Title: Locking the Advanced LIGO Gravitational Wave Detector
Description: The Advanced LIGO gravitational wave detectors have recently achieved a new milestone. The two detector network is now operational and is being tuned for sensitivity. Currently, the state of the art detectors are the most sensitive ground-based interferometers to date and are closer than ever to the reality of a gravitational wave detection. For many years, there has been a worldwide effort to directly detect gravitational waves, a phenomena that was predicted in Einstein's theory of general relativity. A direct detection would further validate Einstein's theory, but more importantly would provide a novel approach to studying the universe and the elusive physics of gravity beyond Einstein's theory. However, none of this would be possible without the success of the arm length stabilization scheme. This recently demonstrated technique, which will be the focus of this thesis, is a critical step required to get the LIGO interferometers operational. This scheme is unique to the advanced generations of detectors and is extremely valuable for such a complex instrument.

As part of my research, I characterized, modeled, and helped design this important technique. I was also a part of a small team that brought the LIGO Hanford interferometer to its operational point for the first time. For astrophysical reasons, the goal of Advanced LIGO's design is to measure a gravitational strain as small as 4x10⁻²⁴/rtHz, requiring a length resolution of approximately 10⁻¹⁹ m. This high sensitivity demands multiple optical cavities to enhance the response of the interferometer. The interferometer is a Michelson interferometer geometry consisting of two 4km arm cavities, whose differential length is measured by the phase change of a resonating infrared laser at the gravitational wave readout port. The Michelson interferometer is enhanced by Fabry-Perot arm cavities, a power recycling cavity, and a signal extraction cavity. The Fabry-Perot arm cavities effectively increase the arm lengths by two orders of magnitude. Meanwhile, the power recycling cavity is used to enhance the circulating power within the interferometer, and the signal extraction cavity is used to enhance the optical response at the gravitational-wave readout.

Besides the increased design sensitivity of Advanced LIGO, a crucial requirement for a gravitational wave detection will be a high duty cycle. As an example, a worldwide Advanced LIGO network of five detectors, each with an 80% up-time, would only produce about 30% network up-time. A deterministic, robust, and fast sequence to transition the interferometer from an uncontrolled to a controlled state is mandatory. Advanced LIGO has five longitudinal degrees of freedom which must be controlled in order for the interferometer to be operational. However, all degrees of freedom are strongly coupled making this a traditionally challenging process. The state of the arm cavities can completely alter the state of the dual-recycled Michelson interferometer. Active feedback control is required to operate these instruments and keep the cavities locked on resonance. The optical response is highly non-linear until a good operating point is reached. The linear operating range is between 0.01% and 1% of a fringe for each degree of freedom.

The resonance lock has to be achieved in all five degrees of freedom simultaneously, making the acquisition difficult. Furthermore, the cavity linewidth seen by the laser is only ~1Hz which is four orders of magnitude smaller than the linewdith of the free running laser. To mitigate several of these critical problems, a new arm length stabilization technique was introduced to the lock sequence. The arm length stabilization technique utilizes two additional green lasers that are brought into resonance in each arm cavity. This effectively decouples the arm cavities from the rest of the interferometer. While the main infrared beam is kept off resonance from the arm cavity, a modulation technique utilizing third harmonics locks the central dual-recycled Michelson interferometer. In the final step, both arm cavities are slowly tuned onto resonance, nominal sensors are used, and full lock is achieved. To ensure a high duty cycle for Advanced LIGO and confirm repeatability of the locking sequence, a detailed study and characterization of the arm length stabilization technique was conducted.

A model of the scheme and a noise budget was developed. The model was beneficial while designing and implementing the scheme for the first time at the Advanced LIGO observatories. Meanwhile, the noise budget was critical to determine if this scheme would be viable in the lock process. Ultimately, the advent of the arm length stabilization to the lock process has been successful, a decisive milestone for future prospect of collecting meaningful astrophysical data. The technique has been implemented at both detectors and proven reliable and robust. Given the complexity of the interferometers, the success of this scheme to bring the detectors operational was a large accomplishment for the collaboration. With the technique's repeatable performance, efforts can be focused on tuning the interferometers sensitivity and achieving a first direct detection. This thesis begins with an introduction on the theory of general relativity and gravitational waves. Common astrophysical sources are described in Chapter 2.

Chapter 3 begins with a description of the installed instrument. A discussion on the detector design sensitivity, limiting noise sources, and estimated detection rates is also given. At the end of Chapter 3, the complications of lock acquisition are highlighted. The arm length stabilization system was introduced to Advanced LIGO as a partial way to solve the difficulties of locking. Chapter 4 discusses the motivation for the use of this scheme and explains the methodology. A detailed discussion on the arm length stabilization model is given, along with the noise budget in Chapters 5 and 6 respectively. The full lock sequence is described in Chapter 7. The thesis concludes with the current status of the interferometers.