1 | Here, we adopt the system of labeling parts of the interferometer by the cardinal directions, they are located with respect
to the interferometer central station, e.g., ![]() ![]() ![]() |
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2 | Here and below we keep to a definition of the reflectivity coefficient of the mirrors that implies that the reflected wave
acquires a phase shift equal to ![]() |
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3 | In fact, the argument of ![]() ![]() ![]() ![]() ![]() |
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4 | In the resonance-tuned case, the phase modulation of the input carrier field creates equal magnitude sideband fields as discussed in Section 2.2.2, and these sideband fields are transmitted to the output port thanks to Schnupp asymmetry in the same state, i.e., they remain equal in magnitude and reside in the phase quadrature. In detuned configurations of GW interferometers, the upper and lower RF-sideband fields are transformed differently, which influences both their amplitudes and phases at the readout port. | |
5 | Insofar as the light beams in the interferometer can be well approximated as paraxial beams, and the polarization
of the light wave does not matter in most of the considered interferometers, we will omit the vector nature
of the electric field and treat it as a scalar field with strength defined by a scalar operator-valued function
![]() |
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6 | Herein, we make use of a double-sided power spectral density defined on a whole range of frequencies, both negative and
positive, that yields the following connection to the variance of an arbitrary observable ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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7 | Hereafter we will omit, for the sake of brevity, the factor ![]() ![]() ![]() |
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8 | Here, we omitted the terms of ![]() ![]() ![]() |
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9 | Personal communication with Yanbei Chen. | |
10 | Note the second term proportional to ![]() ![]() ![]() |
http://www.livingreviews.org/lrr-2012-5 |
Living Rev. Relativity 15, (2012), 5
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