Enhancing high frequency sensitivity of gravitational wave detectors with sloshing-Sagnac interferometer

Sensitivity of gravitational-wave detectors is limited in the high-frequency band by quantum shot noise and eventually limited by the optical loss in signal recycling cavity. This limit is the main obstacle on the way to detect gravitational waves from the binary neutron star mergers in the current and the future generation detectors, as it does not depend on either the arm length, or the injected squeezing level. In this paper, we come up with 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 advanced LIGO+ comparable parameters, a sloshing-Sagnac scheme can achieve 7 times better sensitivity at 2.5\,kHz or 4 times better signal to noise ratio for a typical waveform of binary neutron post merge. Being an evolution of Michelson interferometer, the sloshing-Sagnac interferometer can possibly be used as a topology for the future generation detectors and upgrade of current detectors.