Living Reviews in Relativity

"Quantum Measurement Theory in Gravitational-Wave Detectors"
by
Stefan L. Danilishin and Farid Ya. Khalili 

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Abstract
1 Introduction
2 Interferometry for GW Detectors: Classical Theory
2.1 Interferometer as a weak force probe
2.2 From incident wave to outgoing light: light transformation in the GW interferometers
2.3 Basics of Detection: Heterodyne and homodyne readout techniques
3 Quantum Nature of Light and Quantum Noise
3.1 Quantization of light: Two-photon formalism
3.2 Quantum states of light
3.3 How to calculate spectral densities of quantum noise in linear optical measurement?
4 Linear Quantum Measurement
4.1 Quantum measurement of a classical force
4.2 General linear measurement
4.3 Standard Quantum Limit
4.4 Beating the SQL by means of noise cancellation
4.5 Quantum speed meter
5 Quantum Noise in Conventional GW Interferometers
5.1 Movable mirror
5.2 Fabry–Pérot cavity
5.3 Fabry–Pérot–Michelson interferometer
6 Schemes of GW Interferometers with Sub-SQL Sensitivity
6.1 Noise cancellation by means of cross-correlation
6.2 Quantum speed meter
6.3 Optical rigidity
7 Conclusion and Future Directions
8 Acknowledgements
A Appendices
A.1 Input/Output relations derivation for a Fabry–Pérot cavity
A.2 Proof of Eq. (376), (377) and (378)
A.3 SNR in second-order pole regime
Open References References
Footnotes
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