Enhancing high frequency sensitivity of gravitational wave detectors with a Sagnac interferometer

The sensitivity of gravitational-wave detectors is limited in the high-frequency band by quantum shot noise and eventually limited by the optical loss in the signal recycling cavity. This limit is the main obstacle to detecting gravitational waves from binary neutron star mergers in the current and future-generation detectors, as it does not depend on either the arm length in the high-frequency band or the injected squeezing level. In this paper, we present the sloshing-Sagnac interferometer topology, which can be obtained from the Michelson interferometer by optically connecting the end mirrors into an additional optical cavity. This transforms the interferometer into a triply coupled cavity system capable of beating the loss-induced high-frequency limit of the signal-recycled Michelson interferometer. With the upgrade plan of Advanced LIGO, A+ comparable parameters, a sloshing-Sagnac scheme can achieve 7 times better sensitivity at 2.5 kHz or a 4 times better signal-to-noise ratio for a typical waveform of binary neutron star post merge. Being an evolution of a Michelson interferometer, the sloshing-Sagnac interferometer can possibly be used as a topology for the future-generation detectors and upgrades of current detectors.