Geometric noise spectrum in interferometers

TL;DR

This paper investigates the power spectral density of time delay fluctuations in interferometers as a quantum gravitational observable, deriving a general expression and analyzing various quantum states.

Contribution

It provides a new theoretical framework for calculating the noise spectrum in interferometers related to quantum gravity effects, considering different quantum states.

Findings

Spectra are free of ultraviolet divergences.

Thermal and squeezed states can amplify the spectra.

Fluctuations remain suppressed by the Planck scale.

Abstract

We study the power spectral density of time delay fluctuations in an interferometer as a potential low-energy quantum gravitational observable. We derive a general expression for the spectrum in terms of the Wightman function of linear metric perturbations, which we then apply to a variety of cases. We analyze the intrinsic graviton fluctuations in the vacuum, thermal, and squeezed states, as well as the fluctuations induced by the vacuum stress-energy of a massless scalar field. We find that the resulting spectra are free of ultraviolet divergences and that, while thermal and squeezed states provide a natural amplification mechanism, the spectra remain suppressed by the Planck scale.