Frequency noise and intensity noise of next-generation gravitational-wave detectors with RF/DC readout schemes

The sensitivity of next-generation gravitational-wave detectors such as Advanced LIGO and LCGT should be limited mostly by quantum noise with an expected technical progress to reduce seismic noise and thermal noise. Those detectors will employ the optical configuration of resonant-sideband-extraction that can be realized with a signal-recycling mirror added to the Fabry-Perot Michelson interferometer. While this configuration can reduce quantum noise of the detector, it can possibly increase laser frequency noise and intensity noise. The analysis of laser noise in the interferometer with the conventional configuration has been done in several papers, and we shall extend the analysis to the resonant-sideband-extraction configuration with the radiation-pressure effect included. We shall also refer to laser noise in the case we employ the so-called DC readout scheme.

Figure 1

Power-recycled Fabry-Perot Michelson interferometer (left) and power-recycled RSE interferometer (right). The figure is what has been used in Ref. 26.

Figure 2

Frequency noise (left) and intensity noise (right) on the phasor diagram with the leaked carrier light at the dark port.

Figure 3

Frequency noise (left) and intensity noise (right) of the power-recycled Fabry-Perot Michelson interferometer, calculated. Here the transfer function from each fluctuation to the equivalent strain sensitivity are shown.

Figure 4

Input-output relation of laser noise in the signal-recycling cavity.

Figure 5

DC components of the carrier light and the RF sidebands at the dark port of the RSE interferometer. The offset light caused by radiation pressure of the reinjected contrast-defect light can be suppressed by the control system.

Figure 6

Laser noise of the broadband RSE (top) and the detuned RSE (bottom).

Figure 7

Readout quadrature is determined by the ratio of offset light and contrast-defect light.

Figure 8

Laser noise with the DC and the RF readout scheme.

Figure 9

Phasor diagram of the light field at the detection port with the DC readout scheme. The reference light to probe the signal is the sum of contrast-defect and the offset light excluding rms fluctuation (left panel). Laser noise is obtained from the calculation of the couplings between dc components and ac components of contrast-defect and the offset light including rms fluctuation (middle panel). The offset light consists of rms fluctuation, radiation-pressure offset due to contrast defect, and the control light (right panel). Here rms fluctuation should be so small as not to change the readout phase.

Figure 10

Quantum noise and laser noise of the broadband RSE (left), the detuned RSE with $\zeta$ or ${\zeta }_{\mathrm{DC}}=\pi /2-0.04$ (top right), and the detuned RSE with $\zeta$ or ${\zeta }_{\mathrm{DC}}=0$ (bottom right). Additional quantum noise at the demodulation process of RF readout is not included, which would possibly be removable in several ways [24, 27].