World Science Scholars
2.2 Turning a Thought Experiment into Reality
summary
Interferometry made Gertsenshtein’s thought experiment reality.

• An interferometer works by splitting a laser beam and sending the two resultant beams down orthogonal paths. At the end of each path is a mirrored test mass, which reflects the beams back so that they recombine and produce an interference pattern.
• This method allows for the real-world implementation of the earlier gravitational wave thought experiments because it removes their biggest shortcoming, the need for absolutely precise clocks.
• Instead, movement of the test masses produces subtle changes in the relative frequencies and phases of the two beams. This creates a detectable signal when the beams recombine.

LIGO is based on a Michelson-Morley interferometer.

• The two resultant beams produced when the original laser hits the beam splitter are not identical. Critically, one of them is phase-shifted 180° relative to the other.
• When they recombine, these two beams will actually cancel each other out and produce zero signal at the photodetector. This is because, since they are 180° out of phase, the peaks of one beam will align perfectly with the troughs of the other, resulting in complete destructive interference.
• In order for this system to work properly, the two beams must spend exactly equal amounts of time in their respective arms of the interferometer. If one beam travels even slightly longer than the other, then they will not be perfectly out of phase and a signal will be present. A passing gravitational wave would stretch one arm and shrink the other and cause such a signal to appear.
• The reality of LIGO’s operation is a bit more subtle than this. When the mirrors move at the frequency of the passing gravitational wave, they modulate the reflected beams by adding two sidebands to the carrier frequency. These sidebands have the carrier frequency plus or minus the frequency of the gravitational wave.
• When the two beams recombine, the carrier frequency cancels out but the sidebands add together. This allows the sidebands to be detected and used to determine the gravitational wave characteristics.

The interferometers LIGO uses have additional components to improve sensitivity.

• LIGO has extra mirrors in each arm of the interferometers. The space between these new mirrors and the original test masses is called a Fabry-Perot cavity.
• These cavities serve the purposes of strengthening the side bands because the light bounces back and forth over and over, increasing the distance the light travels and therefore increasing the strength of the gravitational wave signal. LIGO’s arms are 4km long, but the Fabry-Perot cavities increase their effective length significantly.
• There is also a power-recycling mirror that “catches” the extra light coming back toward the laser emitter, sending it back into the interferometer. This significantly increases the intensity of the system, creating an effective beam that can be over 100 times more powerful than the original laser.
• Advanced LIGO includes the addition of a signal recycling mirror as well. This creates another cavity that is resonant for the sidebands, building up the desired signal before passing it to the photodetector.

LIGO’s noise budget

• One of the biggest and most important contributors to noise in LIGO measurements is quantum noise. It has two components: shot noise, which describes the noise caused by the discrete nature of photons, and radiation pressure, which describes the physical force that the lasers apply to the test masses.
• Increased laser power decreases shot noise but correspondingly increases radiation pressure. Quantum noise is one of the biggest limitations to LIGO’s sensitivity.
• Seismic activity is another big contributor to noise in LIGO’s detectors. This noise is a result of all the ambient vibrations, natural and anthropogenic, that permeate the Earth. This is moderated using a variety of active and passive isolation systems.
• The actual thermal motion of the test masses themselves also contributes significant amounts of noise. Because LIGO operates at room temperature, the mirrors have a lot of thermal energy, which results in the vibration of their constituent atoms. Better materials can be used to decrease this noise.
• LIGO’s interferometer arms are enormous vacuum chambers, to avoid noise caused by gas particles interacting with the lasers and mirrors.
• Gravity gradient noise in the lower frequency range (<10Hz) of LIGO’s sensitivity is unavoidable on the Earth. This noise is caused by underground density waves that subtly shift the strength and direction of the gravity experienced by the mirrors. Gravity gradient noise is a major impetus for the development of space-based gravitational wave detectors.

A network of detectors is necessary for accurate source localization.

• Gravitational wave detectors cannot be pointed to find out where a source is in the sky. They are more like microphones than telescopes, collecting data from nearly every direction simultaneously.
• Source localization can therefore only be done by comparing the timing of detections at multiple locations using the method of triangulation. As the name suggests, at least three detectors are necessary for accurate triangulation.
• The two LIGO detectors in the US are supplemented by the VIRGO detector in Italy, though this machine was not online during LIGO’s first detection. Plans are in place to build more detectors, like LIGO-India and KAGRA in Japan.

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