Sagnac interferometer as a speed-meter-type, quantum-nondemolition gravitational-wave detector

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 Purdue and the author. The influence of optical losses is not studied, but it is plausible that they be fairly unimportant for the Sagnac interferometer, as for other speed meters. With squeezed vacuum (squeeze factor e(-2R)=0.1) injected into its dark port, the recycled Sagnac interferometer can beat the SQL by a factor root10 similar or equal to3 over the frequency band 10 Hzless than or similar tofless than or similar to150 Hz using the same circulating power I(c)similar to820 kW as is to be 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).