Increasing the sensitivity of future gravitational-wave detectors with double squeezed-input

We consider improving the sensitivity of future interferometric gravitational-wave detectors by simultaneously injecting two squeezed vacuums (light), filtered through a resonant Fabry-Perot cavity, into the dark port of the interferometer. The same scheme with single squeezed vacuum was first proposed and analyzed by Corbitt et al. [Phys. Rev. D 70, 022002 (2004).]. Here we show that the extra squeezed vacuum, together with an additional homodyne detection suggested previously by one of the authors [F. Ya. Khalili, Phys. Rev. D 77, 062003 (2008).], allows reduction of quantum noise over the entire detection band. To motivate future implementations, we take into account a realistic technical noise budget for Advanced LIGO and numerically optimize the parameters of both the filter and the interferometer for detecting gravitational-wave signals from two important astrophysics sources, namely, neutron-star--neutron-star binaries and bursts. Assuming the optical loss of the $\ensuremath{\sim}30\text{ }\text{ }\mathrm{m}$ filter cavity to be 10 ppm per bounce and 10 dB squeezing injection, the corresponding quantum noise with optimal parameters lowers by a factor of 10 at high frequencies and goes below the technical noise at low and intermediate frequencies.