Sensitivity below the standard quantum limit in gravitational wave detectors with Michelson-Fabry-Perot readout

TL;DR

This paper demonstrates that gravitational wave detectors with Michelson-Fabry-Perot readout can surpass the standard quantum limit using homodyne detection and detuned cavities, achieving unlimited sensitivity with realistic conditions.

Contribution

It introduces a method to surpass the standard quantum limit in gravitational wave detectors using homodyne detection and detuned cavities without additional signal-recycling mirrors.

Findings

Standard quantum limit can be surpassed with resonant cavities and homodyne detection.

Sensitivity can be unlimited with detuned cavities and sufficient optical power.

The study includes realistic effects like mirror losses and cavity delay.

Abstract

We calculate the quantum noise limited displacement sensitivity of a Michelson-Fabry-Perot (MFP) with detuned cavities, followed by phase-sensitive homodyne detection. We show that the standard quantum limit can be surpassed even with resonant cavities and without any signal-recycling mirror nor additional cavities. Indeed, thanks to the homodyne detection, the output field quadrature can be chosen in such a way to cancel the effect of input amplitude fluctuations, i.e., eliminating the force noise. With detuned cavities, the modified opto-mechanical susceptivity allows to reach unlimited sensitivity for large enough (yet finite) optical power. Our expressions include mirror losses and cavity delay effect, for a realistic comparison with experiments. Our study is particularly devoted to gravitational wave detectors and we consider both an interferometer with free-falling mirrors, and a MFP as readout for a massive detector. In the latter case, the sensitivity curve of the recently conceived 'DUAL' detector, based on two acoustic modes, is obtained.