Control scheme for polarization circulation speed meter using a dual-retardation waveplate

In interferometric gravitational wave detectors, quantum radiation pressure noise, which is a back action of the measurement, limits their sensitivity at low frequencies. Speed meters are one of the techniques to reduce the back-action noise and improve the sensitivity. Furthermore, a speed meter detector can surpass the standard quantum limit over a wide range of frequencies. The polarization circulation speed meter (PCSM) is the latest incarnation of the speed meter concept that requires only a modest modification to the conventional interferometer design. However, its control scheme has not been developed. The main difficulty is the length and alignment control of the cavity formed by the polarization circulation mirror and the input test masses, whose round-trip phase shift should be kept at K. In this article, we propose a new control scheme for the PCSM using a dual-retardation waveplate, called Dual-Retardance Control (DRC). We also compare the shot noise level of the DRC to another simpler scheme by using mirror dithering. Finally, we design the experimental setup to demonstrate the feasibility of the DRC and show the expected results through transfer function measurements.