5 Quantum Noise in Conventional GW Interferometers

In Section 4, we have talked about the quantum measurement, the general structure of quantum noise implied by the quantum mechanics and the restrictions on the achievable sensitivity it imposes. In this section, we turn to the application of these general and lofty principles to real life, i.e., we are going to calculate quantum noise for several types of the schemes of GW interferometers and consider the advantages and drawbacks they possess.

To grasp the main features of quantum noise in an advanced GW interferometer it would be elucidating to consider first two elementary examples: (i) a single movable mirror coupled to a free optical field, reflecting from it, and (ii) a Fabry–Pérot cavity comprising two movable mirrors and pumped from both sides. These two systems embody all the main features and phenomena that also mold the advanced and more complicated interferometers’ quantum noise. Should one encounter these phenomena in real-life GW detectors, knowledge of how they manifest themselves in these simple situations would be of much help in successfully discerning them.

 5.1 Movable mirror
  5.1.1 Optical transfer matrix of the movable mirror
  5.1.2 Probe’s dynamics: radiation pressure force and ponderomotive rigidity
  5.1.3 Spectral densities
  5.1.4 Full transfer matrix approach to the calculation of quantum noise spectral densities
  5.1.5 Losses in a readout train
 5.2 Fabry–Pérot cavity
  5.2.1 Optical transfer matrix for a Fabry–Pérot cavity
  5.2.2 Mirror dynamics, radiation pressure forces and ponderomotive rigidity
 5.3 Fabry–Pérot–Michelson interferometer
  5.3.1 Optical I/O-relations
  5.3.2 Common and differential optical modes
  5.3.3 Interferometer dynamics: mechanical equations of motion, radiation pressure forces and ponderomotive rigidity
  5.3.4 Scaling law theorem
  5.3.5 Spectral densities for the Fabry–Pérot–Michelson interferometer
  5.3.6 Full transfer matrix approach to calculation of the Fabry–Pérot–Michelson interferometer quantum noise

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