Principles of calculating the dynamical response of misaligned complex resonant optical interferometers

In the long-baseline laser interferometers for measuring gravitational waves that are now under construction, understanding the dynamical response to small distortions such as angular alignment fluctuations presents a unique challenge. These interferometers comprise multiple coupled optical resonators with light storage times approaching 100 m. We present a basic formalism to calculate the frequency dependence of periodic variations in angular alignment and longitudinal displacement of the resonator mirrors. The electromagnetic field is decomposed into a superposition of higher-order spatial modes, Fourier frequency components, and polarization states. Alignment fluctuations and length variations of free-space propagation are represented by matrix operators that act on the multicomponent state vectors of the field

Experimental test of an alignment-sensing scheme for a gravitational-wave interferometer

An alignment-sensing scheme for all significant angular degrees of freedom of a power-recycled Michelson interferometer with Fabry Perot cavities in the arms was tested on a tabletop interferometer. The response to misalignment of all degrees of freedom was measured at each sensor, and good agreement was found between measured and theoretical values

The advanced LIGO detectors in the era of first discoveries

Following a major upgrade, the two advanced detectors of the Laser Interferometer Gravitational-wave Ob- servatory (LIGO) held their first observation run between September 2015 and January 2016. The product of observable volume and measurement time exceeded that of all previous runs within the first 16 days of coincident observation. On September 14th, 2015 the Advanced LIGO detectors observed the transient gravitational-wave signal GW150914, determined to be the coalescence of two black holes, launching the era of gravitational-wave astronomy. We present the main features of the detectors that enabled this observation. At its core Advanced LIGO is a multi-kilometer long Michelson interferometer employing optical resonators to enhance its sensitivity. Four very pure and homogeneous fused silica optics with excellent figure quality serve as the test masses. The displacement produced by the event GW150914 was one 200th of a proton radius. It was observed with a combined signal-to-noise ratio of 24 in coincidence by the two detectors. At full sensitivity, the Advanced LIGO detectors are designed to deliver another factor of three improvement in the signal-to-noise ratio for binary black hole systems similar in masses to GW150914

Angular instability due to radiation pressure in the LIGO gravitational-wave detector

We observed the effect of radiation pressure on the angular sensing and control system of the Laser Interferometer Gravitational-Wave Observatory (LIGO) interferometer’s core optics at LIGO Hanford Observatory. This is the first measurement of this effect in a complete gravitational-wave interferometer. Only one of the two angular modes survives with feedback control, because the other mode is suppressed when the control gain is sufficiently large. We developed a mathematical model to understand the physics of the system. This model matches well with the dynamics that we observe

Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK

We report on use of a radiation pressure induced restoring force, the optical spring effect, to optically dilute the mechanical damping of a 1 gram suspended mirror, which is then cooled by active feedback (cold damping). Optical dilution relaxes the limit on cooling imposed by mechanical losses, allowing the oscillator mode to reach a minimum temperature of 6.9 mK, a factor of ~40000 below the environmental temperature. A further advantage of the optical spring effect is that it can increase the number of oscillations before decoherence by several orders of magnitude. In the present experiment we infer an increase in the dynamical lifetime of the state by a factor of ~200

The Advanced LIGO timing system

Gravitational wave detection using a network of detectors relies upon the precise time stamping of gravitational wave signals. The relative arrival times between detectors are crucial, e.g. in recovering the source direction, an essential step in using gravitational waves for multi-messenger astronomy. Due to the large size of gravitational wave detectors, timing at different parts of a given detector also needs to be highly synchronized. In general, the requirement toward the precision of timing is determined such that, upon detection, the deduced (astro-) physical results should not be limited by the precision of timing. The Advanced LIGO optical timing distribution system is designed to provide UTC-synchronized timing information for the Advanced LIGO detectors that satisfies the above criterium. The Advanced LIGO timing system has modular structure, enabling quick and easy adaptation to the detector frame as well as possible changes or additions of components. It also includes a self-diagnostics system that enables the remote monitoring of the status of timing. After the description of the Advanced LIGO timing system, several tests are presented that demonstrate its precision and robustness

Arm-length stabilisation for interferometric gravitational-wave detectors using frequency-doubled auxiliary lasers

Residual motion of the arm cavity mirrors is expected to prove one of the principal impediments to systematic lock acquisition in advanced gravitational-wave interferometers. We present a technique which overcomes this problem by employing auxiliary lasers at twice the fundamental measurement frequency to pre-stabilise the arm cavities' lengths. Applying this approach, we reduce the apparent length noise of a 1.3 m long, independently suspended Fabry-Perot cavity to 30 pm rms and successfully transfer longitudinal control of the system from the auxiliary laser to the measurement laser