Quantum-gravitational noise correlation in nearby detectors

We consider quantum gravity fluctuations in a pair of nearby gravitational wave detectors. Quantum fluctuations of long-wavelength modes of the gravitational field induce coherent fluctuations in the detectors, leading to correlated noise. We determine the variance and covariance in the lengths of the arms of the detectors, and thereby obtain the graviton noise correlation. We find that the correlation depends on the angle between the detector arms as well as their separation distance. Using our result, we propose an experimental setup to detect this noise. The suggested interferometer configuration can be used to distinguish quantum-gravitational noise from both correlated and uncorrelated sources of background noise.