Abstract
The speed meter concept has been identified as a technique that can potentially provide laser-interferometric measurements at a sensitivity level which surpasses the standard quantum limit (SQL) over a broad frequency range. As with other sub-SQL measurement techniques, losses play a central role in speed meter interferometers and they ultimately determine the quantum noise limited sensitivity that can be achieved. So far in the literature, the quantum noise limited sensitivity has only been derived for lossless or lossy cases using certain approximations (for instance that the arm cavity round trip loss is small compared to the arm cavity mirror transmission). In this article we present a generalized, analytical treatment of losses in speed meters that allows accurate calculation of the quantum noise limited sensitivity of Sagnac speed meters with arm cavities. In addition, our analysis allows us to take into account potential imperfections in the interferometer such as an asymmetric beam splitter or differences of the reflectivities of the two arm cavity input mirrors. Finally, we use the examples of the proof-of-concept Sagnac speed meter currently under construction in Glasgow and a potential implementation of a Sagnac speed meter in the Einstein Telescope to illustrate how our findings affect Sagnac speed meters with metre- and kilometre-long baselines.
Highlights
The sensitivity of state-of-the-art laser-interferometric gravitational wave detectors, such as the Advanced LIGO detector [1] currently being commissioned, will be limited over most frequencies in its detection band by socalled quantum noise
211 kg 211 kg 10 000 ppm 95% 1000 ppm the loss-driven increase of the quantum noise limited sensitivity is much stronger for the Glasgow speed meter than it is for the Einstein Telescope (ET)-LF speed meter
It is crucial that all quantum noise calculations for the Glasgow speed meter experiment fully account for losses, as we have done in the analysis presented in this article
Summary
The sensitivity of state-of-the-art laser-interferometric gravitational wave detectors, such as the Advanced LIGO detector [1] currently being commissioned, will be limited over most frequencies in its detection band by socalled quantum noise. In this article we further advance the quantum noise models for Sagnac speed meters, firstly by including treatment for asymmetries in the interferometer (such as an asymmetric beam splitter (BS) or arm cavity inputcoupling mirrors with different reflectivities), and secondly by providing a more general treatment of losses. We calculate quantum noise limited sensitivity (or more accurately its spectral density) for an imbalanced Sagnac interferometer featuring arm cavities, as shown in figure 1. This layout is chosen for a reason that it replicates the main design features of a proof-of-concept speed meter interferometer under construction at the University of Glasgow [19]. In the following we will use only the Fourier picture and omit the argument Ω for convenience and clearer presentation
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