensitivity in a given frequency band. Keywords: Gravitational wave detector, frequency stabilisation, Dual Recycling iii iv Contents Zusammenfassung i Summary iii Contents v List of ¯gures ix List of tables xiii Glossary xv 1 The interferometric gravitational-wave detector GEO 600 1 1.1 Introduction . 1 1.1.1 Sensitivity of GEO 600 . 2 1.1.2 Optical setup . 5 1.2 Laser system . 6 1.2.1 Master laser . 7 1.2.2 Slave laser . 8 1.2.3 Laser bench . 10 1.3 Mode cleaners . 12 1.3.1 Mode-cleaner design . 14 1.3.2 Optical layout . 15 1.3.3 Mounting units . 17 1.3.4 Mode matching to the ¯rst mode cleaner . 19 1.3.5 Optical properties of the mode cleaners . 21 1.3.6 Mechanical setup of the suspension system . 22 1.4 Michelson interferometer . 24 1.4.1 Optical layout . 26 1.4.2 Interferometer design . 31 1.4.3 Optical properties . 33 1.5 Output mode cleaner . 34 2 The laser frequency stabilisation for GEO 600 37 2.1 Introduction . 37 2.2 Frequency-noise speci¯cation . 39 v Contents 2.3 Concept of the length and frequency control . 40 2.4 Pound-Drever-Hall control loops . 41 2.4.1 Quadrant cameras . 43 2.4.2 Piezo-electric transducer . 45 2.4.3 Pockels cells . 45 2.4.4 Coil-magnet actuator . 46 2.5 Laser and ¯rst mode cleaner . 48 2.5.1 Servo design . 50 2.5.2 Error-point spectrum . 51 2.5.3 Calibration of frequency-noise measurements . 55 2.5.4 `Current lock': Feeding back to the pump diode current . 57 2.6 Second mode cleaner . 57 2.6.1 Servo design . 58 2.6.2 Error-point spectrum . 59 2.7 Power-Recycling cavity . 61 2.7.1 The `1200 m experiment' . 62 2.7.2 Error-point spectrum . 65 2.7.3 Power-Recycled Michelson interferometer . 65 2.7.4 Higher-order mode e®ects . 68 2.7.5 DC loop . 72 2.8 Remote control and automatic operation . 72 2.8.1 Lock acquisition . 73 2.8.2 Mode-cleaner control . 75 2.8.3 Power-Recycling cavity control . 76 2.9 Automatic alignment system . 76 3 Advanced interferometer techniques 79 3.1 Introduction . 79 3.1.1 Interferometer control . 80 3.1.2 Michelson interferometer . 81 3.1.3 Shot-noise-limited sensitivity . 82 3.1.4 Quantum-noise correlations . 84 3.2 Dual Recycling . 85 3.2.1 Power Recycling . 85 3.2.2 Signal Recycling . 87 3.2.3
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