Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors

We theoretically analyze the quantum noise of signal-recycled laser interferometric gravitational-wave detectors with additional input and output optics, namely, frequency-dependent squeezing of the vacuum state of light entering the dark port and frequency-dependent homodyne detection. We combine the work of Buonanno and Chen on the quantum noise of signal-recycled interferometers with ordinary input and output optics, and the work of Kimble et al. on frequency-dependent input and output optics with conventional interferometers. Analytical formulas for the optimal input and output frequency dependencies are obtained. It is shown that injecting squeezed light with the optimal frequency-dependent squeezing angle into the dark port yields an improvement in the noise spectral density by a factor of $e^{-2r}$ (in power) over the entire squeezing bandwidth, where r is the squeezing parameter. It is further shown that a frequency-dependent (variational) homodyne readout leads to an additional increase in sensitivity which is significant in the wings of the doubly resonant structure. The optimal variational input squeezing in the case of an ordinary output homodyne detection is shown to be realizable by applying two optical filters on a frequency-independent squeezed vacuum. Throughout this paper, we take as an example the signal-recycled topology currently being completed at the GEO 600 site. However, theoretical results obtained here are also applicable to the proposed topology of the Advanced LIGO.