Quantum Noise Reduction in the Space-based Gravitational Wave Antenna DECIGO Using Optical Springs and Homodyne Detection scheme

The DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO) is a planned space-based, next-generation gravitational wave detector aimed at observing primordial gravitational waves originating form cosmic inflation. This work focuses on reducing the quantum noise, in the instrument's observation band of 0.1 to 10 Hz, by employing optical springs and a homodyne detection scheme. Although detuning 1000\,km long arm cavities was previously considered ineffective due to quantum state degradation from diffraction losses, we revisit this problem by formulating a new, rigorous model for quantum state of light by accounting for the vacuum state mixing as a result of diffraction losses. This work shows that high sensitivities can be achieved by employing optimal configurations of optical springs and homodyne detection schemes even with diffraction losses. These improvements alone are still not sufficient to achieve sensitivities to detect primordial gravitational waves as other technical noises limit further improvement.