"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
References
Footnotes
Figures
Tables