Second Order Glauber Correlation of Gravitational Waves using the LIGO observatories as Hanbury Brown and Twiss detectors

In this paper the second order Glauber correlation of a simplified gravitational wave is investigated, using parameters from the first signal detected by LIGO. This simplified model spans the inspiral, merger, and ringdown phases of a black hole merger and was created to have a continuous amplitude, so there is no discontinuity between the phases. This allows for a trivial extraction of the intensity, which is necessary to determine the correlation between detectors. The two LIGO observatories can be used as detectors in a Hanbury Brown and Twiss interferometer for gravitational waves, these observatories measure the amplitude of the wave, so these measurements were used as the basis of the simplified model. The signal detected by the observatories is transient and is not consistent with chaotic or steady electromagnetic waves and thus the second order Glauber correlation function was calculated to produce physically meaningful results. A correlation was also calculated using a sine-Gaussian model in hopes to describe the waveform in an even simpler model. To find correlations that are consistent with applications to electromagnetic waves weighting functions for both models were studied in the integral equations for the Glauber correlation functions. The relationship between the transient and chaotic signals of both waveforms and their respective correlation functions was also examined. The second order Glauber correlation functions are a measure of intensity interference between independent detectors and has proven to be useful in both optics and particle physics. It has also been used in theoretical studies of primordial gravitational waves. The correlations can be used to define the degrees of coherence of a field, characterize multi-particle processes, and assist in image enhancement.