Dual-resonator speed meter for a free test mass

A description and analysis are given of a “speed meter” for monitoring a classical force that acts on a test mass. This speed meter is based on two microwave resonators (“dual resonators”), one of which couples evanescently to the position of the test mass. The sloshing of the resulting signal between the resonators, and a wise choice of where to place the resonators’ output waveguide, produce a signal in the waveguide that (for sufficiently low frequencies) is proportional to the test-mass velocity (speed) rather than its position. This permits the speed meter to achieve force-measurement sensitivities better than the standard quantum limit (SQL), both when operating in a narrow-band mode and a wideband mode. A scrutiny of experimental issues shows that it is feasible, with current technology, to construct a demonstration speed meter that beats the wideband SQL by a factor 2. A concept is sketched for an adaptation of this speed meter to optical frequencies; this adaptation forms the basis for a possible LIGO-III interferometer that could beat the gravitational-wave standard quantum limit $h_{\mathrm{SQL}},$ but perhaps only by a factor $1/\xi {=h}_{\mathrm{SQL}}/h\lesssim 3$ (constrained by losses in the optics) and at the price of a very high circulating optical power—larger by ${\xi }^{-2}$ than that required to reach the SQL.