Shot-noise-limited control-loop noise in an interferometer with multiple degrees of freedom

Abstract

Precise measurements, such as those made with interferometric gravitational-wave detectors, require the measurement device to be properly controlled so that the sensitivity can be as high as possible. Mirrors in the interferometer are to be located at specific operation points to isolate laser noise and to accumulate the signal in resonant cavities. On the other hand, rigid control of an auxiliary degree of freedom may result in imposing sensing noise of the control on the target object as excess force noise. Evaluation of this so-called loop noise is important in order to design a decent control scheme of the measurement device. In this paper, we show the method to calculate the level of loop noise, which has been recently implemented in simulation tools that are broadly used for designing gravitational-wave detectors.

Interferometer design of the KAGRA gravitational wave detector

“…Since each error signal has its own noises, the cross-couplings could inject excess noises from the auxiliary DOFs into the DARM signal. This mechanism is called loop noise coupling [12]. Along with the interfer-TABLE IV.…”

Influence of nonuniformity in sapphire substrates for a gravitational wave telescope

“…According to Ref. [15], the sensing noise level of a 2-dof system with a sensing matrix ((a, b), (c, d)) is given by…”

Construction of KAGRA: an Underground Gravitational Wave Observatory

“…power-and signalrecycling cavity lengths). The loop noise in the observation band mainly comes from sensing noise of the controller that drives the recycling mirrors and beam splitter, and then couples to the gravitational-wave channel [25]. With the low seismic motion in the underground site, the control gain for the auxiliary degrees of freedom can be reduced.…”