Sagnac Interferometer as a Speed-Meter-Type, Quantum-Nondemolition Gravitational-Wave Detector

TL;DR

This paper demonstrates that a Sagnac interferometer can function as a quantum-nondemolition speed meter, potentially surpassing the standard quantum limit in gravitational-wave detection with suitable configurations and squeezed vacuum injection.

Contribution

It shows that a Sagnac interferometer acts as a speed meter capable of beating the SQL, matching the performance of Michelson speed meters, and is a promising design for future gravitational-wave detectors.

Findings

Sagnac interferometer is a quantum-nondemolition speed meter.

Can beat the SQL by a factor of about 3 in certain frequency bands.

Performance comparable to Michelson speed meters with the same circulating power.

Abstract

According to quantum measurement theory, "speed meters" -- devices that measure the momentum, or speed, of free test masses -- are immune to the standard quantum limit (SQL). It is shown that a Sagnac-interferometer gravitational-wave detector is a speed meter and therefore in principle it can beat the SQL by large amounts over a wide band of frequencies. It is shown, further, that, when one ignores optical losses, a signal-recycled Sagnac interferometer with Fabry-Perot arm cavities has precisely the same performance, for the same circulating light power, as the Michelson speed-meter interferometer recently invented and studied by P. Purdue and the author. The influence of optical losses is not studied, but it is plausible that they be fairly unimportant for the Sagnac, as for other speed meters. With squeezed vacuum (squeeze factor $e^{-2R} = 0.1$) injected into its dark port, the recycled Sagnac can beat the SQL by a factor $ \sqrt{10} \simeq 3$ over the frequency band $10 {\rm Hz} \alt f \alt 150 {\rm Hz}$ using the same circulating power $I_c\sim 820$ kW as is used by the (quantum limited) second-generation Advanced LIGO interferometers -- if other noise sources are made sufficiently small. It is concluded that the Sagnac optical configuration, with signal recycling and squeezed-vacuum injection, is an attractive candidate for third-generation interferometric gravitational-wave detectors (LIGO-III and EURO).