Generalized analysis of quantum noise and dynamic back-action in signal-recycled Michelson-type laser interferometers

TL;DR

This paper presents a comprehensive analysis of quantum noise and back-action in asymmetric signal-recycled Michelson interferometers, revealing new optomechanical coupling regimes and their implications for gravitational wave detection and quantum experiments.

Contribution

It introduces a generalized framework for analyzing asymmetric Michelson interferometers, uncovering novel optomechanical coupling types beyond standard classifications.

Findings

Symmetric Michelson with signal-recycling exhibits purely dissipative coupling.

Asymmetry introduces additional dispersive coupling.

Coherent coupling occurs in detectors with both signal- and power-recycling.

Abstract

We analyze the radiation pressure induced interaction of mirror motion and light fields in Michelson-type interferometers used for the detection of gravitational waves and for fundamental research in table-top quantum optomechanical experiments, focusing on the asymmetric regime with a (slightly) unbalanced beamsplitter and a (small) offset from the dark port. This regime, as it was shown recently, provides new interesting features, in particular a stable optical spring and optical cooling on cavity resonance. We show that generally the nature of optomechanical coupling in Michelson-type interferometers does not fit into the standard dispersive/dissipative dichotomy. In particular, a symmetric Michelson interferometer with signal-recycling but without power-recycling cavity is characterized by a purely dissipative optomechanical coupling; only in the presence of asymmetry, additional dispersive coupling arises. In gravitational waves detectors possessing signal- and power-recycling cavities, yet another, "coherent" type of optomechanical coupling takes place. We develop here a generalized framework for the analysis of asymmetric Michelson-type interferometers which also covers the possibility of the injection of carrier light into both ports of the interferometer. Using this framework, we analyze in depth the "anomalous" features of the Michelson-Sagnac interferometer which where discussed and observed experimentally in previous works [1-3].