  The binary neutron star coalescence GW170817 was observed by gravitational
wave detectors during the inspiral phase but sensitivity in the 1-5 kHz band
was insufficient to observe the expected nuclear matter signature of the merger
itself, and the process of black hole formation. This provides strong
motivation for improving 1--5 kHz sensitivity which is currently limited by
photon shot noise. Resonant enhancement by signal recycling normally improves
the signal to noise ratio at the expense of bandwidth. The concept of
optomechanical white light signal recycling (WLSR) has been proposed, but all
schemes to date have been reliant on the development of suitable ultra-low
mechanical loss components. Here for the first time we show demonstrated
optomechanical resonator structures that meet the loss requirements for a WLSR
interferometer with strain sensitivity below 10$^{-24}$ Hz$^{-1/2}$ at a few
kHz. Experimental data for two resonators are combined with analytic models of
4km interferometers similar to LIGO, to demonstrate sensitivity enhancement
across a much broader band of neutron star coalescence frequencies than
dual-recycled Fabry-Perot Michelson detectors of the same length. One candidate
resonator is a silicon nitride membrane acoustically isolated from the
environment by a phononic crystal. The other is a single-crystal quartz lens
that supports bulk acoustic longitudinal waves. Optical power requirements
could prefer the membrane resonator, although the bulk acoustic wave resonator
gives somewhat better thermal noise performance. Both could be implemented as
add-on components to existing detectors.
