Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors

TL;DR

This paper provides a theoretical analysis of quantum noise in advanced gravitational-wave detectors, demonstrating how frequency-dependent squeezing and homodyne detection can significantly enhance sensitivity across the entire detection bandwidth.

Contribution

It introduces analytical formulas for optimal frequency-dependent input and output optics, showing how they improve detector sensitivity beyond previous configurations.

Findings

Optimal frequency-dependent squeezing reduces noise spectral density by exp(-2r).

Frequency-dependent homodyne detection further enhances sensitivity.

The results are applicable to GEO600 and Advanced LIGO topologies.

Abstract

We theoretically analyze the quantum noise of signal-recycled laser interferometric gravitational-wave detectors with additional input and output optics, namely frequency-dependent squeezing of the vacuum entering the dark port and frequency-dependent homodyne detection. We combine the work of Buonanno and Chen on the quantum noise of signal-recycled interferometers with ordinary input-output optics, and the work of Kimble el al. on frequency-dependent input-output optics with conventional interferometers. Analytical formulas for the optimal input and output frequency dependencies are obtained. It is shown that injecting squeezed light with the optimal frequency-dependent squeezing angle into the dark port yields an improvement on the noise spectral density by a factor of exp(-2r) (in power) over the entire squeezing bandwidth, where r is the squeezing parameter. It is further shown that frequency-dependent (variational) homodyne read-out leads to an additional increase in sensitivity which is significant in the wings of the doubly resonant structure. The optimal variational input squeezing in case of an ordinary output homodyne detection is shown to be realizable by applying two optical filters on a frequency-independent squeezed vacuum. Throughout this paper, we take as example the signal-recycled topology currently being completed at the GEO600 site. However, theoretical results obtained here are also applicable to the proposed topology of Advanced LIGO.