Dual-Resonator Speed Meter for a Free Test Mass

TL;DR

This paper introduces a dual-resonator speed meter that measures the velocity of a test mass with quantum-limited sensitivity, surpassing the standard quantum limit in both narrow and wide-band modes, with feasible experimental implementation.

Contribution

It proposes a novel dual-resonator design for a speed meter capable of beating the standard quantum limit in force measurements.

Findings

Can beat the wide-band SQL by a factor of 2 with current technology.

Feasible to construct a demonstration speed meter with existing microwave components.

Potential adaptation to optical frequencies could improve gravitational-wave detection sensitivity.

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 wide-band mode. A scrutiny of experimental issues shows that it is feasible, with current technology, to construct a demonstration speed meter that beats the wide-band 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_SQL, but perhaps only by a factor 1/xi = h_SQL/h ~ 3 (constrained by losses in the optics) and at the price of a very high circulating optical power --- larger by 1/xi^2 than that required to reach the SQL.