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The quantum locking technique, which uses additional short low-losssub-cavities, is effective in reducing quantum noise in space gravitationalwave antenna DECIGO. However, the quantum noise of the main interferometerdepends on the control systems in the sub-cavities. Here we demonstrate a newmethod to optimize the quantum noise independently of the feedback gain bycompleting the square in the quantum locking system. We successfullydemonstrate in simulations that this method is effective in optimizing thehomodyne angle to the best quantum-noise-limited sensitivity.

Optimization of quantum noise by completing the square of multiple interferometer outputs in quantum locking for gravitational wave detectors