First-step experiment for sensitivity improvement of DECIGO: Sensitivity optimization for simulated quantum noise by completing the square

Decihertz Interferometer Gravitational Wave Observatory (DECIGO) is a future mission for a space -borne laser interferometer. DECIGO has 1000-km-long arm cavities mainly to detect the primordial gravitational waves (PGWs) at lower frequencies around 0.1 Hz. Observations in the electromagnetic spectrum have lowered the bounds on the upper limit of PGWs energy density (omega gw similar to 10-15 -> 10-16). As a result, DECIGO's target sensitivity, which is mainly limited by quantum noise, needs further improvement. To maximize the feasibility of detection while constrained by DECIGO's large diffraction loss, a quantum locking technique with an optical spring was theoretically proposed to improve the signal-to-noise ratio of the PGWs. In this paper, we experimentally verify one key element used in the theory: sensitivity optimization by completing the square of multiple detector outputs. This experiment is operated on a simplified tabletop optical setup with classical noise simulating quantum noise. We succeed in getting the best of the sensitivities with two different laser powers by the square completion method.