Dual-resonator speed meter for a free test mass

Abstract

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 $1/\ensuremath{\xi}{=h}_{\mathrm{SQL}}/h\ensuremath{\lesssim}3$ (constrained by losses in the optics) and at the price of a very high circulating optical power---larger by ${\ensuremath{\xi}}^{\ensuremath{-}2}$ than that required to reach the SQL.